This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English version of the page.

Note: This page has been translated by MathWorks. Click here to see
To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

Control System with Multichannel Analysis Points

This example shows how to insert multichannel analysis points in a generalized state-space model of a MIMO control system.

Consider the following two-input, two-output control system.

The plant G has two inputs and two outputs. Therefore, the line marked y in the block diagram represents two signals, y(1) and y(2). Similarly, r and e each represent two signals.

Suppose you want to create tuning requirements or extract responses that require injecting or measuring signals at the locations L and V. To do so, create an AnalysisPoint block and include it in the closed-loop model of the control system as shown in the following illustration.

To create a model of this system, first create the numeric LTI models and control design blocks that represent the plant and controller elements. D is a tunable gain block, and C_L and C_V are tunable PI controllers. Suppose the plant model is the following:

G(s)=175s+1[87.8-86.4108.2-109.6].

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

D = tunableGain('Decoupler',eye(2));
C_L = tunablePID('C_L','pi');  
C_V = tunablePID('C_V','pi');

Create an AnalysisPoint block that bundles together the L and V channels.

AP_1 = AnalysisPoint('AP_1',2)
AP_1 =

Multi-channel analysis point at locations:
   AP_1(1)
   AP_1(2)

Type "ss(AP_1)" to see the current value and "get(AP_1)" to see all properties.

For convenience, rename the channels to match the corresponding signals.

AP_1.Location = {'L';'V'}
AP_1 =

Multi-channel analysis point at locations:
   L
   V

Type "ss(AP_1)" to see the current value and "get(AP_1)" to see all properties.

The following diagram illustrates the input names, output names, and channel names (locations) in the block AP_1.

The input and output names of the AnalysisPoint block are distinct from the channel names. Use the channel names to refer to the analysis-point locations when extracting responses or defining design goals for tuning. You can use the input and output names AP_1.u and AP_1.y, for example, when interconnecting blocks using the connect command.

You can now build the closed-loop model of the control system. First, join all the plant and controller blocks along with the first AnalysisPoint block.

GC = G*AP_1*append(C_L,C_V)*D;

Then, close the feedback loop. Recall that GC has two inputs and outputs.

CL = feedback(GC,eye(2));

You can now use the analysis points for analysis or tuning. For example, extract the SISO closed-loop transfer function from 'L' to the first output. Assign a name to the output so you can reference it in analysis functions. The software automatically expands the assigned name 'y' to the vector-valued output signals {y(1),y(2)}.

CL.OutputName = 'y';
TLy1 = getIOTransfer(CL,'L','y(1)');
bodeplot(TLy1);

See Also

Related Topics