Lecture 22- Feedback Control Systems

Lecture 22- Feedback Control Systems - Lecture 22 ECSE304...

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1 Lecture 22 ECSE304 Signals and Systems II ECSE 304 Signals and Systems II Lecture 22: Feedback Control Systems Reading: O and W - Sections 11.1 – 11.3 Boulet - Chapter 11 Richard Rose McGill University Dept. of Electrical and Computer Engineering 2 Lecture 22 ECSE304 Signals and Systems II Course Outline Discrete-Time Fourier Series and DT Fourier Transform • The Z – Transform • Time and Frequency Analysis of DT Signals and Systems • Sampling Systems • Application to Communications Systems • State Models of Continuous Time LTI Systems – Lecture 18: State Space Analysis – Lecture 19: Solution of State Equations – Lecture 20: Observability and Controllability • Linear Feedback Systems – Lecture 22: Feedback Control Systems – Root Locus Stability – Lecture 23: Stability Analysis – Nyquist Criterion – Lecture 24: Stability Analysis – Gain and Phase Margins
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3 Lecture 22 ECSE304 Signals and Systems II • Introduction to closed loop systems • Example of controller design • Proportional, Integral, Derivative (PID) Control • Root locus stability analysis Outline 4 Lecture 22 ECSE304 Signals and Systems II • Closed-loop (feedback) control systems are distinguished by the existence of one or more feedback paths where the controlled signal is fed back and compared with the reference input: Introduction to Feedback Control Systems • The controlled process or “Plant” is an LTI system that will be represented by its transfer function H(s) • The controller filters the error between the output and the input reference signal and produces the actuating signal for the plant Controller Controlled Process (Plant) Feedback Elements Input Error Output Actuating Signal () ut y t et rt
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5 Lecture 22 ECSE304 Signals and Systems II • Motivation for feedback systems – Improve system performance: • Faster response time, reduced over-shoot, and lower steady state error in control systems • Improved bandwidth and frequency response in amplifiers – Improve stability: Can stabilize an unstable system – Reduce the effect of external disturbances or noise • Applications of Feedback Systems – Control of motors and tracking systems – Modeling of populations – Amplifier design – Oscillator Design Introduction to Feedback Control Systems 6 Lecture 22 ECSE304 Signals and Systems II Tracking System : Control the plant H(s) so it tracks a reference signal r(t): Introduction to Feedback Control Systems • Closed loop transfer function, T(s) : • The desired behavior is for which implies a near unity transfer function: Controller K(s) Plant H(s) Reference (desired Output) Error Output () ut y t et rt () () () 1 Ys KsHs Ts R sK s H s == + yt “Unity” Feedback
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7 Lecture 22 ECSE304 Signals and Systems II Regulator: Control the plant H(s)
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This note was uploaded on 02/08/2012 for the course ECSE 304 taught by Professor Chenandbacsy during the Spring '11 term at McGill.

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Lecture 22- Feedback Control Systems - Lecture 22 ECSE304...

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