How can I minimise or eliminate overshoot from PI controller?

I am trying to control a motor's speed based on torque demand. I have set up a reference torque and reference speed profile, but while the motor is able to track the speed demand relatively well, the torque demand seems to have massive overshoots at the transition points.

The output torque from the motor is as shown:

The input is as shown:

My PI controller parameters are as shown, the gains were achieved via the tuning function:

[Sam Chak]

@Zachary, To get to the bottom of what went wrong with the overshoot, you need to examine the closed-loop model of the entire motor control system. Could you provide the full mathematical model so that others can look into the dynamics?

[Zachary]

Hi Sam, thanks for the reply,

The motor's parameters are as shown:

The motor is connected to a DC-DC converter with an output voltage of 400V, and a rated output power of 200kW.

Here's the rest of the model (forgive the use of many scopes, I'm just trying to look at the different outputs at each point in the simulation),

[Sam Chak]

Hi @Zachary

Thank you for your update. However, without the knowledge of the mathematical model, I can only speculate that the overshoot issues were caused by the "zeros" of the closed-loop dynamics, resulting from the step changes in the input signal.

[Zachary]

@Sam Chak Since the motor is able to track the changes in RPM well, can I assume that the issues stem from the step changes in the torque demand signal? Would a more gradual change in torque demand result in less overshoots?

Answer 1

[Sam Chak]

Hi @Zachary

In theory, a smooth transient change in the torque demand should be able to reduce the overshoot.

Case 1: Step torque demand

% System
w   = 7.108;
sys = tf([5, 2*w, w^2], [1, 2*w, w^2])

sys =
 
  5 s^2 + 14.22 s + 50.52
  -----------------------
   s^2 + 14.22 s + 50.52
 
Continuous-time transfer function.

% Step torque demand input signal
U   = tf(1);
opt = RespConfig;
opt.Delay = 2; 
t   = 0:0.01:8; 
[u1, tout] = step(U, t, opt);

% System's response to step torque demand
figure
lsim(sys, u1, t), grid on
title('System''s response to step torque demand')
ylim([-0.5, 5.5])

●

Case 2: Smooth torque demand

% Smooth torque demand input signal
u2  = (1 - exp(-2*(t - 2))).*heaviside(t - 2);

% System's response to smooth torque demand
figure
lsim(sys, u2, t), grid on
title('System''s response to smooth torque demand')
ylim([-0.5, 1.5])

[Zachary]

@Sam Chak I see, thank you so much for your insight!