design feedback state controller

hi,

I have a pressing system which it's input is the "press velocity" and the output is "exit temperature".SISO system

the matrices for the state space model are scalar and like this: A = [0] B = [16.6] C = [475] D = [0]

I need to design a state controller to keep the exit temperature in a range like 500-600°C by changing the press velocity during the pressing. the desired pole is let say -10.

I appreciate any idea.

Answer 1

[Sam Chak]

Hi @Milad Bahaedini

You can try the following design approach if it works for your application.

A   = 0;
B   = 16.6;
C   = 475;
D   = 0;
sys = ss(A, B, C, D)

sys =
 
  A = 
       x1
   x1   0
 
  B = 
         u1
   x1  16.6
 
  C = 
        x1
   y1  475
 
  D = 
       u1
   y1   0
 
Continuous-time state-space model.

The design task is to analytically compute the control gain K, or tune it

K = 10/16.6

K = 0.6024

until the desired pole is obtained

eig(A - B*K)                % eigenvalue of compensated system

ans = -10

If you understand the theory behind the design, then this place() function is not needed:

https://www.mathworks.com/help/control/ref/place.html

place(A, B, -10)            % should return the same value as K

ans = 0.6024

sysD  = ss(A-B*K, B, C, D);  % dummy
scale = 1/dcgain(sysD)        % scale for input signal

scale = 0.0013

Td    = 550;                % Desired Temperature (input signal)
input = Td*scale            % scaled input signal

input = 0.6975

Compensated System:

sysC  = ss(A-B*K, B*(input), C, D);
step(sysC, 1)

S = stepinfo(sysC)          

S = struct with fields:
         RiseTime: 0.2197
    TransientTime: 0.3912
     SettlingTime: 0.3912
      SettlingMin: 497.4754
      SettlingMax: 549.9855
        Overshoot: 0
       Undershoot: 0
             Peak: 549.9855
         PeakTime: 1.0546