x points: -7, -4+3i HW- 05 Problem:05-01

Slides:

Advertisements

Similar presentations

Pole Placement.

Advertisements

Root Locus Diagrams Professor Walter W. Olson

Feedback Control Systems Dr. Basil Hamed Electrical & Computer Engineering Islamic University of Gaza.

Feedback Control Systems

CHE 185 – PROCESS CONTROL AND DYNAMICS

Feedback Control Systems

Lecture 9: Compensator Design in Frequency Domain.

Examples of Control Systems Application. Modeling the Ball and Beam Experiment.

PID Control and Root Locus Method

Combined State Feedback Controller and Observer

ECE 4115 Control Systems Lab 1 Spring 2005

Ch. 6 Single Variable Control

2-1 (a),(b) (pp.50) Problem: Prove that the systems shown in Fig. (a) and Fig. (b) are similar.(that is, the format of differential equation is similar).

HOMEWORK 08D Block diagrams Problem 1: Problem 2:

Observer-Based Robot Arm Control System Nick Vogel, Ron Gayles, Alex Certa Advised by: Dr. Gary Dempsey.

o Problem Reconsider Problem

DC Motor Speed Modeling in Simulink

Modern Control System EKT 308 Steady-State and Stability.

Problem:05-01 x points: -7, -4+3i HW- 05 In the control system as shown in the figure, a) Write the MATLAB program to plot root-locus diagram for the closed.

System Time Response Characteristics

Automated Control Systems, 8/E by Benjamin C. Kuo and Farid Golnaraghi Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 7-1 (p. 235)

1 Time Response. CHAPTER Poles and Zeros and System Response. Figure 3.1: (a) System showing input and output; (b) Pole-zero plot of the system;

2.1 Step Input Response: Eigenvalues: p 1 =-4.526, p 2,3 = ±2.7883i, p 4 = Final value theorem: Stability: If the step response reaches to.

Find f(kT) if Exercise 1. Solution 1 1 Begin by dividing F(z) by z and performing a partial-fraction expansion. For z = 0.5 For z = 0.7 For z = 0.9.

Intelligent Robot Lab Pusan National University Intelligent Robot Lab Chapter 7. Forced Response Errors Pusan National University Intelligent Robot Laboratory.

Control Systems Lect.3 Steady State Error Basil Hamed.

Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved. Figure 9.1 (p. 664) Two different.

3.0 Time Response OBJECTIVE

O o Problem Reconsider Problem a) Find the closed loop transfer function H(s) of the system. (Use K p as symbol) Answer: Duyarlılık= % 0.1.

Exercise 1 Suppose we have a simple mass, spring, and damper problem. Find The modeling equation of this system (F input, x output). The transfer function.

Lesson 20: Process Characteristics- 2nd Order Lag Process

Control Systems EE 4314 Lecture 12 March 17, 2015

Modern Control Systems EKT 308

Time Response Analysis

Introduction to PID control

6. Nyquist Diagram, Bode Diagram, Gain Margin, Phase Margin,

Lecture 20: Root Locus for Design

x points: -7, -4+3i HW 5 Problem:05-01

PID Controller.

Problem Homework-04 In the control system shown in the figure Gp and Gc are given as Gp(s)=(2s+3)/(s3+6s2-28s) and Gc=K. a)

Chapter 9 Design via Root Locus <<<4.1>>>

Chapter 9 Design via Root Locus <<<4.1>>>

Control System Toolbox

What damping ratio range do we typically want?___0.4~1____

Eigenvalues: p1=-4.526, p2,3= ±2.7883i, p4=

Eigenvalues: p1=-4.526, p2,3= ±2.7883i, p4=

HOMEWORK-04 Problem In a closed loop control system shown in the figure, the process transfer function is Gp(s)=(2s+3)/(s3+6s2-28s) and Gc=K. a)

UNIT-II TIME RESPONSE ANALYSIS

HW-03 Problem Kuo-95 (p. 377) Find the steady-state errors for step, ramp and parabolic inputs. Determine the type of the system. ) s ( R Problem.

Frequency Response Techniques

UNIVERSITI MALAYSIA PERLIS SCHOOL OF ELECTRICAL SYSTEM ENGINEERING

Stability of Closed-Loop Control Systems

E(s): Laplace transform of the error e(t)

Root Locus Techniques CH 8: Islamic University of Gaza

7-5 Relative Stability.

Design via Root Locus Techniques

Root Locus Techniques CH 8: Islamic University of Gaza

o Problem Reconsider Problem

CH. 6 Root Locus Chapter6. Root Locus.

Eigenvalues: p1=-4.526, p2,3= ±2.7883i, p4=

2a. Transfer function of closed loop system

UNIVERSITI MALAYSIA PERLIS SCHOOL OF ELECTRICAL SYSTEM ENGINEERING

o HOMEWORK-02 Problem Reconsider Problem

HOMEWORK-03 Problem Kuo-95 (p. 377)

Frequency Response Techniques

Problem Homework-04 In the control system shown in the figure Gp and Gc are given as Gp(s)=(2s+3)/(s3+6s2-28s) and Gc=K. a)

The Design of Feedback Control Systems

Time Response, Stability, and

Exercise 1 For the unit step response shown in the following figure, find the transfer function of the system. Also find rise time and settling time. Solution.

Presentation transcript:

x points: -7, -4+3i HW- 05 Problem:05-01 In the control system as shown in the figure, a) Write the MATLAB program to plot root-locus diagram for the closed loop system. b) Add the commands the program to plot the line when the damping ratio is 0.707. c) Root-locus diagram resulting in a and b is shown. Find the eigenvalues of the open loop system from the diagram. d) Add the commands that give the value of the gain at the point when any point is clicked on the root-locus diagram. e) The gain is K=250 for the point A. Is the closed loop system stable for K=300? f) It can be found as K=40 at the point B. Find the steady-state error of the closed loop system for the step input. g) If the disturbance exists, find the sensitivity for the gain of K=40. h) Find the eigenvalues of the closed loop system for the gain of K=40.

Answer 05-01: (c) -4±3i, -7,0 ( e) Unstable (f) 0 (g) % 2.5 (h) 2.7 s (a) ng=[1,6];dg=[1,15,81,175,0];rlocus(ng,dg) (b) hold on;plot([0,-8],[0,8]);hold off (d) rlocfind(ng,dg) (h) kp=40;dh=polyadd(dg,kp*ng);p=roots(dh) (i) sys=tf(kp*ng,dh);[c,t]=step(sys);plot(t,c);overs=max(c)-c(length(c)) (overs=3e-4 )

Problem 05-02 Thompson (p. 157) a) Write the MATLAB program to plot root-locus diagram for the closed loop system. b) Add the command to find the critical gain. c) Find the critical gain by Routh criteria. Is the system stable for the gain of K=1. d) Add the commands the program to plot the line when the damping ratio is 0.65. e) Write the MATLAB program to find the values of the eigenvalues, the settling time, the overshoot and to plot the step response of the closed loop system. g) Find the steady-state error of the closed loop system for the step input (K=9). h) If the disturbance exists, find the sensitivity. i) What type of control is added to the system to eliminate the steady-state errors. j) What type of control is added to the system to decrease the level of the overshoot.

Problem 05-03 The block diagram of a DC-motor control system is shown below. Numerical values: J=0.01; b=0.1;K=0.01;R=1;L=0.5; Design criteria: ts<2, Max. overshoot< %5, ess< %1 Solve the problem by using root-locus diagram.