Tham khảo tài liệu 'adaptive control 2011 part 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 268 Adaptive Control 0 if ụ 1 and n- pr - ipd h v 0 y if Ir I ụ 1 4 amax -V-Tpr -ofipd h vs or ụ 1 and n- r - ipd h vs 0 or ụ4 and n pr -Upd hv 0 4 amax y 0 if ụ I and n- pr- ipd h vfl 0 4 amax 32 The adaptive NN-based pre-inversion compensator v is developed to drive the adaptive control signal Tpd to approach the output of hysteresis model Tpr so that the hysteretic effect is counteracted. Controller Design Using Estimated Hysteresis Output It is noticed that the output of hysteresis is not normally measurable for the plant subject to unknown hysteresis. However considering the whole system as a dynamic model preceded by Duhem model we could design an observer to estimate the output of hysteresis based on the input and output of the plant. The velocity of the actuator y t is assumed measurable. Define the error between the outputs of actuator and observer as e y - y 33 The observed output of hysteresis is denoted as ĩpr and the error between the output of hysteresis Tpr and the observed Ỉpr is defined as e2 Tpr Ỉpr . Then the observer is designed as y y Le 34 Tp Kav F L2ei Kpr ipr 35 The error dynamics of the observer is obtained based on the actuator model and hysteresis model. ẻi Le Le e2 Kav F2 L2ei Kpr t pr 36 where the parameter error is defined as Ka Ka Ka . Adaptive Control of Piezoelectric Actuators with Unknown Hysteresis 269 By using the observed hysteresis output Tpr we may define the signal error between the adaptive control signal Tpd and the estimated hysteresis output as T pe T pd T pr 37 The derivative of the signal error is Tpe ipd -Kav F - L-e- KpTpr. 38 A hysteresis pre-inversion compensator is designed V d kb -ĩpe T pd F2 rp . 39 By substituting the neural network output F2 Wỵ h vs and pre-inversion compensator output into the derivative of the signal error one obtains T . X-Í rr X Tr 1 rr TTrl x-xxí X Tr T rr Í A rw pe 1-Kaĩi Ìpd KaFiWpe 1-KaFW @ h VsyKa d-rp Í1- Kpripr 40 The weight matrix update rule is chosen as W1 r h vs ĩpe kp .
