Lecture Fundamentals of control systems: Chapter 3 - TS. Huỳnh Thái Hoàng

Lecture "Fundamentals of control systems - Chapter 3: System dynamics" presentation of content: The concept of system dynamics, dynamics of typical components, dynamics of control systems. Invite you to reference.

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Lecture Fundamentals of control systems: Chapter 3 - TS. Huỳnh Thái Hoàng Lecture Notes Fundamentals of Control Systems Instructor: Assoc. Prof. Dr. Huynh Thai Hoang Department of Automatic Control Faculty of Electrical & Electronics Engineering Ho Chi Minh City University of Technology Email: hthoang@hcmut.edu.vn huynhthaihoang@yahoo.com Homepage: www4.hcmut.edu.vn/~hthoang/6 December 2013 © H. T. Hoang - www4.hcmut.edu.vn/~hthoang/ 1 Chapter 3 SYSTEM DYNAMICS6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 2 Content The concept of ssystem stem ddynamics namics  Time response  Frequency response Dynamics of typical components Dynamics y of control systems y6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 3 The concept of system dynamics6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 4 The concept of system dynamics System dynamics is the study to understanding the behaviour of complex systems over time. Systems described by similar mathematical model will expose similar dynamic responses. To study st d the dynamic d namic responses responses, input inp t signals are usually s all chosen to be basic signals such as Dirac impulse signal, step signal, or sinusoidal signal. Time response  Impulse response  Step response Frequency response 6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 5 Impulse response U (s) Y (s) G(s) Impulse response: behavior of a system to a Dirac impulse Y ( s )  U ( s ).G ( s )  G ( s ) (due to U(s) = 1) y (t )  L 1Y ( s )  L 1G ( s )  g (t ) Impulse response is the inverse Laplace transform of the TF. Impulse response is also referred as weighting function. It is possible to calculate the response of a system to a arbitrarily input by taking convolution of the weighting function & the input. t y (t )  g (t ) * u (t )   g ( )u (t   )d 0 6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 6 Step response U (s) Y (s) G(s) Step response: behavior of a system to a step input G (s) Y ( s )  U ( s ).G ( s )  (because U(s) = 1/s) s   t y (t )  L 1Y ( s )  L 1  G ( s )    g ( )d  s  0 The step response is the integral of the impulse response The step response is also referred as the transient function of the system. 6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 7 Impulse and step response example Calculate the impulse response and step response of the system described by the transfer function: s 1 U (s) Y (s) G(s)  G(s) ( ) s ( s  5) Impulse response: 1  s  1  1  1 4  g (t )  L G ( s )  L  1 L     s ( s  5)   5s 5( s  5)  1 4 5t  g t   e ( ) 5 5 Step response: 1  G ( s )  1  s 1  4 1 4 h(t )  L  L  2   2  s   s ( s  5)  25s 5s 25( s  5) 1 4 5t 4  h(t )  t  e  5 25 25 6 Dece ...