remove LQG

The functionality was very buggy and poorly tested. A much improved version with proper tests are available in https://github.com/JuliaControl/RobustAndOptimalControl.jl/blob/master/src/lqg.jl

example/dc_motor_lqg_design.jl

@@ -29,7 +29,7 @@ function motor(Ke, Kt, L, R, J, b=1e-3)
 end
 
 p60 = motor(Ke, Kt, L, Rel, J)
-f1 = stepplot(p60)
+f1 = stepplot(p60, 1)
 f2 = bodeplot(p60)
 
 # LQR control
@@ -45,12 +45,20 @@ Nbar = 1. ./ (p60.D - (p60.C - p60.D*K) * inv(p60.A - p60.B*K) * p60.B)
 Vd = [10.     0   # covariance of the speed estimation
      0       10]; # covariance of the current estimation
 Vn = 0.04;       # covariance for the speed measurement (radians/s)^2
-G = LQG(p60, Q, mat(R), Vd, mat(Vn))
-Gcl = G[:cl]
-T = G[:T]
-S = G[:S];
+Ka = kalman(p60, Vd, mat(Vn))
+C = ControlSystems.observer_controller(p60, K, Ka)
+
+Gcl = let (A,B,C,D) = ssdata(p60)
+     Acl = [A-B*K B*K; zero(A) A-Ka*C]
+     Bcl = [B * Nbar; zero(B)]
+     Ccl = [C zero(C)]
+     ss(Acl, Bcl, Ccl, 0)
+end
+
+T = Gcl
+S = 1-T
 
 # 1000 logarithmically spaced values from -3 to 3
-f3 = sigmaplot([S,T], exp10.(range(-3, stop=3, length=1000)))
-f4 = stepplot(Gcl, label=["Closed loop system using LQG"])
+f3 = bodeplot([Gcl, S, T], exp10.(range(-3, stop=3, length=1000)))
+f4 = stepplot(Gcl, 1, label="Closed loop system using LQG")
 Plots.plot(f1, f2, f3, f4, layout=(2,2), size=(800, 600))

src/ControlSystems.jl

@@ -11,7 +11,6 @@ export  LTISystem,
         ss,
         tf,
         zpk,
-        LQG,
         isproper,
         # Linear Algebra
         balance,
@@ -142,8 +141,6 @@ include("types/DelayLtiSystem.jl")
 include("types/tf.jl")
 include("types/zpk.jl")
 
-include("types/lqg.jl") # QUESTION: is it really motivated to have an LQG type?
-
 include("utilities.jl")
 
 include("types/promotion.jl")

src/synthesis.jl

@@ -13,8 +13,6 @@ For the continuous time model `dx = Ax + Bu`.
 Solve the LQR problem for state-space system `sys`. Works for both discrete
 and continuous time systems.
 
-See also `LQG`
-
 Usage example:
 ```julia
 using LinearAlgebra # For identity matrix I
@@ -44,8 +42,6 @@ end
     kalman(sys, R1, R2)
 
 Calculate the optimal Kalman gain
-
-See also `LQG`
 """
 kalman(A, C, R1,R2) = Matrix(lqr(A',C',R1,R2)')
 

test/runtests.jl

@@ -21,7 +21,6 @@ my_tests = [
             "test_timeresp",
             "test_analysis",
             "test_matrix_comps",
-            "test_lqg",
             "test_synthesis",
             "test_pid_design",
             "test_partitioned_statespace",