How to get the output of a controller from MATLAB codes not simulink

In simulink, it is easy to get the control output (or input to the actuator) by connecting a scope to the controller output. How do you get the output of the controller in MATLAB codes? I need the output to apply to another system as well as the plant infront of the controller.

Thanks.

Answer 1

[Sam Chak]

Hi @ojonugwa adukwu

Since a sample plant is not provided, we will use a 1st-order plant as an example:

Gp = tf(1, [1 2])

Gp =
 
    1
  -----
  s + 2
 
Continuous-time transfer function.

step(Gp, 5)

If we want to improve the settling time at 1 second and to eliminate the steady-state error, we can try:

kp = 5;
ki = 10;
Gc = pid(kp, ki)

Gc =
 
             1 
  Kp + Ki * ---
             s 

  with Kp = 5, Ki = 10
 
Continuous-time PI controller in parallel form.

The closed-loop system is given by

Gcl = feedback(Gc*Gp, 1)

Gcl =
 
     5 s + 10
  --------------
  s^2 + 7 s + 10
 
Continuous-time transfer function.

step(Gcl, 5)

And the output of the PI controller, is given by

Gu  = feedback(Gc, Gp)

Gu =
 
  5 s^2 + 20 s + 20
  -----------------
   s^2 + 7 s + 10
 
Continuous-time transfer function.

step(Gu, 5)

[Sam Chak]

Hi @ojonugwa adukwu

For the controller output, or in s-domain, we know the compensator transfer function,

... or .

To find the closed-loop transfer function relating the controller output to the input

we start from , and we need to find the error :

.

From the plant transfer function , we know that

.

Substituiting it back to , we get

.

Similarly, substituiting it back to , we get

Separating at one side and on another side

.

Rearranging that yields

This implies that is on the feedback loop, and thus, it can be obtained with the following syntax:

Gu = feedback(Gc, Gp)

Answer 2

[Paul]

I suggest using interconnection functions to build a single system model that has the control input to the plant as one of the outputs from the overall system model

One approach, for example:

Define the plant

sysp = tf(1,[1 0],'InputName','u','OutputName','y');

Define the controller

sysc = tf(1,1,'InputName','e','OutputName','u');

Unitfy feedback to form the closed loop system. Specify the outputs from the closed loop system as the output and input to the plant

sysclosed = connect(sysc,sysp,sumblk('e = r - y'),'r',{'y' 'u'});

Now we can plot the step (or any other response)

step(sysclosed)

Also, sysclosed can then be connected to other systems to build a large model if desired.

[ojonugwa adukwu]

Thanks so much

Answer 3

[ojonugwa adukwu]

Oh really? Many thanks.

But why is it the transfer function (tf) of Gu and not GC? Because for simulink, it is the transfer function of the controller.

Many thanks

[Sam Chak]

You are welcome, @ojonugwa adukwu. If you find the solution in MATLAB code is helpful, please consider accepting ✔ and voting 👍 the Answer. Thanks!

I have added an explanation in the comment under my Answer. It's almost the same argument of why use to get the system output , but not the plant itself.