Tham khảo tài liệu 'adaptive control design and analysis part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 182 Chapter 4 Adaptive State Feedback Control which satisfy Assumptions - in Section . The control objective is to design an adaptive state feedback model reference control law for u i to ensure closed-loop signal boundedness and asymptotic tracking of a chosen reference signal ymit by the plant output t i despite the uncertainties in A B Bd C and du t dy t . We consider the reference model and use the controller structure u t f i z i fc2 i r t k3 t where ks t R is an adaptive compensation term for cancelling the effect of the actuation disturbance Bddu and output disturbance dy on the tracking error e i y t ym t and the gains ki t and fc2 t are adaptive gains whose ideal values kỵ and fcj are defined in Section . Similar to that in Section for the continuous-time case next we will first develop ideal parametrizations and the associated error equations for the compensation term ks i for three types of disturbances constant sinusoidal and nonsinusoidal and then develop the adaptive scheme for updating fc3 t . Rejection of Constant Disturbances For d t dUữ and dy t dyũ being some unknown constants fc3 t is the estimate of a constant parameter k . To derive this ideal value fc3 of fc3 t we apply the ideal form of for this case u t k Tx i k 2r t kị to the plant to get the closed-loop system in the frequency z-domain y z ym z A z where ym z c zl A Bk2r z and A z C zl - A - Bkf B - z J. C zl -A- Bkfr Bd - z 1 z 1 From Assumption all zeros and poles of c zl A BẢ T -1B are inside the unit circle of the complex plane so that lim z 1 A z Ci e3 c2 dyo for some constants Cl 0 and c2 which depends on BdduữP We then set k 3 _ l ảọ. Discrete-Time Adaptive Control 183 With this fcg from - in the time domain we have lim y i - ymịtỴ lim ố í 0 t 00 t 00 exponentially fast where J t Z_1 A z . To develop adaptive laws to update the controller parameters fcj t k2 t and 3 t in
