frequency domain modelling

frequency domain modelling - Course Outline Week Date...

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1 Mech Mech 3800 : System Control 3800 : System Control Frequency Domain Modelling Frequency Domain Modelling Dr. Stefan B. Williams Dr. Stefan B. Williams Mech 3800 : Introduction 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 : Introduction Slide 3 A Familiar Mechanical Example A Familiar Mechanical Example • In the last lecture, we considered this mechanical system • We derived a differential equation defining this system • How do we solve for y(t)? M f(t) y(t) () y d d FM y t f tK y y tM y t My y y t f t = −− = ++ = ±± ± ± Dr. Stefan B. Williams Mech 3800 : Introduction Slide 4 How do we find y(t y(t )? • As we saw, the input-output relationship is usually expressed in terms of a differential equation h(t) u(t) y(t) • If we can describe the characteristics of the plant using a general function, h(t), we can compute the output y(t) given some arbitrary input u(t) 1 10 0 1 nn m nm m dyt d yt dut aa y t b b u t dt dt dt + = + + ""
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2 Dr. Stefan B. Williams Mech 3800 : Introduction Slide 5 LTI Systems LTI Systems • In this course, we will consider Linear Time Invariant Systems Linear : the output of the system is equal to the sum of the input responses Time Invariant : the system’s dynamic characteristics are time independent 1 1 () n i i n i i yy f u = = = = y u 1 u 2 u 3 Plant Dr. Stefan B. Williams Mech 3800 : Introduction Slide 6 The Unit Impulse The Unit Impulse • Recall the impulse function, δ (t) • In the limit, we can represent an arbitrary function as a sum of impulses • By the principal of superposition, if we can find the response of the system to an impulse, we will be able to find the response to an arbitrary input ()( ) f tdf t τδ τ τ −∞ −= f(t) t Dr. Stefan B. Williams Mech 3800 : Introduction Slide 7 Impulse Response Impulse Response • The impulse response represents the system response to an impulse input • We will examine techniques for calculating the impulse response shortly • We usually denote the impulse response of a system as h(t) 1 10 1 nn n dyt d yt aa y t t dt dt δ ++ + = " Dr. Stefan B. Williams Mech 3800 : Introduction Slide 8 Convolution Integral Convolution Integral • If we consider the input to a system as a sum of impulses, we can solve for the system output by integrating the signal with its impulse response over time • This yields the system response to the an arbitrary input signal ( ) ( ) ()* () yt ut h d or ut ht τ ττ −∞ =− =
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3 Dr. Stefan B. Williams Mech 3800 : Introduction Slide 9 Example : Solving in time Example : Solving in time
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frequency domain modelling - Course Outline Week Date...

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