• To learn the need of controller • Types of Basic Controllers (P, I and D Controllers) and their properties. • Controller combinations (PI, PD and PID Controllers) and their properties. • PID tunning by MATLAB. • Comparative performance analysis of PI, PD and PID Controllers

1. Department of Avionics Engineering
Modern Control Systems
Experiment No.4
Analysis and Design of PID controller with control parameters in
MATLAB and SIMULINK
Prepared for
By:
Name:
ID:
Section:
Semester:
Total Mark:_____________
Obtained Marks:________
Signature:___________
Date:__________________

2. Objectives
• To learn the need of controller
• Types of Basic Controllers (P, I and D Controllers) and their properties.
• Controller combinations (PI, PD and PID Controllers) and their properties.
• PID tunning by MATLAB.
• Comparative performance analysis of PI, PD and PID Controllers.
Theory:
Why we need Controllers?
Performance of a system is usually analyzed on few basic parameters. These parameters are of time
domain as well as of frequency domain. Following are parameters:
Domain Parameters Desired Value Effect of Parameter
Rise Time (𝑇𝑟) Lower is Better
Lower value makes system's
response faster
Maximum Overshoot
(𝑀𝑝)
Lower is Better
Lower value makes system more
stable
Time
Domain
Settling Time (Ts) Lower is Better
Output settles faster to final
values if it has lower value
Steady State Error (𝑒𝑠𝑠)
Lower is Better (Zero
required)
Output reaches to desired value
if steady state error is zero
Phase Margin (PM) Higher is better
System becomes more stable
(More stability margins)
Frequency
Domain
Gain crossover frequency
(𝑤𝑔) & Phase crossover
frequency (𝑤𝑝)
𝑤𝑝>𝑤𝑔 𝑤𝑝 > 𝑤𝑔 makes system stable
• Controllers are actually system response modifiers.
• A controller is introduced with main plant transfer function in feed forward loop as shown below:
Different types of controllers:

3. Basic Modes:
• Proportional (P) Controller
• Integral (I) Controller
• Derivative (D) Controller
Combination Mode
• Proportional + Integral (PI) Controller
• Proportional + Derivative (PD) Controller
• Proportional + Integral + Derivative (PID)
Controller
Proportional (P) Controller
• Proportional Controller is simply an amplifier.
• Its transfer function is 𝐺𝑐(𝑠)=𝐾𝑝 . It does not add any new pole or zero to the system.
Derivative (D) Controller
used alone.
• Its transfer function is 𝐺𝑐(𝑠) = 𝐾𝑑 𝑠 . It adds a
zero to the system.
• D-Controllers give faster action when input
changes rapidly. However, D-Controllers are not
With P-ControIIer, response of closed loop
system becomes faster. But maximum
overshoot also increases. The large value of Kp
can make system unstable.
P-ControIIer cannot handle steady state error.
It provides offset error too.

4. • Because, if error e(t) is constant then its output is zero and hence actuator's output will also be
zero.
• Also, if error e(t) changes suddenly (Step) then output of D-controller will be impulsive.
Integral (I) Controller:
• Its transfer function is 𝐺𝑐(𝑠)= 𝐾 𝑠𝑖 It adds a pole and hence increases the order of the system
by 1.
PID in MATLAB and SIMULINK:
In MATLAB, the best way to stabilize the plant response so to have the desired output response is by
using PID Tuner tool in both Simulink and MATLAB coding.
Syntax:
pidTuner(sys)
//Where “sys” will be your transfer function
Example:
• With I-Controller, offset error of P-
controllers is removed.
• Steady state error in step response is also
eliminated.
• However, system's response becomes
slightly slower.
• Oscillations in system's response
increase. Maximum overshoot increases.
This can make system
• unstable.

5. Lab Task:
Lab Tasks:
Parameters
(kp, kd and ki)
Required response
setting
Type of
Controller
Simulink Model:

6. Use PID tuner for the following transfer functions on MATLAB and change the stability
parameters to achieve a stable response with PI, PD and PID controller
a)
b)
Screenshot the graph and Parameters
Simulink Modeling:
On which P, I and D value the response of the plant will be as per given graph:
Figure 1: Graph without PID controller Figure 2: Graph with PID controller