National Instruments 370753C-01 lqgcomp( )

Chapter 6 State-Space Design

lqgcomp( )

SysC = lqgcomp(Sys,Kr,Ke,{direct})

The lqgcomp( ) function creates a dynamic compensator given a

dynamic system having at least one state and the regulator and estimator

gain matrices. The returned compensator SysC is always in state-space

form.

The regulator and estimator gains Kr and Ke need to have been calculated

prior to the call to lqgcomp( ). You can use regulator( ) and

estimator( ) to compute these gains if they are not already available.

These functions give you the option to incorporate the presence of the white

process and measurement noises ω and ν in your model, as shown in

Figure 6-6.

Example 6-7 uses the inverted pendulum problem estimator and regulator

gain vectors (obtained in the preceding two examples) to form a

compensator. Notice that for this example you use the optional fields of the

system( ) function to store information that will be useful when you

combine and simulate the compensator-plant system.

Example 6-7 Combining the Regulator and Estimator into a Full Compensator

A = [0,1,0,0; 21,0,0,0.8; 0,0,0,1; 0,0,0,–4];

B = [0,–2,0,1]';

C = [1,0,0,0;0,0,1,0];

D = [0;0];

ipsys = system(A,B,C,D, {inputNames = "Force (u)",

outputNames = ["phi","x"],

stateNames = ["phi","d(phi)","x","d(x)"]});

Kr=regulator(ipsys,diagonal([1,0,.1,0]),1e-5);

Ke=estimator(ipsys,0.25*B*B',

diagonal([1e-6,3e-6]));

ipsysc=lqgcomp(ipsys,Kr,Ke);

Now that you have the compensator, you need to connect it to the original

plant:

ipsyscl = afeedback(ipsys, ipsysc);

The system now has eight states (four from the compensator, four from the

original plant), three individual inputs (u and y, where y comprises φ and x)

and three outputs (again, u and y). Here you have not added additional

inputs to the system for process and measurement noise. Now you can