Specifications

Extract Controller
4-25
Extract Controller
This example shows how to obtain an LTI representation of an unconstrained Model
Predictive Control Toolbox controller using ss. You can use this to analyze the
controller's closed-loop frequency response, etc.
For example, consider the controller designed in “Create a Controller Object” on page 4-2.
To extract the controller, you could type:
MPCss = ss(MPCobj);
You could then construct an LTI model of the closed-loop system using the feedback
function (see Control System Toolbox for details) by typing:
CSTRd = c2d(CSTR, MPCss.Ts);
Feedin = 1;
Feedout = 1;
Sign = 1;
CLsys = feedback(CSTRd, MPCss, Feedin, Feedout, Sign);
Note The CSTR model must be converted to discrete form with the same control interval
as the controller.
Recall that the CSTR plant has two inputs and two outputs. The first input is the
manipulated variable and the other is an unmeasured disturbance. The first output
is measured for feedback and the other is not. The Feedin and Feedout parameters
specify the input and output to be used for control. The Sign parameter signifies that the
MPC object uses positive feedback, i.e., the measured outputs enter the controller with
no sign change. Omission of this would cause the feedback command to use negative
feedback by default and would almost certainly lead to an unstable closed-loop system.
You could then type
eig(CLsys)
to verify that all closed-loop poles are within the unit circle, or
bode(CLsys)
to compute a closed-loop Bode plot.