Engineering Lab - Automatic Control Systems (MATLAB & Simulink)

This report covers the analysis of the lift in s-domain and the frequency domain, obtaining desirable behavior using a PID controller, and control of a landing rocket using Simulink. The report includes stability analysis, controlling acceleration, and designing a closed-loop system. The report also covers the transfer function relating thrust angle to the vehicle angle of landing.

INSTITUTIONAL AFFILIATION
FACULTY OR DEPARTMENT
COURSE ID & NAME
TITLE: ENGINEERING LAB- AUTOMATIC CONTROL SYSTEMS (MATLAB &
SIMULINK)
STUDENT NAME
STUDENT ID NUMBER
PROFESSOR (TUTOR)
DATE OF SUBMISSION
2018

Patient lift Simulink model,
1
Add
60
Kp Add1
20
1/L
1
s
Integrator
0.084
Ke
3
R
Add2
1/93
GearBox
0.05
Pulley
1
s
Integrator1
1
s
Integrator2
9.8
Constant
Add3
100
Weight
Add4
0.05
Pulley1
1/93
Gearbox1
Product
14
WeightDisturbance
Step
1
s
Integrator3
1e-5
Gain10
1.2e4
Gain11
0.084
Gain12
0.5
Gain13
0.5
Gain14
Add5
1
Desired Height
1
Out1
InputOutput
Accelerometer

TASK 1
Analysis of the lift in s-domain and the frequency domain
Step 1: Stability
Creating a subsystem of the model above,
Desired Height Out1
patient_lift
Scopedesired height
PID(s)
Control_point
Linearizing the system, we obtain,
>> mdl='order750864'
>> open_system(mdl)
>> io(1)=linio('order750864/Control_point',1,'input');
>> io(2)=linio('order750864/patient_lift',1,'openoutput');
>> %% To linearise the model
>> linsys1=linearize(mdl,io)
Analyzing the response of the linearized model using the bode response,
2

-200
-150
-100
-50
0
Magnitude (dB)
From: Controlpoint To: patientlift
10-15 10-10 10-5 100
-270
-180
-90
0
Phase (deg)
Bode Diagram
Frequency (rad/s)
Figure 1 For an unstable system, before kp is set
To determine the system stability of the closed loop system,
3

-70 -60 -50 -40 -30 -20 -10 0 10
-50
-40
-30
-20
-10
0
10
20
30
40
50
0.280.42
0.975
0.8
0.140.280.420.560.680.8
0.91
0.975
0.140.560.68
0.91
10203040506070
Root Locus
Real Axis (seconds-1)
Imaginary Axis (seconds-1)
From the output, having set the Kp=50.
4

Setting the Kp=15, a value less than the critical value ,
Setting the Kp=80, a value greater than the settled value,
5

The simulation output is a bit smoother than the set value. There is no discrepancy at the end
point of the rise time.
Step 2: Controlling acceleration
Setting the value of Kp=60, the simulation was run and the acceleration of the load in a scope
plot was evaluated,
Value of acceleration of the load in a scope plot, it demonstrates a deceleration of the speed of
3.7 m/ s2
TASK 2
Obtaining desirable behavior using a PID controller
Weight is set to 100kg with no disturbance weight included,
6

Using the PID controller, tune the system using the response optimization.
Step response before the PID,
7

Step response after PID
Discussion
The proportional constant reduces the oscillations present in the yield, the integral component
reduces the overshoot at the yield, and the derivative component manages the system stability,
8

rise time, and reduces oscillations. The signal input has a value of the desired height. The desired
height is set to 4 and the input is fed into the system as a step input with a magnitude of 4. The
output value ranges between 3.5 and 4. There is a slight error of 0.3 as the value output is 3.7 as
the height of the weight load.
Part 2 (optional): Control of a landing rocket
Transfer function relating thrust angle to the vehicle angle of landing is modelled using the
equation,
G ( s )= ψ ( s )
Θ ( s ) =
T l1
J
s2− ( cn l1
J )
The problem is simplified by setting T l1
J =1.0 and cn l1
J =1.0
The transfer function simplifies further to,
G ( s ) = ψ ( s )
Θ ( s ) = 1
s2−1
Requirements:
 About 3% overshoot.
 Landing time- settling time 3 seconds.
 Closed loop system- Block diagram.
uniy feedback
Transfer Fcn
PID(s)
PID ControllerStep Scope
Using Simulink,
9

%% part 2 - landing system design
clc
clear
close all
format short
% transfer function
s=tf('s')
Gs=1/(s^2 -1)
Gss=ss(Gs)
%% step response
t=0:0.01:50
figure (1)
step(Gs,t)
%% test for stability- prompts a logical response
isstable(Gs)
%% show the poles of the open-loop system
figure(2)
rlocus(Gs)
title('Root Locus - Gs System')
pole(Gs)
grid on
%% designing a closed loop system
Gs_cl=feedback(Gs,1) % unity feedback
10

% step response of the closed loop system
figure(3)
step(Gs_cl,t)
grid on
%adding a controller
kp=10;
ki=5;
kd=15;
PID=[kp,ki,kd]
Gs_ctrl=PID*Gs;
step(t,Gs_ctrl)
11