PLEASE HELP!!! If possible, also supply MATLAB code. Will definitely upvote once completed! Thanks.
Consider the following spring-mass-damper system:
m
k
b
x
F
m = 0.5 kg
b = 5 kg/s
k = 20 N/m
F: input
x: output
The goal of this assignment is to employ the controller to the system above for automatic regulation.
For this assignment, the following unity feedback system is considered and the PID controller is implemented.
controller
plant P(s)
C(s)
de(t)
u(t) = Kp * e(t) + K * ∫e(t)dt + Ka * ∂e(t)
Select the controller gains (Kp, Ki, Ka), such that the following criteria are satisfied for the unit step input:
- Zero steady-state error
- Maximum overshoot of less than 5%
- Rise time of less than 1 s
Make sure that the system is stable and use the concept of dominant pole(s) to design the controller. Once the gains are selected, confirm your design by utilizing the MATLAB simulation. The example code is provided below:
s = tf('s');
sys = (10*s + 50)/(s^3 + 5*s^2 + 10*s + 20); % closed loop transfer function
t = 0:0.01:3;
step(sys, t);
title('Step Response')
xlabel('Time (s)')
ylabel('Amplitude (m)')
Show all your work and present the step response plot of the final closed loop system.
