Lecture Fundamentals of control systems: Chapter 6 - TS. Huỳnh Thái Hoàng

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Lecture Fundamentals of control systems: Chapter 6 - 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 6 DESIGN OF CONTINUOUS CONTROL SYSTEMS6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 2 Content Introduction Effect of controllers on system performance Control systems design using the root locus method Control systems design in the frequency domain Design g of PID controllers Control systems design in state-space Design of state estimators6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 3 Introduction6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 4 Introduction to design process Design is a process of adding/configuring hardware as well as software in a system so that the new system satisfies the d i d specifications. desired ifi ti 6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 5 Series compensator The controller is connected in series with the plant. plant R(s) Y(s) + GC(s) G(s) Controllers: phase lead, phase lag, lead-lag compensator, P, PD PI, PD, PI PID,… PID Design method: root locus, locus frequency response 6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 6 State feedback control All the states of the system are fed back to calculate the control rule. r(t) u(t) x(t) y(t) +  x (t )  Ax (t )  Bu (t ) C K State feedback controller: u (t )  r (t )  Kx (t ) K  k1 k2  kn  Design method: pole placement, placement LQR,… LQR 6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 7 Effects of controller on system performance6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 8 Effects of the addition of poles The addition of a pole (in the left left-half half ss-plane) plane) to the open open- loop transfer function has the effect of pushing the root locus to the right, tending to lower the system’s relative stability and t slow to l d down th settling the ttli off the th response. Im s Im s Im s Re s Re s Re s 6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 9 Effects of the addition of zeros The addition of a zero (in the left left-half half ss-plane) plane) to the open open- loop transfer function has the effect of pulling the root locus to the left, tending to make the system more stable and to speed up the th settling ttli off the th response. Im s Im s Im s Re s Re s Re s 6 December 2013 © H. T. Hoàng - www4.hcmut.edu.vn/~hthoang/ 10 Effects of lead compensators Transfer function: 1  Ts GC ( s )  K C (  1) 1  Ts Frequency response: 1  Tj GC ( j )  K C 1  Tj Characteristics of th ...