Section 4.1 Traditional Design Methods Tuning Rules Assume that the step response model is K G(s)= e-0s Ts+ and the ultimate cycle model is Ku and Tu Table:Frequently used tuning methods. uning methods R-C method C-C method Z-N method KKe 1.2(0/r-1 1.35(0/r)-1+0.27 0.6KK T 2(0/r) 2.5(0/r)[1+(8/r)/5] 1+0.6(0/r) 0.5Tu/T To/T 0.5(0/r) 0.37(0/r) 1+0.2(0/r) 0.125Tu/r 240 Zhang.W.D..CRC Press.2011 Version 1.0 5/71
Section 4.1 Traditional Design Methods Tuning Rules Assume that the step response model is G(s) = K τ s + 1 e −θs and the ultimate cycle model is Ku and Tu Table: Frequently used tuning methods. Tuning methods R-C method C-C method Z-N method KKc 1.2(θ/τ ) −1 1.35(θ/τ ) −1 + 0.27 0.6KKu TI /τ 2(θ/τ ) 2.5(θ/τ )[1 + (θ/τ )/5] 1 + 0.6(θ/τ ) 0.5Tu/τ TD/τ 0.5(θ/τ ) 0.37(θ/τ ) 1 + 0.2(θ/τ ) 0.125Tu/τ Zhang, W.D., CRC Press, 2011 Version 1.0 5/71
Section 4.1 Traditional Design Methods RZN Tuning Z-N method:The most widely used method Disadvantage:The resulting PID controller usually gives excessive overshoot A solution:Refined Z-N (RZN)method.Perhaps the most famous improved method The modified PID controller is ()=()(()dt+T de(t) Band u are determined by extensive simulation studies.Define Normalized gain:K=KK,Normalized time delay:0=0/T 4口，404注4生定分QC Zhang.W.D..CRC Press.2011 Version 1.0 6/71
Section 4.1 Traditional Design Methods RZN Tuning Z-N method: The most widely used method Disadvantage: The resulting PID controller usually gives excessive overshoot A solution: Refined Z-N (RZN) method. Perhaps the most famous improved method The modified PID controller is u(t) = Kc [βr(t) − y(t)] + 1 µTI Z e(t)dt + TD de(t) dt β and µ are determined by extensive simulation studies. Define Normalized gain:Kn = KKu, Normalized time delay:θn = θ/τ Zhang, W.D., CRC Press, 2011 Version 1.0 6/71
Section 4.1 Traditional Design Methods RZN Tuning Z-N method:The most widely used method Disadvantage:The resulting PID controller usually gives excessive overshoot A solution:Refined Z-N(RZN)method.Perhaps the most famous improved method The modified PID controller is k.((t 3 and u are determined by extensive simulation studies.Define Normalized gain:Kn=KKu;Normalized time delay:0n=0/T 定0QC Zhang.W.D..CRC Press.2011 Version 1.0 6/71
Section 4.1 Traditional Design Methods RZN Tuning Z-N method: The most widely used method Disadvantage: The resulting PID controller usually gives excessive overshoot A solution: Refined Z-N (RZN) method. Perhaps the most famous improved method The modified PID controller is u(t) = Kc [βr(t) − y(t)] + 1 µTI Z e(t)dt + TD de(t) dt β and µ are determined by extensive simulation studies. Define Normalized gain:Kn = KKu, Normalized time delay:θn = θ/τ Zhang, W.D., CRC Press, 2011 Version 1.0 6/71
Section 4.1 Traditional Design Methods When 2.25 Kn<15 and 0.16<0n<0.57,for a 10%overshoot: B= 15-K 15+K ,4=1 and for a 20%overshoot: 36 B= 27+5K:“=1 If1.5<Kn<2.25and0.57<0n<0.96, =（信，+u=音k Z-N/RZN usually gives very bad response for the plant with large time delay.Hence.some designers believe that PID cannot be used for the plant with large time delay.Actually.with proper design methods PID can be applied to such systems 4口，48,4注4生，定0C Zhang.W.D..CRC Press.2011 Version 1.0 7/71
Section 4.1 Traditional Design Methods When 2.25 < Kn < 15 and 0.16 < θn < 0.57, for a 10% overshoot: β = 15 − Kn 15 + Kn , µ = 1 and for a 20% overshoot: β = 36 27 + 5Kn , µ = 1 If 1.5 < Kn < 2.25 and 0.57 < θn < 0.96, β = 8 17 4 9 Kn + 1 , µ = 4 9 Kn Z-N/RZN usually gives very bad response for the plant with large time delay. Hence, some designers believe that PID cannot be used for the plant with large time delay. Actually, with proper design methods PID can be applied to such systems Zhang, W.D., CRC Press, 2011 Version 1.0 7/71
Section 4.1 Traditional Design Methods When 2.25 Kn<15 and 0.16<0n<0.57,for a 10%overshoot: B= 15-K 15+K ,4=1 and for a 20%overshoot: 36 B= 27+5K,:4=1 If1.5<Kn<2.25and0.57<0n<0.96, B=吕（信+）u=音k Z-N/RZN usually gives very bad response for the plant with large time delay.Hence,some designers believe that PID cannot be used for the plant with large time delay.Actually,with proper design methods PID can be applied to such systems Zhang.W.D..CRC Press.2011 Version 1.0 7/71
Section 4.1 Traditional Design Methods When 2.25 < Kn < 15 and 0.16 < θn < 0.57, for a 10% overshoot: β = 15 − Kn 15 + Kn , µ = 1 and for a 20% overshoot: β = 36 27 + 5Kn , µ = 1 If 1.5 < Kn < 2.25 and 0.57 < θn < 0.96, β = 8 17 4 9 Kn + 1 , µ = 4 9 Kn Z-N/RZN usually gives very bad response for the plant with large time delay. Hence, some designers believe that PID cannot be used for the plant with large time delay. Actually, with proper design methods PID can be applied to such systems Zhang, W.D., CRC Press, 2011 Version 1.0 7/71