Chapter 8( Control of Unstable Plants 4口，+@，4定4=定0C Zhang.W.D..CRC Press.2011 Version 1.0 1/89
Chapter 8 Control of Unstable Plants Zhang, W.D., CRC Press, 2011 Version 1.0 1/89
Control of Unstable Plants 18.1 Controller Parameterization for General Plants 28.2 Ho PID Controllers for Unstable Plants 3 8.3 H2 PID Controllers for Unstable Plants 4 8.4 Performance Limitation and Robustness 58.5 Maclaurin PID Controllers for Unstable Plants 68.6 PID Design for the Best Achievable Performance 78.6 All Stabilizing PID Controllers for Unstable Plants 4口，44定4生，分QC Zhang.W.D..CRC Press.2011 Version 1.0 2/89
Control of Unstable Plants 1 8.1 Controller Parameterization for General Plants 2 8.2 H∞ PID Controllers for Unstable Plants 3 8.3 H2 PID Controllers for Unstable Plants 4 8.4 Performance Limitation and Robustness 5 8.5 Maclaurin PID Controllers for Unstable Plants 6 8.6 PID Design for the Best Achievable Performance 7 8.6 All Stabilizing PID Controllers for Unstable Plants Zhang, W.D., CRC Press, 2011 Version 1.0 2/89
Section 8.1 Controller Parameterization for General Plants 8.1 Controller Parameterization for General Plants Three types of plants:Stable,integrating,and unstable Why categorizing:Controllers can be designed aiming at the reduced scope of plants,so that the design is more effective and simple controllers are easier to obtain Plants considered in this section:Unstable plants with time delay Difficulties in the design: The existence of RHP poles makes the stabilization of the closed-loop system difficult to achieve 2The combined effect of the RHP poles and the time delay greatly limits the achievable performance 4口，+@4定4生 定9AC Zhang.W.D..CRC Press.2011 Version 1.0 3/89
Section 8.1 Controller Parameterization for General Plants 8.1 Controller Parameterization for General Plants Three types of plants: Stable, integrating, and unstable Why categorizing: Controllers can be designed aiming at the reduced scope of plants, so that the design is more effective and simple controllers are easier to obtain Plants considered in this section: Unstable plants with time delay Difficulties in the design: 1 The existence of RHP poles makes the stabilization of the closed-loop system difficult to achieve 2 The combined effect of the RHP poles and the time delay greatly limits the achievable performance Zhang, W.D., CRC Press, 2011 Version 1.0 3/89
Section 8.1 Controller Parameterization for General Plants 8.1 Controller Parameterization for General Plants Three types of plants:Stable,integrating,and unstable Why categorizing:Controllers can be designed aiming at the reduced scope of plants,so that the design is more effective and simple controllers are easier to obtain Plants considered in this section:Unstable plants with time delay Difficulties in the design: The existence of RHP poles makes the stabilization of the closed-loop system difficult to achieve 2 The combined effect of the RHP poles and the time delay greatly limits the achievable performance 定9QC Zhang.W.D..CRC Press.2011 Version 1.0 3/89
Section 8.1 Controller Parameterization for General Plants 8.1 Controller Parameterization for General Plants Three types of plants: Stable, integrating, and unstable Why categorizing: Controllers can be designed aiming at the reduced scope of plants, so that the design is more effective and simple controllers are easier to obtain Plants considered in this section: Unstable plants with time delay Difficulties in the design: 1 The existence of RHP poles makes the stabilization of the closed-loop system difficult to achieve 2 The combined effect of the RHP poles and the time delay greatly limits the achievable performance Zhang, W.D., CRC Press, 2011 Version 1.0 3/89
Section 8.1 Controller Parameterization for General Plants Assumption For the control system with an unstable plant,there exists a limit on the ratio of the time constant to the time delay.If no further explanation is given,it is assumed that the condition is satisfied The design method in this chapter is based on a new parameterization.As a matter of fact,special cases of the new parameterization were already used in the foregoing chapters Why not the Youla parameterization? It cannot be directly used for a plant with time delay 2 To obtain it,one has to compute the coprime factorization of the plant.No analytical methods are available 3 The Q(s)in the general parameterization no longer corresponds to the IMC controller 定9QC Zhang.W.D..CRC Press.2011 Version 1.0 4/89
Section 8.1 Controller Parameterization for General Plants Assumption For the control system with an unstable plant, there exists a limit on the ratio of the time constant to the time delay. If no further explanation is given, it is assumed that the condition is satisfied The design method in this chapter is based on a new parameterization. As a matter of fact, special cases of the new parameterization were already used in the foregoing chapters Why not the Youla parameterization? 1 It cannot be directly used for a plant with time delay 2 To obtain it, one has to compute the coprime factorization of the plant. No analytical methods are available 3 The Q(s) in the general parameterization no longer corresponds to the IMC controller Zhang, W.D., CRC Press, 2011 Version 1.0 4/89