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Advances in PID Control Part 2

Tham khảo tài liệu 'advances in pid control part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 10 Advances in PID Control The relationship between the control variable and the system output is 1 U s 27 and since G s G s Eq. 26 becomes Yf s G s G s e_TsY s eTsY s . 28 This shows that the internal loop containing the plant model feeds back a signal that is a prediction of the output since eTs represents a prediction y t T in the time domain. The closed loop transfer function of the system can be determined by using Y s G s e-TsU s U s Gc s R s - Yf s and Eq. 26 to obtain Y s _ G s e-TsGc s R s 1 G s Gc s . According to Dorf Bishop 2011 the sensitivity expression in this case can be defined as 1 S s 1 G s Gc s . 32 29 30 31 As can be seen the controller can now be designed without considering the effect of the time delay. Hagglund 1992 1996 combined the properties of the Smith predictor with a PI controller to control a first order plant with a time delay. The transfer function of the plant is given by Ke-Ts Gp s K Ĩ 33 where K 0 is the plant gain T the time constant and T the time-delay of the plant. The PI controller is given by Gc s Kp 1 -V 34 X Lis where the Kp is the proportional gain and Ti is the integral time constant. The control structure is given in Fig. 5 The time delay can be approximated by a first order Padé approximation with the time delay T 0. This control structure results in five parameters that need tuning Kp Ti K T T . Example Consider the following first order plant with a time-delay of two seconds 2 Gp s G s Gd s 2 1 e-2s 35 Predictive PID Control of Non-Minimum Phase Systems 11 Fig. 5. PI with Smith predictor control structure where Gd s represents the time-delay dynamics. Let the model of the plant be given by Gm s G s Gd s 2 -2s 2 2s 1 2s 2 36 where Gd s represents the Padé approximation of the time-delay. The PI control constants are set to Kp 1 and Ti 1.67 resulting in the following PI controller Gc s 1 . 37 A predictive PID controller C s as shown in Fig. 6 needs to be derived based on the predictive properties of the Smith .