Control and instrumentation PDF

CONTROL AND
INSTRUMENTATIONREPORT

Table of Contents
1. INTRODUCTION...............................................................................................................................1
2. ROTARY INVERTED PENDULUM SIMULINK MODEL..............................................................4
2.1. SYSTEM DESIGN..........................................................................................................................4
2.2. SYSTEM METHODOLOGY..........................................................................................................6
2.2.1. System Simulink..........................................................................................................................8
3. DISCUSSION......................................................................................................................................9
3.1. OPEN-LOOP SYSTEM SIMULATION RESULTS.......................................................................9
3.2. LINEARIZATION PROCESS AROUND THE PENDULUM ANGLE.......................................11
3.3. DESIGN OF FULL FEEDBACK CONTROLLER: LINEARIZED MODEL...............................11
3.4. CLOSED LOOP SYSTEM SIMULATION RESULTS................................................................11
4. EXPERIMENT: BEHAVIOUR OF THE MODEL AND REAL PENDULUM................................12
5. DISCUSSION....................................................................................................................................18
6. CONCLUSION & FUTURE WORK................................................................................................21
LIST OF FIGURES
Figure 1 Block diagram for the comprehensive control based system.........................................................3
Figure 2 The free body diagram for the Pendulum......................................................................................3
Figure 3ROTPENT inverted pendulum MATLAB simulink.......................................................................8
Figure 4 The Internal connection of the ROTPENT Matlab Simulink.........................................................9
Figure 5 Open loop system MATLAB simulink........................................................................................10
Figure 6 Block diagram of the open loop System design...........................................................................10
Figure 7 MATLAB simulink of the open loop system design...................................................................11
Figure 8 Open loop system response compared to the signal input............................................................11
Figure 9 Block diagram of the State Feedback control with the inverted plant..........................................12
Figure 10 MATLAB simulink for the closed loop system Simulation.......................................................12
Figure 11 System Response of the MATLAB simulation for closed loop system.....................................13
Figure 12 Step response with LQR control................................................................................................14
Figure 13 Varied Step response with LQR control....................................................................................16
Figure 14 Implementation of a Pre-compensator for transient control.......................................................16
Figure 15 step response with pre-compensation and LQR control.............................................................17
Figure 16 Implementation of an observer for the closed loop system........................................................18
Figure 17 Step Response with Observer-Based State-Feedback control....................................................19
Figure 18 LABVIEW closed loop implementation of the Pendulum Control Mode..................................20
Figure 19 LABVIEW Inverted pendulum Control Response....................................................................21
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1. INTRODUCTION
The rotary inverted pendulum has a cart and a pendulum and the motion is controlled by an
attached motor which provides the external force. The QNET rotary inverted pendulum kit which
is made of DC motor, L-shaped arm, pendulum, two optical encoder, an Elvis II board, and the
LABVIEW software [1]-[3]. The two encoders are used to measure the movement of the
pendulum and the arm angle. The input voltage to the pulse-width modulated amplifier that
drives the motor as the control variable. The illustration below demonstrates the kit as well as the
ROTPENT components,
Some of the common applications of the inverted pendulum are in the processing industries
and in the construction industry. There are several controller used in the systems. The PID
controllers are implemented in many systems as they provide a comprehensive control based on
the feedback obtained from the output [4].
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Figure 1 Block diagram for the comprehensive control based system
The free body diagram of the inverted pendulum section is given as,
Figure 2 The free body diagram for the Pendulum
The control theory is applied to the system to develop different types of controllers which
are tuned to specific components. There are different types of controller that can be implemented
as actuators such as the proportional controller, proportional integral controller, and PID
controllers, the phase lead, phase lag, and phase lead-lag controller. The axis of rotation of the
pendulum link is considered to be horizontal and it is perpendicular to the cart’s direction of
motion [5]. The input of the system is the force that is applied to the cart through the motor. The
pendulum is suspended on a horizontal axis at the end of the arm. The pendulum and arm angle
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are measured by two separate encoders. The kinetic and potential energy within the free body
diagram and the equation of motion is described using the Laplace transform as,
AIMS OF THE EXPERIMENT
a) To determine the MATLAB Simulink design for open loop and closed loop design of the
ROTPENT rotary inverted pendulum.
b) To determine the suitable controller to monitor the system response as well as to control
the transient response of the MATLAB closed loop ROTPENT system.
c) To determine the LABVIEW experiment on the ROTPENT LABVIEW design and
compare it with the simulation output.
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2. ROTARY INVERTED PENDULUM SIMULINK MODEL
2.1.SYSTEM DESIGN
Using the free body diagram of the rotary inverted pendulum, the equation of motion can
be determined. The ROTPEN system design is obtained considering the x-direction motion
as a result of the motor moving the cart forward and backward [6]. Assuming the external
force from the motor to be F,
M ̈x+b ̇x+N=F
The sum of forces in the vertical direction of the cart is not considered as the motion is
horizontal. Assuming reactive forces acting on the system,
N=m ̈x+ml ̈θcosθ−ml ̈θ2 sin θ
(M+m) ̈x+b ̇x+ml ̈θcosθ−ml ̈θ2sin θ=F
The forces are perpendicular to the cart such that,
Psin θ+Ncosθ−mgsin θ=ml ̈θ+m ̈xcosθ
−Plsin θ−Nlcosθ=I ̈θ
(I+ml2) ̈θ+mglsin θ=−ml ̈xcosθ
Assumptions are made to control the pendulum to ensure that the pendulum’s position
does not exceed 20 degrees from its perpendicular state. It is given as shown based on the
small deviation of the pendulum,
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