Simulink Control Design™ - MathWorks

Tune MIMO Control System for Specified Bandwidth

This example shows how to tune the following control system to achieve a loop crossover

frequency between 0.1 and 1 rad/s, using looptune.

The plant, G, is a two-input, two-output model (y is a two-element vector signal). For this

example, the transfer function of G is given by:

Gs =

1

75 s+1

87.8 −86.4

108.2−109.6

.

This sample plant is based on the distillation column described in more detail in the

example “Decoupling Controller for a Distillation Column” (Control System Toolbox).

To tune this control system, you first create a numeric model of the plant. Then you create

tunable models of the controller elements and interconnect them to build a controller

model. Then you use looptune to tune the free parameters of the controller model.

Finally, examine the performance of the tuned system to confirm that the tuned controller

yields desirable performance.

Create a model of the plant.

s = tf('s');

G = 1/(75*s+1)*[87.8 -86.4; 108.2 -109.6];

G.InputName = {'qL','qV'};

G.OutputName = 'y';

When you tune the control system, looptune uses the channel names G.InputName and

G.OutputName to interconnect the plant and controller. Therefore, assign these channel

names to match the illustration. When you set G.OutputName = 'y', the

G.OutputName is automatically expanded to {'y(1)';'y(2)'}. This expansion occurs

because G is a two-output system.

Represent the components of the controller.

12 Loop-Shaping Design