PID_Controller_Demo.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    },
    "widgets": {
      "application/vnd.jupyter.widget-state+json": {
        "85c4c3a22fb94dd3b8e5fa817c173fe1": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "VBoxModel",
          "model_module_version": "1.5.0",
          "state": {
            "_dom_classes": [
              "widget-interact"
            ],
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "VBoxModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/controls",
            "_view_module_version": "1.5.0",
            "_view_name": "VBoxView",
            "box_style": "",
            "children": [
              "IPY_MODEL_5b0d7d8723c64ecdb48e5f4efe366dc5",
              "IPY_MODEL_dd97f0e039884672a36677ffd2001496",
              "IPY_MODEL_a806a27e1f474d5d8e112ca66501e735",
              "IPY_MODEL_ed3d8c8f08bf4c189cfb3e20fccf0a52"
            ],
            "layout": "IPY_MODEL_7881ed5a89fc403f85afb521a63e5adf"
          }
        },
        "5b0d7d8723c64ecdb48e5f4efe366dc5": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "FloatSliderModel",
          "model_module_version": "1.5.0",
          "state": {
            "_dom_classes": [],
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "FloatSliderModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/controls",
            "_view_module_version": "1.5.0",
            "_view_name": "FloatSliderView",
            "continuous_update": true,
            "description": "P Gain:",
            "description_tooltip": null,
            "disabled": false,
            "layout": "IPY_MODEL_1f271b152d6349099c0b5fb2b5a63696",
            "max": 5,
            "min": 0,
            "orientation": "horizontal",
            "readout": true,
            "readout_format": ".2f",
            "step": 0.1,
            "style": "IPY_MODEL_bc84c0482c0d4dffa12c6d2911a55ef8",
            "value": 0.7
          }
        },
        "dd97f0e039884672a36677ffd2001496": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "FloatSliderModel",
          "model_module_version": "1.5.0",
          "state": {
            "_dom_classes": [],
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "FloatSliderModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/controls",
            "_view_module_version": "1.5.0",
            "_view_name": "FloatSliderView",
            "continuous_update": true,
            "description": "I Gain:",
            "description_tooltip": null,
            "disabled": false,
            "layout": "IPY_MODEL_c38f04a7eabb4d1ea7e580cab4a515ff",
            "max": 5,
            "min": 0,
            "orientation": "horizontal",
            "readout": true,
            "readout_format": ".2f",
            "step": 0.1,
            "style": "IPY_MODEL_d10b914155884456bdd11c5eb6bda94e",
            "value": 0
          }
        },
        "a806a27e1f474d5d8e112ca66501e735": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "FloatSliderModel",
          "model_module_version": "1.5.0",
          "state": {
            "_dom_classes": [],
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "FloatSliderModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/controls",
            "_view_module_version": "1.5.0",
            "_view_name": "FloatSliderView",
            "continuous_update": true,
            "description": "D Gain:",
            "description_tooltip": null,
            "disabled": false,
            "layout": "IPY_MODEL_c2b59dbea17a4de4a479b2987c46e87d",
            "max": 5,
            "min": 0,
            "orientation": "horizontal",
            "readout": true,
            "readout_format": ".2f",
            "step": 0.1,
            "style": "IPY_MODEL_994bcbee02644b50a7a15e4ef47c195a",
            "value": 0
          }
        },
        "ed3d8c8f08bf4c189cfb3e20fccf0a52": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "model_module_version": "1.0.0",
          "state": {
            "_dom_classes": [],
            "_model_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_model_name": "OutputModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/output",
            "_view_module_version": "1.0.0",
            "_view_name": "OutputView",
            "layout": "IPY_MODEL_f8392030ff34437a93a72ef3a1ebcee0",
            "msg_id": "",
            "outputs": [
              {
                "output_type": "display_data",
                "data": {
                  "text/plain": "<Figure size 1000x500 with 1 Axes>",
                  "image/png": "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\n"
                },
                "metadata": {}
              }
            ]
          }
        },
        "7881ed5a89fc403f85afb521a63e5adf": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "model_module_version": "1.2.0",
          "state": {
            "_model_module": "@jupyter-widgets/base",
            "_model_module_version": "1.2.0",
            "_model_name": "LayoutModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "LayoutView",
            "align_content": null,
            "align_items": null,
            "align_self": null,
            "border": null,
            "bottom": null,
            "display": null,
            "flex": null,
            "flex_flow": null,
            "grid_area": null,
            "grid_auto_columns": null,
            "grid_auto_flow": null,
            "grid_auto_rows": null,
            "grid_column": null,
            "grid_gap": null,
            "grid_row": null,
            "grid_template_areas": null,
            "grid_template_columns": null,
            "grid_template_rows": null,
            "height": null,
            "justify_content": null,
            "justify_items": null,
            "left": null,
            "margin": null,
            "max_height": null,
            "max_width": null,
            "min_height": null,
            "min_width": null,
            "object_fit": null,
            "object_position": null,
            "order": null,
            "overflow": null,
            "overflow_x": null,
            "overflow_y": null,
            "padding": null,
            "right": null,
            "top": null,
            "visibility": null,
            "width": null
          }
        },
        "1f271b152d6349099c0b5fb2b5a63696": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "model_module_version": "1.2.0",
          "state": {
            "_model_module": "@jupyter-widgets/base",
            "_model_module_version": "1.2.0",
            "_model_name": "LayoutModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "LayoutView",
            "align_content": null,
            "align_items": null,
            "align_self": null,
            "border": null,
            "bottom": null,
            "display": null,
            "flex": null,
            "flex_flow": null,
            "grid_area": null,
            "grid_auto_columns": null,
            "grid_auto_flow": null,
            "grid_auto_rows": null,
            "grid_column": null,
            "grid_gap": null,
            "grid_row": null,
            "grid_template_areas": null,
            "grid_template_columns": null,
            "grid_template_rows": null,
            "height": null,
            "justify_content": null,
            "justify_items": null,
            "left": null,
            "margin": null,
            "max_height": null,
            "max_width": null,
            "min_height": null,
            "min_width": null,
            "object_fit": null,
            "object_position": null,
            "order": null,
            "overflow": null,
            "overflow_x": null,
            "overflow_y": null,
            "padding": null,
            "right": null,
            "top": null,
            "visibility": null,
            "width": null
          }
        },
        "bc84c0482c0d4dffa12c6d2911a55ef8": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "SliderStyleModel",
          "model_module_version": "1.5.0",
          "state": {
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "SliderStyleModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "StyleView",
            "description_width": "",
            "handle_color": null
          }
        },
        "c38f04a7eabb4d1ea7e580cab4a515ff": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "model_module_version": "1.2.0",
          "state": {
            "_model_module": "@jupyter-widgets/base",
            "_model_module_version": "1.2.0",
            "_model_name": "LayoutModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "LayoutView",
            "align_content": null,
            "align_items": null,
            "align_self": null,
            "border": null,
            "bottom": null,
            "display": null,
            "flex": null,
            "flex_flow": null,
            "grid_area": null,
            "grid_auto_columns": null,
            "grid_auto_flow": null,
            "grid_auto_rows": null,
            "grid_column": null,
            "grid_gap": null,
            "grid_row": null,
            "grid_template_areas": null,
            "grid_template_columns": null,
            "grid_template_rows": null,
            "height": null,
            "justify_content": null,
            "justify_items": null,
            "left": null,
            "margin": null,
            "max_height": null,
            "max_width": null,
            "min_height": null,
            "min_width": null,
            "object_fit": null,
            "object_position": null,
            "order": null,
            "overflow": null,
            "overflow_x": null,
            "overflow_y": null,
            "padding": null,
            "right": null,
            "top": null,
            "visibility": null,
            "width": null
          }
        },
        "d10b914155884456bdd11c5eb6bda94e": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "SliderStyleModel",
          "model_module_version": "1.5.0",
          "state": {
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "SliderStyleModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "StyleView",
            "description_width": "",
            "handle_color": null
          }
        },
        "c2b59dbea17a4de4a479b2987c46e87d": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "model_module_version": "1.2.0",
          "state": {
            "_model_module": "@jupyter-widgets/base",
            "_model_module_version": "1.2.0",
            "_model_name": "LayoutModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "LayoutView",
            "align_content": null,
            "align_items": null,
            "align_self": null,
            "border": null,
            "bottom": null,
            "display": null,
            "flex": null,
            "flex_flow": null,
            "grid_area": null,
            "grid_auto_columns": null,
            "grid_auto_flow": null,
            "grid_auto_rows": null,
            "grid_column": null,
            "grid_gap": null,
            "grid_row": null,
            "grid_template_areas": null,
            "grid_template_columns": null,
            "grid_template_rows": null,
            "height": null,
            "justify_content": null,
            "justify_items": null,
            "left": null,
            "margin": null,
            "max_height": null,
            "max_width": null,
            "min_height": null,
            "min_width": null,
            "object_fit": null,
            "object_position": null,
            "order": null,
            "overflow": null,
            "overflow_x": null,
            "overflow_y": null,
            "padding": null,
            "right": null,
            "top": null,
            "visibility": null,
            "width": null
          }
        },
        "994bcbee02644b50a7a15e4ef47c195a": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "SliderStyleModel",
          "model_module_version": "1.5.0",
          "state": {
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "SliderStyleModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "StyleView",
            "description_width": "",
            "handle_color": null
          }
        },
        "f8392030ff34437a93a72ef3a1ebcee0": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "model_module_version": "1.2.0",
          "state": {
            "_model_module": "@jupyter-widgets/base",
            "_model_module_version": "1.2.0",
            "_model_name": "LayoutModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "LayoutView",
            "align_content": null,
            "align_items": null,
            "align_self": null,
            "border": null,
            "bottom": null,
            "display": null,
            "flex": null,
            "flex_flow": null,
            "grid_area": null,
            "grid_auto_columns": null,
            "grid_auto_flow": null,
            "grid_auto_rows": null,
            "grid_column": null,
            "grid_gap": null,
            "grid_row": null,
            "grid_template_areas": null,
            "grid_template_columns": null,
            "grid_template_rows": null,
            "height": null,
            "justify_content": null,
            "justify_items": null,
            "left": null,
            "margin": null,
            "max_height": null,
            "max_width": null,
            "min_height": null,
            "min_width": null,
            "object_fit": null,
            "object_position": null,
            "order": null,
            "overflow": null,
            "overflow_x": null,
            "overflow_y": null,
            "padding": null,
            "right": null,
            "top": null,
            "visibility": null,
            "width": null
          }
        },
        "460dac19916e422689f4bd0189a48b5f": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "VBoxModel",
          "model_module_version": "1.5.0",
          "state": {
            "_dom_classes": [
              "widget-interact"
            ],
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "VBoxModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/controls",
            "_view_module_version": "1.5.0",
            "_view_name": "VBoxView",
            "box_style": "",
            "children": [
              "IPY_MODEL_d74069c3efc54f9daf4eeae330200543",
              "IPY_MODEL_fc28b2477e5442b1b1b56713fb2dad21",
              "IPY_MODEL_9ff5a05512d24aa8b7b0d2d672f2f490",
              "IPY_MODEL_903b50b4ab0244af89b56321c44cfabf"
            ],
            "layout": "IPY_MODEL_3d13a7f87a16465e9a490a861eaa28a9"
          }
        },
        "d74069c3efc54f9daf4eeae330200543": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "FloatSliderModel",
          "model_module_version": "1.5.0",
          "state": {
            "_dom_classes": [],
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "FloatSliderModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/controls",
            "_view_module_version": "1.5.0",
            "_view_name": "FloatSliderView",
            "continuous_update": true,
            "description": "P Gain:",
            "description_tooltip": null,
            "disabled": false,
            "layout": "IPY_MODEL_9bf57348f40f4b6996feedff486cf4ee",
            "max": 5,
            "min": 0,
            "orientation": "horizontal",
            "readout": true,
            "readout_format": ".2f",
            "step": 0.1,
            "style": "IPY_MODEL_d494e65bfb554ff291ba61fb62c734c9",
            "value": 0
          }
        },
        "fc28b2477e5442b1b1b56713fb2dad21": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "FloatSliderModel",
          "model_module_version": "1.5.0",
          "state": {
            "_dom_classes": [],
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "FloatSliderModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/controls",
            "_view_module_version": "1.5.0",
            "_view_name": "FloatSliderView",
            "continuous_update": true,
            "description": "I Gain:",
            "description_tooltip": null,
            "disabled": false,
            "layout": "IPY_MODEL_9b38610aa97c42c4b9b706f5c3f7a8ff",
            "max": 5,
            "min": 0,
            "orientation": "horizontal",
            "readout": true,
            "readout_format": ".2f",
            "step": 0.1,
            "style": "IPY_MODEL_a653157a0e7649dcb11eebd229fb4ad9",
            "value": 0
          }
        },
        "9ff5a05512d24aa8b7b0d2d672f2f490": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "FloatSliderModel",
          "model_module_version": "1.5.0",
          "state": {
            "_dom_classes": [],
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "FloatSliderModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/controls",
            "_view_module_version": "1.5.0",
            "_view_name": "FloatSliderView",
            "continuous_update": true,
            "description": "D Gain:",
            "description_tooltip": null,
            "disabled": false,
            "layout": "IPY_MODEL_651df581c38f472397db66f73a0d80a3",
            "max": 5,
            "min": 0,
            "orientation": "horizontal",
            "readout": true,
            "readout_format": ".2f",
            "step": 0.1,
            "style": "IPY_MODEL_6105995f34304b85b02f98f48e9b48c0",
            "value": 0
          }
        },
        "903b50b4ab0244af89b56321c44cfabf": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "model_module_version": "1.0.0",
          "state": {
            "_dom_classes": [],
            "_model_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_model_name": "OutputModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/output",
            "_view_module_version": "1.0.0",
            "_view_name": "OutputView",
            "layout": "IPY_MODEL_2aa4e1d53a7743c88b62eb2d4ef6b478",
            "msg_id": "",
            "outputs": [
              {
                "output_type": "display_data",
                "data": {
                  "text/plain": "<Figure size 1000x500 with 1 Axes>",
                  "image/png": "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\n"
                },
                "metadata": {}
              }
            ]
          }
        },
        "3d13a7f87a16465e9a490a861eaa28a9": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "model_module_version": "1.2.0",
          "state": {
            "_model_module": "@jupyter-widgets/base",
            "_model_module_version": "1.2.0",
            "_model_name": "LayoutModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "LayoutView",
            "align_content": null,
            "align_items": null,
            "align_self": null,
            "border": null,
            "bottom": null,
            "display": null,
            "flex": null,
            "flex_flow": null,
            "grid_area": null,
            "grid_auto_columns": null,
            "grid_auto_flow": null,
            "grid_auto_rows": null,
            "grid_column": null,
            "grid_gap": null,
            "grid_row": null,
            "grid_template_areas": null,
            "grid_template_columns": null,
            "grid_template_rows": null,
            "height": null,
            "justify_content": null,
            "justify_items": null,
            "left": null,
            "margin": null,
            "max_height": null,
            "max_width": null,
            "min_height": null,
            "min_width": null,
            "object_fit": null,
            "object_position": null,
            "order": null,
            "overflow": null,
            "overflow_x": null,
            "overflow_y": null,
            "padding": null,
            "right": null,
            "top": null,
            "visibility": null,
            "width": null
          }
        },
        "9bf57348f40f4b6996feedff486cf4ee": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "model_module_version": "1.2.0",
          "state": {
            "_model_module": "@jupyter-widgets/base",
            "_model_module_version": "1.2.0",
            "_model_name": "LayoutModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "LayoutView",
            "align_content": null,
            "align_items": null,
            "align_self": null,
            "border": null,
            "bottom": null,
            "display": null,
            "flex": null,
            "flex_flow": null,
            "grid_area": null,
            "grid_auto_columns": null,
            "grid_auto_flow": null,
            "grid_auto_rows": null,
            "grid_column": null,
            "grid_gap": null,
            "grid_row": null,
            "grid_template_areas": null,
            "grid_template_columns": null,
            "grid_template_rows": null,
            "height": null,
            "justify_content": null,
            "justify_items": null,
            "left": null,
            "margin": null,
            "max_height": null,
            "max_width": null,
            "min_height": null,
            "min_width": null,
            "object_fit": null,
            "object_position": null,
            "order": null,
            "overflow": null,
            "overflow_x": null,
            "overflow_y": null,
            "padding": null,
            "right": null,
            "top": null,
            "visibility": null,
            "width": null
          }
        },
        "d494e65bfb554ff291ba61fb62c734c9": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "SliderStyleModel",
          "model_module_version": "1.5.0",
          "state": {
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "SliderStyleModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "StyleView",
            "description_width": "",
            "handle_color": null
          }
        },
        "9b38610aa97c42c4b9b706f5c3f7a8ff": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "model_module_version": "1.2.0",
          "state": {
            "_model_module": "@jupyter-widgets/base",
            "_model_module_version": "1.2.0",
            "_model_name": "LayoutModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "LayoutView",
            "align_content": null,
            "align_items": null,
            "align_self": null,
            "border": null,
            "bottom": null,
            "display": null,
            "flex": null,
            "flex_flow": null,
            "grid_area": null,
            "grid_auto_columns": null,
            "grid_auto_flow": null,
            "grid_auto_rows": null,
            "grid_column": null,
            "grid_gap": null,
            "grid_row": null,
            "grid_template_areas": null,
            "grid_template_columns": null,
            "grid_template_rows": null,
            "height": null,
            "justify_content": null,
            "justify_items": null,
            "left": null,
            "margin": null,
            "max_height": null,
            "max_width": null,
            "min_height": null,
            "min_width": null,
            "object_fit": null,
            "object_position": null,
            "order": null,
            "overflow": null,
            "overflow_x": null,
            "overflow_y": null,
            "padding": null,
            "right": null,
            "top": null,
            "visibility": null,
            "width": null
          }
        },
        "a653157a0e7649dcb11eebd229fb4ad9": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "SliderStyleModel",
          "model_module_version": "1.5.0",
          "state": {
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "SliderStyleModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "StyleView",
            "description_width": "",
            "handle_color": null
          }
        },
        "651df581c38f472397db66f73a0d80a3": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "model_module_version": "1.2.0",
          "state": {
            "_model_module": "@jupyter-widgets/base",
            "_model_module_version": "1.2.0",
            "_model_name": "LayoutModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "LayoutView",
            "align_content": null,
            "align_items": null,
            "align_self": null,
            "border": null,
            "bottom": null,
            "display": null,
            "flex": null,
            "flex_flow": null,
            "grid_area": null,
            "grid_auto_columns": null,
            "grid_auto_flow": null,
            "grid_auto_rows": null,
            "grid_column": null,
            "grid_gap": null,
            "grid_row": null,
            "grid_template_areas": null,
            "grid_template_columns": null,
            "grid_template_rows": null,
            "height": null,
            "justify_content": null,
            "justify_items": null,
            "left": null,
            "margin": null,
            "max_height": null,
            "max_width": null,
            "min_height": null,
            "min_width": null,
            "object_fit": null,
            "object_position": null,
            "order": null,
            "overflow": null,
            "overflow_x": null,
            "overflow_y": null,
            "padding": null,
            "right": null,
            "top": null,
            "visibility": null,
            "width": null
          }
        },
        "6105995f34304b85b02f98f48e9b48c0": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "SliderStyleModel",
          "model_module_version": "1.5.0",
          "state": {
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "SliderStyleModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "StyleView",
            "description_width": "",
            "handle_color": null
          }
        },
        "2aa4e1d53a7743c88b62eb2d4ef6b478": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "model_module_version": "1.2.0",
          "state": {
            "_model_module": "@jupyter-widgets/base",
            "_model_module_version": "1.2.0",
            "_model_name": "LayoutModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/base",
            "_view_module_version": "1.2.0",
            "_view_name": "LayoutView",
            "align_content": null,
            "align_items": null,
            "align_self": null,
            "border": null,
            "bottom": null,
            "display": null,
            "flex": null,
            "flex_flow": null,
            "grid_area": null,
            "grid_auto_columns": null,
            "grid_auto_flow": null,
            "grid_auto_rows": null,
            "grid_column": null,
            "grid_gap": null,
            "grid_row": null,
            "grid_template_areas": null,
            "grid_template_columns": null,
            "grid_template_rows": null,
            "height": null,
            "justify_content": null,
            "justify_items": null,
            "left": null,
            "margin": null,
            "max_height": null,
            "max_width": null,
            "min_height": null,
            "min_width": null,
            "object_fit": null,
            "object_position": null,
            "order": null,
            "overflow": null,
            "overflow_x": null,
            "overflow_y": null,
            "padding": null,
            "right": null,
            "top": null,
            "visibility": null,
            "width": null
          }
        }
      }
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# CPSC5207EL2: Intelligent Mobile Robotics\n",
        "\n",
        "This Python code implements a simulation to demonstrate how a PID (Proportional-Integral-Derivative) controller can adjust an agent's position to follow a target line using interactive PID gain tuning. The simulation uses ipywidgets for creating interactive sliders to adjust the gains.\n",
        "\n",
        "PID Parameters Initialization: The initial PID gains (P, I, D) are set to 0. These gains determine how the controller responds to the difference between the agent's current position and the target position (set point).\n",
        "\n",
        "Simulation Parameters: Defines the time step (dt) and total simulation time (total_time). These parameters control the resolution and duration of the simulation.\n",
        "\n",
        "PID Controller Function (pid_controller): This function takes the PID gains (P, I, D) as inputs and simulates how the agent's position changes over time under PID control. It:\n",
        "\n",
        "Initializes the agent's position and velocity.\n",
        "Calculates the error between the agent's position and the target line position at each time step.\n",
        "Computes the PID control signal based on the current error, the integral of past errors, and the rate of change of the error.\n",
        "Updates the agent's position based on the control signal.\n",
        "Plots the agent's position over time and the target line for visual analysis.\n",
        "Interactive Sliders for PID Gains: Utilizes ipywidgets.interact along with FloatSlider widgets to allow real-time adjustment of the P, I, and D gains. Adjusting these sliders dynamically updates the simulation to reflect how changes in the PID gains affect the agent's ability to follow the target line accurately.\n",
        "\n",
        "How the Simulation Works:\n",
        "Starting Conditions: The simulation begins with the agent positioned away from the target line. The goal of the PID controller is to adjust the agent's position so that it converges to this target line.\n",
        "\n",
        "Real-Time PID Tuning: Users can interactively adjust the P, I, and D gains using the sliders. The effect of these adjustments on the agent's position relative to the target line is immediately reflected in the plot, demonstrating the impact of each PID component:\n",
        "\n",
        "P Gain: Influences the controller's response strength to the current error.\n",
        "I Gain: Compensates for accumulated errors over time, addressing any persistent offset.\n",
        "D Gain: Dampens the rate of change of the error, helping to stabilize and prevent overshooting.\n",
        "Visualization: The plot dynamically updates to show the agent's position across the simulation timeframe, illustrating how closely and quickly the agent can align with the target line under different PID gain settings."
      ],
      "metadata": {
        "id": "ysMbQC-mguaV"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "f2sIBz6C8kWn",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e70e6d90-4662-448b-a24b-1541458efd8d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: ipywidgets in /usr/local/lib/python3.10/dist-packages (7.7.1)\n",
            "Requirement already satisfied: matplotlib in /usr/local/lib/python3.10/dist-packages (3.7.1)\n",
            "Requirement already satisfied: ipykernel>=4.5.1 in /usr/local/lib/python3.10/dist-packages (from ipywidgets) (5.5.6)\n",
            "Requirement already satisfied: ipython-genutils~=0.2.0 in /usr/local/lib/python3.10/dist-packages (from ipywidgets) (0.2.0)\n",
            "Requirement already satisfied: traitlets>=4.3.1 in /usr/local/lib/python3.10/dist-packages (from ipywidgets) (5.7.1)\n",
            "Requirement already satisfied: widgetsnbextension~=3.6.0 in /usr/local/lib/python3.10/dist-packages (from ipywidgets) (3.6.6)\n",
            "Requirement already satisfied: ipython>=4.0.0 in /usr/local/lib/python3.10/dist-packages (from ipywidgets) (7.34.0)\n",
            "Requirement already satisfied: jupyterlab-widgets>=1.0.0 in /usr/local/lib/python3.10/dist-packages (from ipywidgets) (3.0.10)\n",
            "Requirement already satisfied: contourpy>=1.0.1 in /usr/local/lib/python3.10/dist-packages (from matplotlib) (1.2.0)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.10/dist-packages (from matplotlib) (0.12.1)\n",
            "Requirement already satisfied: fonttools>=4.22.0 in /usr/local/lib/python3.10/dist-packages (from matplotlib) (4.49.0)\n",
            "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.10/dist-packages (from matplotlib) (1.4.5)\n",
            "Requirement already satisfied: numpy>=1.20 in /usr/local/lib/python3.10/dist-packages (from matplotlib) (1.25.2)\n",
            "Requirement already satisfied: packaging>=20.0 in /usr/local/lib/python3.10/dist-packages (from matplotlib) (23.2)\n",
            "Requirement already satisfied: pillow>=6.2.0 in /usr/local/lib/python3.10/dist-packages (from matplotlib) (9.4.0)\n",
            "Requirement already satisfied: pyparsing>=2.3.1 in /usr/local/lib/python3.10/dist-packages (from matplotlib) (3.1.1)\n",
            "Requirement already satisfied: python-dateutil>=2.7 in /usr/local/lib/python3.10/dist-packages (from matplotlib) (2.8.2)\n",
            "Requirement already satisfied: jupyter-client in /usr/local/lib/python3.10/dist-packages (from ipykernel>=4.5.1->ipywidgets) (6.1.12)\n",
            "Requirement already satisfied: tornado>=4.2 in /usr/local/lib/python3.10/dist-packages (from ipykernel>=4.5.1->ipywidgets) (6.3.2)\n",
            "Requirement already satisfied: setuptools>=18.5 in /usr/local/lib/python3.10/dist-packages (from ipython>=4.0.0->ipywidgets) (67.7.2)\n",
            "Collecting jedi>=0.16 (from ipython>=4.0.0->ipywidgets)\n",
            "  Downloading jedi-0.19.1-py2.py3-none-any.whl (1.6 MB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m1.6/1.6 MB\u001b[0m \u001b[31m8.2 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hRequirement already satisfied: decorator in /usr/local/lib/python3.10/dist-packages (from ipython>=4.0.0->ipywidgets) (4.4.2)\n",
            "Requirement already satisfied: pickleshare in /usr/local/lib/python3.10/dist-packages (from ipython>=4.0.0->ipywidgets) (0.7.5)\n",
            "Requirement already satisfied: prompt-toolkit!=3.0.0,!=3.0.1,<3.1.0,>=2.0.0 in /usr/local/lib/python3.10/dist-packages (from ipython>=4.0.0->ipywidgets) (3.0.43)\n",
            "Requirement already satisfied: pygments in /usr/local/lib/python3.10/dist-packages (from ipython>=4.0.0->ipywidgets) (2.16.1)\n",
            "Requirement already satisfied: backcall in /usr/local/lib/python3.10/dist-packages (from ipython>=4.0.0->ipywidgets) (0.2.0)\n",
            "Requirement already satisfied: matplotlib-inline in /usr/local/lib/python3.10/dist-packages (from ipython>=4.0.0->ipywidgets) (0.1.6)\n",
            "Requirement already satisfied: pexpect>4.3 in /usr/local/lib/python3.10/dist-packages (from ipython>=4.0.0->ipywidgets) (4.9.0)\n",
            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.10/dist-packages (from python-dateutil>=2.7->matplotlib) (1.16.0)\n",
            "Requirement already satisfied: notebook>=4.4.1 in /usr/local/lib/python3.10/dist-packages (from widgetsnbextension~=3.6.0->ipywidgets) (6.5.5)\n",
            "Requirement already satisfied: parso<0.9.0,>=0.8.3 in /usr/local/lib/python3.10/dist-packages (from jedi>=0.16->ipython>=4.0.0->ipywidgets) (0.8.3)\n",
            "Requirement already satisfied: jinja2 in /usr/local/lib/python3.10/dist-packages (from notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (3.1.3)\n",
            "Requirement already satisfied: pyzmq<25,>=17 in /usr/local/lib/python3.10/dist-packages (from notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (23.2.1)\n",
            "Requirement already satisfied: argon2-cffi in /usr/local/lib/python3.10/dist-packages (from notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (23.1.0)\n",
            "Requirement already satisfied: jupyter-core>=4.6.1 in /usr/local/lib/python3.10/dist-packages (from notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (5.7.1)\n",
            "Requirement already satisfied: nbformat in /usr/local/lib/python3.10/dist-packages (from notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (5.9.2)\n",
            "Requirement already satisfied: nbconvert>=5 in /usr/local/lib/python3.10/dist-packages (from notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (6.5.4)\n",
            "Requirement already satisfied: nest-asyncio>=1.5 in /usr/local/lib/python3.10/dist-packages (from notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (1.6.0)\n",
            "Requirement already satisfied: Send2Trash>=1.8.0 in /usr/local/lib/python3.10/dist-packages (from notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (1.8.2)\n",
            "Requirement already satisfied: terminado>=0.8.3 in /usr/local/lib/python3.10/dist-packages (from notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (0.18.0)\n",
            "Requirement already satisfied: prometheus-client in /usr/local/lib/python3.10/dist-packages (from notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (0.20.0)\n",
            "Requirement already satisfied: nbclassic>=0.4.7 in /usr/local/lib/python3.10/dist-packages (from notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (1.0.0)\n",
            "Requirement already satisfied: ptyprocess>=0.5 in /usr/local/lib/python3.10/dist-packages (from pexpect>4.3->ipython>=4.0.0->ipywidgets) (0.7.0)\n",
            "Requirement already satisfied: wcwidth in /usr/local/lib/python3.10/dist-packages (from prompt-toolkit!=3.0.0,!=3.0.1,<3.1.0,>=2.0.0->ipython>=4.0.0->ipywidgets) (0.2.13)\n",
            "Requirement already satisfied: platformdirs>=2.5 in /usr/local/lib/python3.10/dist-packages (from jupyter-core>=4.6.1->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (4.2.0)\n",
            "Requirement already satisfied: jupyter-server>=1.8 in /usr/local/lib/python3.10/dist-packages (from nbclassic>=0.4.7->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (1.24.0)\n",
            "Requirement already satisfied: notebook-shim>=0.2.3 in /usr/local/lib/python3.10/dist-packages (from nbclassic>=0.4.7->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (0.2.4)\n",
            "Requirement already satisfied: lxml in /usr/local/lib/python3.10/dist-packages (from nbconvert>=5->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (4.9.4)\n",
            "Requirement already satisfied: beautifulsoup4 in /usr/local/lib/python3.10/dist-packages (from nbconvert>=5->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (4.12.3)\n",
            "Requirement already satisfied: bleach in /usr/local/lib/python3.10/dist-packages (from nbconvert>=5->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (6.1.0)\n",
            "Requirement already satisfied: defusedxml in /usr/local/lib/python3.10/dist-packages (from nbconvert>=5->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (0.7.1)\n",
            "Requirement already satisfied: entrypoints>=0.2.2 in /usr/local/lib/python3.10/dist-packages (from nbconvert>=5->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (0.4)\n",
            "Requirement already satisfied: jupyterlab-pygments in /usr/local/lib/python3.10/dist-packages (from nbconvert>=5->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (0.3.0)\n",
            "Requirement already satisfied: MarkupSafe>=2.0 in /usr/local/lib/python3.10/dist-packages (from nbconvert>=5->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (2.1.5)\n",
            "Requirement already satisfied: mistune<2,>=0.8.1 in /usr/local/lib/python3.10/dist-packages (from nbconvert>=5->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (0.8.4)\n",
            "Requirement already satisfied: nbclient>=0.5.0 in /usr/local/lib/python3.10/dist-packages (from nbconvert>=5->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (0.9.0)\n",
            "Requirement already satisfied: pandocfilters>=1.4.1 in /usr/local/lib/python3.10/dist-packages (from nbconvert>=5->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (1.5.1)\n",
            "Requirement already satisfied: tinycss2 in /usr/local/lib/python3.10/dist-packages (from nbconvert>=5->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (1.2.1)\n",
            "Requirement already satisfied: fastjsonschema in /usr/local/lib/python3.10/dist-packages (from nbformat->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (2.19.1)\n",
            "Requirement already satisfied: jsonschema>=2.6 in /usr/local/lib/python3.10/dist-packages (from nbformat->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (4.19.2)\n",
            "Requirement already satisfied: argon2-cffi-bindings in /usr/local/lib/python3.10/dist-packages (from argon2-cffi->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (21.2.0)\n",
            "Requirement already satisfied: attrs>=22.2.0 in /usr/local/lib/python3.10/dist-packages (from jsonschema>=2.6->nbformat->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (23.2.0)\n",
            "Requirement already satisfied: jsonschema-specifications>=2023.03.6 in /usr/local/lib/python3.10/dist-packages (from jsonschema>=2.6->nbformat->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (2023.12.1)\n",
            "Requirement already satisfied: referencing>=0.28.4 in /usr/local/lib/python3.10/dist-packages (from jsonschema>=2.6->nbformat->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (0.33.0)\n",
            "Requirement already satisfied: rpds-py>=0.7.1 in /usr/local/lib/python3.10/dist-packages (from jsonschema>=2.6->nbformat->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (0.18.0)\n",
            "Requirement already satisfied: anyio<4,>=3.1.0 in /usr/local/lib/python3.10/dist-packages (from jupyter-server>=1.8->nbclassic>=0.4.7->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (3.7.1)\n",
            "Requirement already satisfied: websocket-client in /usr/local/lib/python3.10/dist-packages (from jupyter-server>=1.8->nbclassic>=0.4.7->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (1.7.0)\n",
            "Requirement already satisfied: cffi>=1.0.1 in /usr/local/lib/python3.10/dist-packages (from argon2-cffi-bindings->argon2-cffi->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (1.16.0)\n",
            "Requirement already satisfied: soupsieve>1.2 in /usr/local/lib/python3.10/dist-packages (from beautifulsoup4->nbconvert>=5->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (2.5)\n",
            "Requirement already satisfied: webencodings in /usr/local/lib/python3.10/dist-packages (from bleach->nbconvert>=5->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (0.5.1)\n",
            "Requirement already satisfied: idna>=2.8 in /usr/local/lib/python3.10/dist-packages (from anyio<4,>=3.1.0->jupyter-server>=1.8->nbclassic>=0.4.7->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (3.6)\n",
            "Requirement already satisfied: sniffio>=1.1 in /usr/local/lib/python3.10/dist-packages (from anyio<4,>=3.1.0->jupyter-server>=1.8->nbclassic>=0.4.7->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (1.3.1)\n",
            "Requirement already satisfied: exceptiongroup in /usr/local/lib/python3.10/dist-packages (from anyio<4,>=3.1.0->jupyter-server>=1.8->nbclassic>=0.4.7->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (1.2.0)\n",
            "Requirement already satisfied: pycparser in /usr/local/lib/python3.10/dist-packages (from cffi>=1.0.1->argon2-cffi-bindings->argon2-cffi->notebook>=4.4.1->widgetsnbextension~=3.6.0->ipywidgets) (2.21)\n",
            "Installing collected packages: jedi\n",
            "Successfully installed jedi-0.19.1\n"
          ]
        }
      ],
      "source": [
        "pip install ipywidgets matplotlib"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from ipywidgets import interact, FloatSlider\n",
        "import ipywidgets as widgets\n",
        "\n",
        "# Initial PID parameters\n",
        "P = 0.0\n",
        "I = 0.0\n",
        "D = 0.0\n",
        "\n",
        "# Target line position\n",
        "target_line_position = 0\n",
        "\n",
        "# Simulation parameters\n",
        "dt = 1  # Time step\n",
        "total_time = 100  # Total simulation time\n",
        "\n",
        "def pid_controller(P, I, D):\n",
        "    # Reinitialize these variables inside the function to ensure reset on each call\n",
        "    agent_position = 10  # Initial position away from the line\n",
        "    agent_velocity = 0  # Initial velocity\n",
        "    error_integral = 0  # For integral term in PID\n",
        "    previous_error = agent_position - target_line_position  # For derivative term in PID\n",
        "\n",
        "    time_steps = int(total_time / dt)\n",
        "    positions = [agent_position]  # Start with the initial position\n",
        "\n",
        "    for _ in range(time_steps):\n",
        "        # Calculate error\n",
        "        error = agent_position - target_line_position\n",
        "\n",
        "        # PID control\n",
        "        error_integral += error * dt\n",
        "        error_derivative = (error - previous_error) / dt\n",
        "        control_signal = P*error + I*error_integral + D*error_derivative\n",
        "\n",
        "        # Update agent's state\n",
        "        agent_velocity = control_signal\n",
        "        agent_position -= agent_velocity * dt  # Simple motion model\n",
        "\n",
        "        positions.append(agent_position)  # Append the updated position\n",
        "\n",
        "        previous_error = error\n",
        "\n",
        "    # Plotting\n",
        "    plt.figure(figsize=(10, 5))\n",
        "    plt.plot(positions, label=\"Agent Position\")\n",
        "    plt.axhline(y=target_line_position, color='r', linestyle='-', label=\"Target Line\")\n",
        "    plt.xlabel(\"Time Step\")\n",
        "    plt.ylabel(\"Position\")\n",
        "    plt.legend()\n",
        "    plt.grid(True)\n",
        "    plt.title(\"PID Controller for Line Following\")\n",
        "    plt.show()\n",
        "\n",
        "# Interactive sliders for PID gains\n",
        "interact(pid_controller,\n",
        "         P=FloatSlider(value=0.0, min=0, max=5, step=0.1, description='P Gain:'),\n",
        "         I=FloatSlider(value=0.0, min=0, max=5, step=0.1, description='I Gain:'),\n",
        "         D=FloatSlider(value=0.0, min=0, max=5, step=0.1, description='D Gain:'))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 670,
          "referenced_widgets": [
            "85c4c3a22fb94dd3b8e5fa817c173fe1",
            "5b0d7d8723c64ecdb48e5f4efe366dc5",
            "dd97f0e039884672a36677ffd2001496",
            "a806a27e1f474d5d8e112ca66501e735",
            "ed3d8c8f08bf4c189cfb3e20fccf0a52",
            "7881ed5a89fc403f85afb521a63e5adf",
            "1f271b152d6349099c0b5fb2b5a63696",
            "bc84c0482c0d4dffa12c6d2911a55ef8",
            "c38f04a7eabb4d1ea7e580cab4a515ff",
            "d10b914155884456bdd11c5eb6bda94e",
            "c2b59dbea17a4de4a479b2987c46e87d",
            "994bcbee02644b50a7a15e4ef47c195a",
            "f8392030ff34437a93a72ef3a1ebcee0"
          ]
        },
        "id": "o9CN38FU9vx5",
        "outputId": "4dc1ca24-4f2e-4a69-ba98-c2ca685ef9ae"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "interactive(children=(FloatSlider(value=0.0, description='P Gain:', max=5.0), FloatSlider(value=0.0, descripti…"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "85c4c3a22fb94dd3b8e5fa817c173fe1"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<function __main__.pid_controller(P, I, D)>"
            ],
            "text/html": [
              "<div style=\"max-width:800px; border: 1px solid var(--colab-border-color);\"><style>\n",
              "      pre.function-repr-contents {\n",
              "        overflow-x: auto;\n",
              "        padding: 8px 12px;\n",
              "        max-height: 500px;\n",
              "      }\n",
              "\n",
              "      pre.function-repr-contents.function-repr-contents-collapsed {\n",
              "        cursor: pointer;\n",
              "        max-height: 100px;\n",
              "      }\n",
              "    </style>\n",
              "    <pre style=\"white-space: initial; background:\n",
              "         var(--colab-secondary-surface-color); padding: 8px 12px;\n",
              "         border-bottom: 1px solid var(--colab-border-color);\"><b>pid_controller</b><br/>def pid_controller(P, I, D)</pre><pre class=\"function-repr-contents function-repr-contents-collapsed\" style=\"\"><a class=\"filepath\" style=\"display:none\" href=\"#\">/content/&lt;ipython-input-2-7c7fcd08a870&gt;</a>&lt;no docstring&gt;</pre></div>"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Adjust PID Controller to Counteract the Bias ( using just a P-controller will not work!): The PID controller, particularly the integral term, will work to counteract this constant disturbance by accumulating error over time and adjusting the control signal accordingly to bring the system back to its set point.\n",
        "\n",
        "- Disturbance: The disturbance variable simulates an external force acting continuously against the agent. This could represent any persistent bias in the system that the controller needs to overcome.\n",
        "\n",
        "Integral Gain's Role: Over time, the I gain accumulates the error caused by this disturbance and adjusts the control signal to counteract it, aiming to eliminate the steady-state error and bring the agent back to the set point.\n",
        "\n",
        "Reaching the Set Point: With appropriate tuning of the I gain, the system can still reach the set point despite the constant disturbance. The I gain works to offset any continuous bias or disturbance, ensuring the agent's position converges to the desired set point over time.\n",
        "\n",
        "This approach more accurately demonstrates the importance of each PID component, showing that while P gain can quickly reduce error, I gain is crucial for correcting steady-state errors introduced by constant disturbances, and D gain helps dampen overshoot and oscillations for a smoother approach to the set point."
      ],
      "metadata": {
        "id": "qXCMcK5zfgXO"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from ipywidgets import interact, FloatSlider\n",
        "import ipywidgets as widgets\n",
        "\n",
        "# Initial PID parameters\n",
        "P = 0.0\n",
        "I = 0.0\n",
        "D = 0.0\n",
        "\n",
        "# Target line position\n",
        "target_line_position = 0\n",
        "\n",
        "# Simulation parameters\n",
        "dt = 1  # Time step\n",
        "total_time = 100  # Total simulation time\n",
        "\n",
        "def pid_controller(P, I, D):\n",
        "    agent_position = 10  # Initial position away from the line\n",
        "    agent_velocity = 0  # Initial velocity\n",
        "    error_integral = 0  # For integral term in PID\n",
        "    previous_error = agent_position - target_line_position\n",
        "    disturbance = 0.5  # Constant disturbance affecting the agent's position\n",
        "\n",
        "    time_steps = int(total_time / dt)\n",
        "    positions = [agent_position]\n",
        "\n",
        "    for _ in range(time_steps):\n",
        "        # Calculate error\n",
        "        error = agent_position - target_line_position\n",
        "\n",
        "        # PID control\n",
        "        error_integral += error * dt\n",
        "        error_derivative = (error - previous_error) / dt\n",
        "        control_signal = P*error + I*error_integral + D*error_derivative\n",
        "\n",
        "        # Apply disturbance to the agent's movement\n",
        "        agent_velocity = control_signal\n",
        "        agent_position -= (agent_velocity * dt) + disturbance  # Disturbance affects movement\n",
        "\n",
        "        positions.append(agent_position)\n",
        "\n",
        "        previous_error = error\n",
        "\n",
        "    # Plotting\n",
        "    plt.figure(figsize=(10, 5))\n",
        "    plt.plot(positions, label=\"Agent Position\")\n",
        "    plt.axhline(y=target_line_position, color='r', linestyle='-', label=\"Target Line\")\n",
        "    plt.xlabel(\"Time Step\")\n",
        "    plt.ylabel(\"Position\")\n",
        "    plt.legend()\n",
        "    plt.grid(True)\n",
        "    plt.title(\"PID Controller for Line Following\")\n",
        "    plt.show()\n",
        "\n",
        "# Interactive sliders for PID gains\n",
        "interact(pid_controller,\n",
        "         P=FloatSlider(value=0.0, min=0, max=5, step=0.1, description='P Gain:'),\n",
        "         I=FloatSlider(value=0.0, min=0, max=5, step=0.1, description='I Gain:'),\n",
        "         D=FloatSlider(value=0.0, min=0, max=5, step=0.1, description='D Gain:'))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 670,
          "referenced_widgets": [
            "460dac19916e422689f4bd0189a48b5f",
            "d74069c3efc54f9daf4eeae330200543",
            "fc28b2477e5442b1b1b56713fb2dad21",
            "9ff5a05512d24aa8b7b0d2d672f2f490",
            "903b50b4ab0244af89b56321c44cfabf",
            "3d13a7f87a16465e9a490a861eaa28a9",
            "9bf57348f40f4b6996feedff486cf4ee",
            "d494e65bfb554ff291ba61fb62c734c9",
            "9b38610aa97c42c4b9b706f5c3f7a8ff",
            "a653157a0e7649dcb11eebd229fb4ad9",
            "651df581c38f472397db66f73a0d80a3",
            "6105995f34304b85b02f98f48e9b48c0",
            "2aa4e1d53a7743c88b62eb2d4ef6b478"
          ]
        },
        "id": "J4mTQT2QF-nk",
        "outputId": "740308d5-b71a-4d87-892d-622bcba8f092"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "interactive(children=(FloatSlider(value=0.0, description='P Gain:', max=5.0), FloatSlider(value=0.0, descripti…"
            ],
            "application/vnd.jupyter.widget-view+json": {
              "version_major": 2,
              "version_minor": 0,
              "model_id": "460dac19916e422689f4bd0189a48b5f"
            }
          },
          "metadata": {}
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<function __main__.pid_controller(P, I, D)>"
            ],
            "text/html": [
              "<div style=\"max-width:800px; border: 1px solid var(--colab-border-color);\"><style>\n",
              "      pre.function-repr-contents {\n",
              "        overflow-x: auto;\n",
              "        padding: 8px 12px;\n",
              "        max-height: 500px;\n",
              "      }\n",
              "\n",
              "      pre.function-repr-contents.function-repr-contents-collapsed {\n",
              "        cursor: pointer;\n",
              "        max-height: 100px;\n",
              "      }\n",
              "    </style>\n",
              "    <pre style=\"white-space: initial; background:\n",
              "         var(--colab-secondary-surface-color); padding: 8px 12px;\n",
              "         border-bottom: 1px solid var(--colab-border-color);\"><b>pid_controller</b><br/>def pid_controller(P, I, D)</pre><pre class=\"function-repr-contents function-repr-contents-collapsed\" style=\"\"><a class=\"filepath\" style=\"display:none\" href=\"#\">/content/&lt;ipython-input-3-5f4aa894f9ed&gt;</a>&lt;no docstring&gt;</pre></div>"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    }
  ]
}