root locus notes internet

# root locus notes internet - Course Outline Week Content 1...

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1 Mech Mech 3800 : System Control 3800 : System Control Root Locus Root Locus Dr. Stefan B. Williams Dr. Stefan B. Williams Mech 3800 : Root Locus Slide 2 Course Outline Course Outline BREAK 14 Assignment 4 Due Advanced Control Systems Topics 27 Oct. 13 Case Study 20 Oct. 12 Design Techniques for Feedback 2 13 Oct. 11 Design Techniques for Feedback 06 Oct. 10 Assignment 3 Due Bode Plots 2 22 Sept. 9 Bode Plots 15 Sept. 8 Root Locus 2 08 Sept. 7 Assignment 2 Due Root Locus 01 Sept. 6 Feedback System Characteristics 25 Aug. 5 Assignment 1 Due System Response 18 Aug. 4 Block Diagrams 11 Aug. 3 Frequency Domain Modelling 04 Aug. 2 Introduction 28 July 1 Assignment notes Content Date Week Dr. Stefan B. Williams Mech 3800 : Root Locus Slide 3 Designing Control Systems Designing Control Systems • We have had a quick look at a number of methods for specifying system performance • We have examined some methods for designing systems to meet these specifications for first and second order systems • We will now look at a graphical approach, known as the root locus method, for designing control systems • As we have seen, the root locations are important in determining the nature of the system response Dr. Stefan B. Williams Mech 3800 : Root Locus Slide 4 Proportional Controller Proportional Controller • When the feedback control signal is made to be linearly proportional to the system error, we call this proportional feedback • We have seen how this form of feedback is able to minimize the effect of disturbances K - + R(s) E(s) C(s) G(s)

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2 Dr. Stefan B. Williams Mech 3800 : Root Locus Slide 5 Proportional Controller Proportional Controller • The closed look transfer function is given by • Assuming we have two poles, G(s)=1/(s+a)(s+b) () 1( ) KG s Ts KG s = + 2 K s ab sa bK = + ++ + Dr. Stefan B. Williams Mech 3800 : Root Locus Slide 6 Proportional Controller Proportional Controller • We can also look at the system parameters as a function of the gain, K • Given fixed values for the roots of the plant, we can find K to meet performance specifications 2 K s = + + 2 2 n ss ab K ab K ab e ab K ω ζ σ =+ + = + + = = + Dr. Stefan B. Williams Mech 3800 : Root Locus Slide 7 Root Location • The location of the roots, and hence the nature of the system performance, are a function of the system gain K • In order to solve for this system performance, we must factor the denominator for specific values of K • We define the root locus as the path of the closed-loop poles as the system parameter varies from 0 to Dr. Stefan B. Williams Mech 3800 : Root Locus Slide 8 Example: Second order system Example: Second order system • A system to automatically track a subject in a visual image can be modelled as follows • We can solve for the closed loop transfer function as a function of the system parameter, K
3 Dr. Stefan B. Williams Mech 3800 : Root Locus Slide 9 Example: Second order system Example: Second order system • We can also determine the closed loop poles as a function of the gain for the system Dr. Stefan B. Williams Mech 3800 : Root Locus Slide 10 Example: Second order system

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## This note was uploaded on 01/23/2012 for the course EE 4580 taught by Professor Gu during the Fall '10 term at LSU.

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root locus notes internet - Course Outline Week Content 1...

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