Inverted pendulum on a cart using a PID controller

[saeede-]

hi everyone. in my project , I'm facing with a problem. in PID controller , desire poles are -1+j3 & -1-j3
after design , the overshoot is very high and the settling time more than PD controller
i change the K and zi (pi) several times . but not better.
the pd controller : (s+23)
pid controller : 0.7856*(s+0.3)*(s+23)/s

the code :

M = 1 %%kg
m = 0.5 %%kg
l = 0.4 %%m
g = 9.81 %%m/s^2
s = tf('s')
G1 = 1/((M*l*(s)^2)-((m+M)*g))

c1 = 0.7856*(s+23)*(s+0.3)/(s)
G2 = feedback(c1*G1,1)
figure(1)
rlocus(c1*G1)
figure(2)
impulse(G2)

can you help me to decrease the overshoot ?

 

[NateD]

There are a couple of things you can try to reduce the overshoot in your PID controller design. First, you can try increasing the proportional gain (Kp) or decreasing the integral gain (Ki). Increasing Kp will increase the speed of response, which can reduce the overshoot, while decreasing Ki will reduce the steady-state error associated with the system. You can also try to increase the damping factor (zeta) of the system, which can reduce the overshoot for a given set of gains. This is done by adding additional zeros to the transfer function of the controller. Finally, you can try designing a more sophisticated controller such as a Smith Predictor, which can provide better control performance compared to a basic PID controller.