Tham khảo tài liệu 'adaptive control system part 13', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Adaptive Control Systems 281 Designs for nonlinear dynamics The adaptive inverse approach developed in Sections can also be applied to systems with nonsmooth nonlinearities at the inputs of smooth nonlinear dynamics 16 17 . State feedback and output feedback adaptive inverse control schemes may be designed for some special cases of a nonlinear plant Xw f W N rW yự hịxự where f v G Rn g x G Rn and h x G R are smooth functions of X G Rn N represents an unknown nonsmooth actuator uncertainty as a dead-zone backlash hysteresis or piecewise-linear characteristic and r t G R is the control input while u t is not accessible for either control or measurement. The main idea for the control of such plants is to use an adaptive inverse v t NI ud to cancel the effect of the unknown nonlinearity N so that feedback control schemes designed for without N with the help of NI can be applied to with N to achieve desired system performance. To illustrate this idea we present an adaptive inverse design 16 for a third-order parametric-strict-feedback nonlinear plant 6 with an actuator nonlinearity N X 1 .V e i vi 2 x3 3 t 2 1 2 G iúj I 6 t 3 v u N r where X vi 2 xĩf xi i 1 2 3 are the state variables available for measurement 6 G Rn is a vector of unknown constant parameters with a known upper bound Ms 0 2 Ms for the Euclidean vector norm II 2 Pn c R fill G R and Pi G Rp Ỉ 1 2 3 are known smooth nonlinear functions and bl o Ỗ2 for some positive constants bl Ỗ2 and Vv G R3. To develop an adaptive inverse controller for we assume that the nonlinearity N is parametrized by ỡ G Rn as in and its inverse NI is parametrized by 0 G Rne an estimate of Ớ as in with the stated properties. Then the adaptive backstepping method 6 can be combined with an adaptive inverse NI to control the plant in a three-step design Step 1 Let the desired output be r t to be tracked by the plant output y t with bounded derivatives r k t k 1
