PID tuning Gain Scheduling Technique for Temperature Control System

It is my final year project and I can find any tutorial to show do i use and design a Gain Scheduling to tuning a pid controller.

[Sam Chak]

Hi Isyraf

Would you show the mathematical model of the Temperature Control System? With the model, we can probably advise you accordingly.

Please also specify the Temperature Setpoint that you want to regulate at.

[Isyraf Izuddin]

thank you for responding. this is the mathemathical model for an electric furnace that i refer from a research paper. about the temperature im not sure.

this the plant that i tune using cohen coon and zieger nichols and pid auto tuning using matlab.

Answer 1

[Sam Chak]

Hi @Isyraf Izuddin

Thanks for showing the model of the furnace system. First things first, perform a basic analysis to understand the behavior of system. Since a transfer function is given, then the model is obviously a linear system.

num = [-0.1125 0.15];
den = [0.75 1.825 1.25 0.2];
Gp  = tf(num, den)
p = pole(Gp)
step(Gp, 50)

p =

-1.3333

-0.8702

-0.2298

All of its poles have negative real parts and so the furnace is inherently stable to begin with. Since the poles have no imaginary parts, then the response is overdamped. The steady-state value is 0.75.

steadystate = dcgain(Gp)

steadystate =

0.7500

It means if the input is set as 100°C as the desired furnace temperature, then the output converges to 75°C at approximately 20 sec.

Control Design:

To fix this issue, you can connect a proportional gain K before the plant Gp, in series to properly rescale the output. This is an open-loop system.

K = 1/steadystate
Gol = series(K, Gp)
step(Gol, 50)
S = stepinfo(Gol)

K =

1.3333

S =

struct with fields:

RiseTime: 10.2201

SettlingTime: 19.7804

SettlingMin: 0.9012

SettlingMax: 0.9987

Overshoot: 0

Undershoot: 2.0829

Peak: 0.9987

PeakTime: 31.7066

If the settling time (~20 sec) of the furnace temperature control system is acceptable, then Gc = K is the simplest controller (open-loop, non-feedback) and no Gain-scheduling technique is required.

If you want to shorten the settling time, then a feedback PID controller can be implemented.

% to improve the settling time via adjusting the crossover frequency, wc
wc = linspace(0.25, 0.5, 11);
for i = 1:11
    Gc = pidtune(Gp, 'PID', wc(i));
    Gcl = feedback(Gc*Gp, 1);
    step(Gcl, 50)
    hold on
    S = stepinfo(Gcl)
end
hold off

Gain-scheduling technique is unnecessary unless you really want to have multiple PID controllers the heat up the furnace at different settings of settling times.

[Isyraf Izuddin]

Thank you very much for the answer.. Can you show me some example for Gain scheduling to tune the pid controller. if you dont mind

[Sam Chak]

You can find examples here:

https://www.mathworks.com/help/slcontrol/ug/designing-a-family-of-pid-controllers-for-multiple-operating-points.html

https://www.mathworks.com/help/control/gain-scheduled-controller-tuning.html

[Isyraf Izuddin]

Thank Youuuu