Question

Using MATLAB. We want to control output(y) using PID control in Kds? +Kps+Ki C(s) S Input(r) is a magnitude1 step. Plant is given by 1 (s+1)(3+2)(s+5 ) controller plant + 14 y C(s) P(S) a) Calculate Closed Loop characteristics and steady-state error(unity feedback and Kp=1, Kd=1, Ki=0)) 2.Using automatic PID tuning function, reduce steady-state error=0 and report Kp=?, Kd=? And Ki=?

Answer 1

a)

Simulink model:

х untitled * - Simulink academic use File Edit View Display Diagram Simulation Analysis Code Tools Help 10 Normal untitled untitled G G * 回回 口 1 PID(s) den(s) Transfer Fon Step PID Controller Scope LE >> Ready 248% ode45 Type here to search i E a )) BENG 19:42 31-07-2020

Specifications:

Step input: unit step, step time at 1 second.

PID block: Kp=1 Kd=1 Ki=0

Transfer function block: numerator = [1], denominator = $s^{3}+8s^{2}+17s+10$ [ As, $(s+1)(s+2)(s+5)=s^{3}+8s^{2}+17s+10$ ]

2.

The PID block parameters were opened and autotune function was used. The results are given below:

APID Tuner (untitled/PID Controller) - Step Plot: Reference tracking Х PID TUNER VIEW Plant: Plant Type: PIDF 1.537 Domain: Time << Slower Form: Parallel Response Time (seconds) Faster 0.6 Inspect A Add Plot Options Reset Show Design Parameters Update Block- Aggressive Transient Behavior Robust TUNING TOOLS RESULTS PLANT CONTROLLER DESIGN Step Plot: Reference tracking X Data Browser Step Plot: Reference tracking 1.2 Tuned response --Block response 1 0.8 Amplitude 0.6 0.4 0.2 0 0 2 4 5 6 3 Time (seconds) | Type here to search e Controller Parameters: P = 19.45, I = 15.34, D = 4.928, N = 148.7 18:53 (4) ENG 31-07-2020 E

The tuned values of Kp, Kd and Ki for which steady state error will be zero, was found as:

thank you.