Section 9.1 The 2DOF Structure for Stable Plants Explanation For RZN PID Figure:RZN PID control structure In section 4.1,the RZN PID controller depicted in Figure ?was introduced.By utilizing two parameters B and u,an improved reference response is obtained 20C Zhang.W.D..CRC Press.2011 Version 1.0 16/95
Section 9.1 The 2DOF Structure for Stable Plants Explanation For RZN PID Figure: RZN PID control structure In section 4.1, the RZN PID controller depicted in Figure ?? was introduced. By utilizing two parameters β and µ, an improved reference response is obtained Zhang, W.D., CRC Press, 2011 Version 1.0 16/95
Section 9.1 The 2DOF Structure for Stable Plants It is easy to verify that G(s)Kc T(s)= 1+G(s)Kc （1+5s+TDs Kc B+ 1 +TDs G(s)Kc ++ Kc ++T1+gk:(++7o Let c的=k+六+） 4口，+@，4定4=定0C Zhang.W.D..CRC Press.2011 Version 1.0 17/95
Section 9.1 The 2DOF Structure for Stable Plants It is easy to verify that T(s) = G(s)KC β + 1 µTIs + TDs 1 + G(s)KC 1 + 1 TIs + TDs = KC β + 1 µTIs + TDs KC 1 + 1 TIs + TDs G(s)KC 1 + 1 TIs + TDs 1 + G(s)KC 1 + 1 TIs + TDs Let C1(s) = KC 1 + 1 TIs + TDs Zhang, W.D., CRC Press, 2011 Version 1.0 17/95
Section 9.1 The 2DOF Structure for Stable Plants C2(s)= k(++o Kc(1+7 +os Evidently,the introduction of B and u is equivalent to providing an additional degree of freedom to the original system The resulting system is in fact a 2DOF system 4口，+@，4定4=定0C Zhang,W.D..CRC Press.2011 Version 1.0 18/95
Section 9.1 The 2DOF Structure for Stable Plants C2(s) = KC β + 1 µTIs + TDs KC 1 + 1 TIs + TDs Evidently, the introduction of β and µ is equivalent to providing an additional degree of freedom to the original system The resulting system is in fact a 2DOF system Zhang, W.D., CRC Press, 2011 Version 1.0 18/95
Section 9.2 2DOF Structure for Unstable Plants 9.2 2DOF Structure for Unstable Plants Problem:The reference response of the 1DOF system with an unstable plant usually exhibits excessive overshoot Solution:The 2DOF system can be used to overcome this problem.This is because the 2DOF system can roll off high frequency signals in the reference independently Design procedure:Similar to that for stable plants.To guarantee the intemal stability,the controller for the disturbance loop can only be implemented in the unity feedback loop The procedure will be illustrated by utilizing the first-order unstable plant.The design procedure for high-order plants is similar 4口+@4定4生定9QC Zhang.W.D..CRC Press.2011 Version 1.0 19/95
Section 9.2 2DOF Structure for Unstable Plants 9.2 2DOF Structure for Unstable Plants Problem: The reference response of the 1DOF system with an unstable plant usually exhibits excessive overshoot Solution: The 2DOF system can be used to overcome this problem. This is because the 2DOF system can roll off high frequency signals in the reference independently Design procedure: Similar to that for stable plants. To guarantee the internal stability, the controller for the disturbance loop can only be implemented in the unity feedback loop The procedure will be illustrated by utilizing the first-order unstable plant. The design procedure for high-order plants is similar Zhang, W.D., CRC Press, 2011 Version 1.0 19/95
Section 9.2 2DOF Structure for Unstable Plants 9.2 2DOF Structure for Unstable Plants Problem:The reference response of the 1DOF system with an unstable plant usually exhibits excessive overshoot Solution:The 2DOF system can be used to overcome this problem.This is because the 2DOF system can roll off high frequency signals in the reference independently Design procedure:Similar to that for stable plants.To guarantee the internal stability,the controller for the disturbance loop can only be implemented in the unity feedback loop The procedure will be illustrated by utilizing the first-order unstable plant.The design procedure for high-order plants is similar 定)AC Zhang.W.D..CRC Press.2011 Version 1.0 19/95
Section 9.2 2DOF Structure for Unstable Plants 9.2 2DOF Structure for Unstable Plants Problem: The reference response of the 1DOF system with an unstable plant usually exhibits excessive overshoot Solution: The 2DOF system can be used to overcome this problem. This is because the 2DOF system can roll off high frequency signals in the reference independently Design procedure: Similar to that for stable plants. To guarantee the internal stability, the controller for the disturbance loop can only be implemented in the unity feedback loop The procedure will be illustrated by utilizing the first-order unstable plant. The design procedure for high-order plants is similar Zhang, W.D., CRC Press, 2011 Version 1.0 19/95