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Control System I Lab Reports AUST
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Department of EEE
Course No: EEE- 4106
Course Title: Control System-I Laboratory
Experiment No: 06
Experiment Name: Study of PID (Three-Term) Control System on a PC using
‘MATLAB’ Software.
Date of Performance: 15 July, 2018
Date of Submission: 22 July, 2018
Semester: 4.
Section: C- 1
Group: 05
To meet the given specifications of Overshoot and Settling Time without
changing the pole of the system.
To find the effect of Proportional Band, Integral Action and Derivative Action.
To find the range of Kp for the system to be stable.
A proportional–integral–derivative controller (PID controller) is a control loop feedback
mechanism. As the name suggests, PID algorithm consists of three basic coefficients:
proportional, integral and derivative which are varied to get optimal response.
Figure 1 : Block Diagram of a System with Three-Term Control
However in the sophisticated control system to improve the steady state and transient
performance respectively an integral and a derivative of the error (e) are added to the
proportional term to make a composite control or drive signal (u). Mathematically,
𝑐
𝑖
𝑑
Where, 𝑘
𝑐
, 𝑘
𝑖
𝑎𝑛𝑑 𝑘
𝑑
are gain of proportional, integral and derivative blocks respectively.
MATLAB Code
clc;
clear all;
close all;
k=0:0.001:10;
num=[0 1]; %taking kp=
den=conv([1 1],[1 2]);
rlocus(num,den,k);
G=0.707;
W=1.4142;
sgrid(G,W);
[kp,poles]=rlocfind(num,den);
[numc,denc]=cloop((kp)*num,den);
t=0:0.01:20;
step(numc,denc,t);
Note: System doesn’t meet the required specs.
For PI,
2
𝑝
𝑖
𝑝
MATLAB Code
clc;
clear all;
close all;
k=0:0.001:10;
num=[1 1]; %taking ki/kp=
den=conv(conv([1 1],[1 2]),[1 0]);
rlocus(num,den,k);
G=0.707;
W=1.4142;
sgrid(G,W);
[kp,poles]=rlocfind(num,den);
[numc,denc]=cloop((kp)*num,den);
t=0:0.01:20;
step(numc,denc,t);
Note: Tendency towards instability created.
Selected point = - 0.9914 + 1.0029i
Range of 𝒌 𝒑
: 0.0031 to ∞
In this experiment our goal was to fulfill the given specifications for the system without
changing the pole, which was successfully accomplished. We used integrator,
differentiator blocks which added extra pole to the system.
We obtained range of the Kp from the graph which is not exactly equal to the
theoretical value.
This difference between the theoretical and graphical value of Kp is because of our
selection point.
If we can select the point on graph more precisely we can get closer value of Kp to the
theoretical one.
