k = 1 >> x1=1; x2=2; x3=1; x4=0; >> alpha1=(x1/x2); y1=(x3alpha1*x4); alpha2=(x2/y1); >> if alpha1>0 else if alpha2>0 disp('the system is stable') else disp('the system is not stable') alpha1, alpha2 end 1
ASIAN INSTITUTE OF TECHNOLOGY
CONTROL THEORY
end the system is not stable alpha1 = 0.5000
alpha2 = 2
(b) Assume that PID controller, K (s) K P K I / s K D s , is selected to compensate the requirement of system stability and zero steady state error to unit step input, use the RouthHurwitz test to show that a cascade of PID controller with the original plant and unity negative feedback configuration can meet the requirements. Remember that the system must be stabilized first before the consideration of steady state error.
...5951 – Mechatronics II
Lab #4 – Velocity and Position
Control of a Servomotor
Submitted By: ____________________________________________________________
Introduction:
This report covers the methods, procedures and results of lab #4. During this lab, an understanding of the velocity and position control of a servomotor was developed. MatlabSimulink was used to represent the transfer functions used during thislab.
Results:
This section of the report goes over the results of the lab questions, including the procedure and how the results were obtained.
We were presented with a linear and nonliner motor model for this lab. The nonlinear model accounted for the friction and is more realistic when compared to the linear model. Both MatlabSimulink Models (block diagrams) can be seen in Figures 1 and 2. For the purpose of this lab, the various motor parameters were taking from the Pittman S232S003 DC data sheet.
The system parameters are expressed below in Table 1.
Table 1: System Parameters for Servomotor (with friction, nonlinear)
Velocity Control:
1A. In Figure 3, we implemented a proportional controller (Kp) and used the model to determine the motor velocity, wm, as a function of time for a Vd = 2V u(t). Table 12 below summarizes the systems parameters used for this analysis, and the results for this...
...CONTROL DESIGN OF A SINGLE DEGREE OF FREEDOM MAGNETIC LEVITATION SYSTEM USING FEEDBACK THEORY
Vishnu Dev
Department of electrical engineering
National Institute Of Technology , Rourkela
Email: vishnudev29@gmail.com
ABSTRACT
Because of the nature of magnetic force, maglev is inherently nonlinear and open loop unstable hence we need to design the linearized model in which most of the controllers are based on. The main parameters need to be satisfied by these controllers are the gain margin and phase margin of the system which are sensitive to changes in system and surrounding. In this paper we will use robust control design of a single degree of freedom maglev system using quantitative feedback theory.
I. INTRODUCTION
Magnetic levitation (or maglev) systems are electromechanical devices that suspend ferromagnetic materials using electromagnetism which are unstable in open loop and has nonlinear dynamics and thus needs the stabilizing controllers. Conventionally we first linearize system nonlinearity and then design a controller for linearized model. Maglev systems are able to achieve levitation with controllers designed using these approaches, but they require the levitated objects to stay in the region of the linearized point. It deviates from its linearized point whenever there is a parameter change in the system which makes it unstable
A disturbance observer was introduced to subdue the...
...INTRODUCTION
Control engineering is the discipline that applies controltheory to design systems with predictable behaviors. The practice uses sensors to measure the output performance of the device being controlled and those measurements can be used to give feedback to the input actuators that can make corrections toward desired performance. There are two major divisions in controltheory, namely, classical and modern, which have direct implications over the control engineering applications.
Classical ControlTheory
The scope of classical controltheory is limited to singleinput and singleoutput (SISO) system design. The system analysis is carried out in time domain using differential equations, in complexs domain with Laplace transform or in frequency domain by transforming from the complexs domain. All systems are assumed to be second order and single variable, and higherorder system responses and multivariable effects are ignored. A controller designed using classical theory usually requires onsite tuning due to design approximations.
Modern ControlTheory
Modern controltheory is carried out strictly in the complexs or the frequency domain, and can deal with multiinput and multioutput (MIMO) systems. This overcomes the limitations of classical...
...ME2142/ME2142E
NATIONAL UNIVERSITY OF SINGAPORE
ME2142/ME2142E – FEEDBACK CONTROL SYSTEMS
(Semester II : AY2009/2010)
Time Allowed : 2 Hours
INSTRUCTIONS TO CANDIDATES:
1.
This examination paper contains FOUR (4) questions and comprises FOUR (4)
printed pages.
2.
Answer ALL FOUR (4) questions.
3.
All questions carry equal marks.
4.
This is a CLOSEDBOOK EXAMINATION with authorized materials: each
student is allowed to bring in ONE (1) A4sheet of personal notes for his/her own
use. No stickons are allowed on this one sheet of personal notes.
PAGE 2
ME2142/ME2142E
QUESTION 1 (25 MARKS)
(a)
Ω( s )
2
,
=
V ( s ) (0.01s + 1)(0.1s + 1)
where Ω(s ) and V (s ) are the Laplace transforms of the motor speed, ω (t ) , and the
applied voltage, v(t ) , respectively. Determine the time response the motor speed,
ω (t ) , when the applied input voltage, v(t ) , is a unit step. Sketch the response for
ω (t ) .
(10 marks)
The transfer function of a motor is determined to be
Motor
(b)
R +
E
+
K
2
( s + 1)
5


Ω
1
s
θ
Figure P1.1
The position feedback control system shown in Figure P1.1 has a proportional
controller with gain, K, and an inner speed feedback loop.
(i)
Determine the value of the proportional gain, K, for the system to have a
damping ratio of 0.5. Determine the corresponding damped natural frequency.
(7 marks)
(ii)
For the...
...ASIAN INSTITUTE OF TECHNOLOGY
CONTROLTHEORY
Name: Dilesha Herath
ID.No: st20000297
Date 13/03/2013
Exercise
Solve the following problem with the help of Matlab as much as possible. All the Matlab command inputs used in this problem should be listed in the report in accordance with the command results. Only the commands studied in the class are allowed to use. Problem Assume that the relation between input, u, and output, y, of a system shown below is represented by the transfer function, s3 . G( s) 4 3 s 12s 49s 2 78s 40
U(s)
G(s)
Y(s)
(a) By RouthHurwitz stability criteria, determine that the system under consideration is stable or not. >> alpha3=b1/c1; >> d1=b2; >> alpha4=c1/d1; >> alpha5=d1; >> alpha1, alpha2, alpha3, alpha4, alpha5 alpha1 = 0.0833 alpha2 = 0.2824 alpha4 = 1.6676 alpha5 = 40
1
ASIAN INSTITUTE OF TECHNOLOGY
CONTROLTHEORY
Since alpha1, alpha2, alpha3, alpha4, alpha5 are positive the system is stable. (b) Dominant time constant is a number determined when the system is stable. This number informs about speed of system response. It is defined as absolute inverse of real part of the root locating the nearest with the imaginary axis. Find the system’s dominant time constant. >> [x y z] = residue([1 3], [1 12 49 78 40]); >> r = max(y); >> time_constant = 1/(r) time_constant = 1.0000 (c) For this problem, a choice to improve the system’s dominant time...
...KULLIYYAH OF ENGINEERING
DEPARTMENT OF MECHATRONICS ENGINEERING
Laboratory Manual
MECHATRONICS ENGINEERING LAB V (MCT 4239)
INDUSTRIAL AUTOMATION
EXPERIMENT 4
Control Loop
*
* 4 : CONTROL LOOP EXPERIMENTS
The following list of experiments are closed loop experiments that are specified for tuning and P,I, D studies.
* Experiment 4.1: EFFECT OF P, I and D on process Plant
Objectives:
 To familiarize with the Tuning Panel of the DCS
 To capture Trending on the DCS
 To understand the effect of Proportional (P), Integral (I) and Derivative (D) to
the setpoint change or load disturbance
*
* Procedures:
*
1) Set the Setpoint on the DCS to 50%. Record the PV value it should be near the 50% mark. Now set the DCS Controller faceplate to ‘Auto’ and let it stabilize.Make sure the discharge valve on plant is fully opened.
2) Set P = 30 , I = 3, D = 3 as initial values of PID.
3) When stabilize Change the P Value , while maintaining the I and D Values. Note the responses by disturbing the setpoint up or down about 5%.
4) Save the trend values at the DCS. Comment on the effect of P to a disturbance.
5) Stabilize the Process at the 50 % mark and leave it at ‘Automatic’ control. Now change the I values , while maintaining the P and D Values. Note the responses by disturbing the...
...
3304ENG/7517ENG – Control Systems
Semester 1, 2012
System Response in Time Domain
Name
Student No
Time Slot
Signature
1
Monday
Tuesday
Wednesday
Thursday
Friday
2
We, by signing this page, declare that the work presented in this report is all work done by us, unless appropriate reference has been made to the work of others. We acknowledge that should this not be the case the report will receive zero marks and due action may be taken.
Lab Number:
Demonstrator
Submitted on
Mark Received
REQUIREMENT OF EXPERIMENT 1
Before the laboratory session begins, laboratory demonstrator gave a brief summary about safety and health issue to all students. He also took attendees of students present in the laboratory session. A computer (PC) is provided for each group consist of two students per group and PC are installed Matlab R2011b software, and Electromechanical Servomechanism Virtual Laboratory (ESVL) virtual software for the purpose of conducting the experiment. A scientific calculator is also needed for calculation. The experiment requires student to obtain result from Matlab calculation of transfer function in time domain and compare the result with data obtain from ESVL software.
INTRODUCTION
The system’s response to input consists of the forced response and the natural response, where a pole of the input function generates the form of the forced...
...Robust control systems may successfully be designed by ~'=optimization,
in particular, by reformulating the design problem as a mixed sensitivity
problem.
Key Words~=optimal control; robust control.
AbstractThe paper presents a tutorial exposition of
~=optimal regulation theory, emphasizing the relevance of
the mixed sensitivity problem for robust control system
design.
1. INTRODUCTION
THE INVESTIGATION OF ~®optimization of control
systems began in 1979 with a conference paper by
Zames (1979), who considered the minimization of
the oonorm of the sensitivity function of a
singleinputsingleoutput linear feedback system.
The work dealt with some of the basic questions of
"classical" controltheory, and immediately caught a
great deal of attention. It was soon extended to more
general problems, in particular when it was recognized
that the approach allows dealing with robustness far
more directly than other optimization methods.
The name "~K~optimization" is somewhat unfortunate.
~® is one member of the family of spaces
introduced by the mathematician Hardy. It is the
space of functions on the complex plane that are
analytic and bounded in the righthalf plane. The
space plays an important role in the deeper
mathematics needed to solve Koptimal control
problems.
This paper presents a tutorial exposition of the...