Tham khảo tài liệu 'adaptive control design and analysis part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 22 Chapter 1 Introduction To generate such a desired parameter estimate ap t we choose a stable filter with df 0 and express the plant as ỹ -a y ap y u which can be further written as y t df ap ị y t M t 8 df 8 df Wi TTT-MW. 1-72 8 df e p df dp ộự 1 y i . s r CL f Letting ớp t be the estimate of the unknown parameter 0 ỡp t df dp . Op 0p t df we introduce the estimation error e t 0p t 0 i - y t u t . s -r CLf It follows from and that e t ớp t t 0p i ớp t - ổ . We then choose the adaptive law for ớp t as w 7 01 - i-76 to ensure dp t and e t small see below where m t ựl m Considering the measure of the parameter error 0P v p 92pr and its time derivative at m2 t we conclude that dp t is bounded and so are and ỡp í and that fOO fOQ . dt oo ớp t dt oo. Jo mz t Jo p From these properties of the parameter estimation algorithm the desired closed-loop system properties that j t and u t are bounded and that limt_ 00 y t - 0 are ensured see Section . Simple Adaptive Control Systems 23 Discrete-Time Designs Adaptive control schemes for discrete-time systems can also be developed based on two approaches direct or indirect adaptation of the controller parameters. Next we give two such discrete-time design examples. Direct Adaptive Control Design Example Example Consider a first-order discrete-time time-invariant plant y t 1 ữpy í u i t e 0 1 2 . where Qp is the unknown plant parameter y t is the plant output and u t is the control input. The control objective is to design a feedback control li t such that all closed-loop system signals are bounded and the plant output y t asymptotically tracks the output ym t of a chosen reference model ym í 1 -amym t r t t 0 1 2 . where am 1 for the reference model system stability and performance and r t is a bounded reference input. For a discrete-time design it is common to choose am 0 so that ym t r t 1 . The control structure and plant-model .
