Question

...use the Matlab command C pid (Kp, Ki, Kd, Tf) to create your PID controller for Tr 0.5, KI = Kp = 0.5, and 1 < Kp < 10. c. (20 POINTS) REFER TO SLIDE 3: Create your frequency-domain plant as a state-space object, such that Mss1 ss (A,B,C,D) where D = 0.Similarly, Mss2 = ss (GC) d. (20 points) Use the feedback command to connect your system together in the unity-feedback loop shown below, such that unityloop = feedback (Mss1*Ms s2,1). PID Controller Cam System (Plant) F&(s) (s) 1 Σ + Gc ms2+cs+k AERSTIHUIER 1947
Solve C & D please slide 3 is the one with the pendulum

Answer 1

The MATLAB code is given below in bold letters.

clc;
close all;
clear all;

% Question C
% define the parameters
m = 1;
l = 1;
g = 9.81;
T = 10;

% define the matrices
A = [0 1 ;-g/l 0];
B = [1/(m*l^2);0];
C = [1 0];
D = 0;

% define the state space system
Mss1 = ss(A,B,C,D);

% define kp, ki and kd
kp = 10;
ki = 0.5;
kd = 0.5;
Tf = 0.5;

% define the controller C
C = pid(kp,ki,kd,Tf);

% convert from transfer function model to state space model
Mss2 = ss(C);

% Question D
% connecting the systems using the feedback command
unityloop = feedback(Mss1*Mss2,1)

Result:

a =
x1 x2 x3 x4
x1 -11 1 0.5 1
x2 -9.81 0 0 0
x3 -1 0 0 0
x4 2 0 0 -2

b =
u1
x1 11
x2 0
x3 1
x4 -2

c =
x1 x2 x3 x4
y1 1 0 0 0

d =
u1
y1 0

Continuous-time model.