TAILIEUCHUNG - Adaptive Control System Part 11

Tham khảo tài liệu 'adaptive control system part 11', 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 231 for measurement p 6ị E R and fl E Rz are unknown parameters. ội R Rm and p R - Rz are known and bounded functions of the state variable. Ap is nonlinear in p and fi is nonlinear in both and Oi. Our goal is to find an input u such that the closed loop system has globally bounded solutions and so that Xp tracks as closely as possible the state xm of a reference model specified in equation where r is a bounded scalar input. We make the following assumptions regarding the plant and the model Al Xp t is accessible for measurement. A2 Oị G Oj where Oj ớminjí ớmax i and ớminjí and ớmaXjí are known p is unknown and lies in a known interval V Pmin -Pmax c R. A3 and p t are known bounded functions of the state variable Xp. A4 f is a known bounded function of its arguments. A5 All elements of J p are known continuous functions of the parameter p. A6 bm bpa where a is an unknown scalar with a known sign and upper bound on its modulus o max. A7 p bp is controllable for all values of p E with Ả p bmgT p Am where g is a known function of p. A8 Am is an asymptotically stable matrix in R with det iZ Am Rm 5 5 k R s k 0 Except for assumption Al the others are satisfied in most dynamic systems and are made for the sake of analytical tractability. Assumption A2 is needed due to the nonlinearity in the parametrization. Assumptions A3 - A5 are needed for analytical tractability. Assumptions A6 and A7 are matching conditions that need to be satisfied in LP-adaptive control as well. A8 can be satisfied without loss of generality in the choice of the reference model and is needed to obtain a scalar error model. Assumption Al is perhaps the most restrictive of all assumptions and is made here to accomplish the first step in the design of stable adaptive NLP-systems. Our objective is to construct the control input u so that the error E Xp xm converges to zero asymptotically with the signals in the closed loop system remaining bounded. The structure of the .

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