Merge pull request #135 from ufechner7/doc

Fixed error in docstring, improved example in docstring of LQG.

Author: baggepinnen

example/dc_motor_lqg_design.jl

@@ -0,0 +1,54 @@
+using ControlSystems
+"""
+Example for designing an LQG speed controller for an electrical DC motor.
+"""
+
+# Constants
+Ke = 0.006156                                # electromotive force constant in V/rpm
+Kt                      = 0.0728             # Torque constant (Nm/A)
+J                       = 2.8*700e-6;        # Inertia of motor plus load (kgm^2)
+Rel                     = 0.11;              # DC motor resistance (Ω)
+L                       = 34e-6;             # DC motor inductance (H)
+
+# helper to convert a scalar into an 1x1 Matrix
+mat(sc) = reshape([sc],1,1)
+
+# Create an instance of a DC motor model in state space form.
+# Ke: electromotive force constant in V/rpm
+# Kt: torque constant (Nm/A)
+# L: Inductance; R: Resistance, J: Inertia; b: viscous friction coefficient
+function motor(Ke, Kt, L, R, J, b=1e-3)
+    Ke1 = Ke*60.0/2π   # change unit to rad/s
+    A = [-b/J     Kt/J
+         -Ke1/L   -R/L];
+    B = [0
+        1/L];
+    C = [1     0];
+    D = 0;
+    sys = ss(A, B, C, D);
+end
+
+p60 = motor(Ke, Kt, L, Rel, J)
+stepplot(p60, 0.2, 0.001)
+bodeplot(p60)
+
+# LQR control
+Q = [1.     0;
+     0      1]
+
+R = 20.
+K = lqr(p60.A, p60.B, Q, R)
+# needs to be modified if Nbar is not a scalar
+Nbar = 1. / (p60.D - (p60.C - p60.D*K) * inv(p60.A - p60.B*K) * p60.B)
+
+# Kalman filter based observer
+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];
+f1 = sigmaplot([S,T],logspace(-3,3,1000))
+f2 = stepplot(Gcl, label=["Closed loop system using LQG"])
+Plots.plot(f1,f2)

src/types/lqg.jl

@@ -6,9 +6,9 @@ import Base.getindex
     G = LQG(sys, args...; kwargs...)
 
 Return an LQG object that describes the closed control loop around the process `sys=ss(A,B,C,D)`
-where the controller is of LQG-type. The controller is specified by weight matrices `R1,R2`
+where the controller is of LQG-type. The controller is specified by weight matrices `Q1,Q2`
 that penalizes state deviations and control signal variance respectively, and covariance
-matrices `Q1,Q2` which specify state drift and measurement covariance respectively.
+matrices `R1,R2` which specify state drift and measurement covariance respectively.
 This constructor calls [`lqr`](@ref) and [`kalman`](@ref) and forms the closed-loop system.
 
 If `integrator=true`, the resulting controller will have intregral action.
@@ -50,6 +50,9 @@ It is also possible to access all fileds using the `G[:symbol]` syntax, the fiel
 # Example
 
 ```julia
+s = tf("s")
+P = [1/(s+1) 2/(s+2); 1/(s+3) 1/(s-1)]
+sys = ss(P)
 eye(n) = Matrix{Float64}(I,n,n) # For convinience
 
 qQ = 1