Lecture Fundamentals of control systems: Chapter 2 - TS. Huỳnh Thái Hoàng

Lecture "Fundamentals of control systems - Chapter 2: Mathematical models of continuous control systems" presentation of content: Presentation of content, transfer function, block diagram algebra, signal flow diagram, state space equation, linearized models of nonlinear systems.

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Lecture Fundamentals of control systems: Chapter 2 - 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 2 Mathematical Models of Continuous Control Systems6 December 2013 © H. T. Hoang - www4.hcmut.edu.vn/~hthoang/ 2 Content The concept of mathematical model Transfer function Block diagram algebra Signal flow diagram State space equation Linearized models of nonlinear systems  Nonlinear state equation  Linearized equation of state6 December 2013 © H. T. Hoang - www4.hcmut.edu.vn/~hthoang/ 3 The concept of mathematical models6 December 2013 © H. T. Hoang - www4.hcmut.edu.vn/~hthoang/ 4 Question If you design a control system system, what do you need to know about the plant or the process to be controlled? What are the advantages of mathematical models? 6 December 2013 © H. T. Hoang - www4.hcmut.edu.vn/~hthoang/ 5 Why mathematical model? Practical control systems are diverse and different in nature nature. It is necessary to have a common method for analysis and design of different type of control systems  Mathematics The relationship between input and output of a LTI system of can be described by linear constant coefficient equations: u(t) Linear Time- y(t) Invariant System d n y (t ) d n 1 y (t ) dy (t )a0 n  a1 n 1    an 1  an y (t )  dt dt dt d mu (t ) d m 1u (t ) du (t ) b0 m  b1 m 1    bm 1  bmu (t ) dt dt dtn: system order,order for proper systems: nm. mai, bi: parameter of the system 6 December 2013 © H. T. Hoang - www4.hcmut.edu.vn/~hthoang/ 6 Example: Car dynamics dv (t ) M  Bv (t )  f (t ) dt M: mass of the car, car B friction coefficient: system parameters f(t): engine driving force: input v(t): car speed: output6 December 2013 © H. T. Hoang - www4.hcmut.edu.vn/~hthoang/ 7 Example: Car suspension d 2 y (t ) dy (t ) M 2 B  Ky (t )  f (t ) dt dt M: equivalent mass B friction constant, K spring stiffness f(t): external force: input (t) travel y(t): t l off the th car body: b d output t t6 December 2013 © H. T. Hoang - www4.hcmut.edu.vn/~hthoang/ 8 Example: Elevator ML: mass of cabin and load, MB: counterbalance t b l B friction constant, MB Kg gear box constant Counter- (t): driving moment of the motor ML balance y(t): position of the cabin Cabin & load d 2 y (t ) dy (t ) ML 2 B  M T g  K (t )  M B g dt dt6 December 2013 © H. T. Hoang - www4.hcmut.edu.vn/~hthoang/ 9 Disadvantages of differential equation model Difficult to solve differential equation order n (n ...