Study On Control Design For Uncertain Flexible Joint Manipulator

Flexible joint manipulator is an under-actuated, highly nonlinear, mismatched system and is always subject to unknown model uncertainty and external disturbance. In this dissertation, we consider the control problems of uncertain flexible joint manipulator system (unconstrained and constrained)via Lyapunov stability theory.We first propose a robust control for uncertain flexible joint manipulator whose uncertainty bound is known a priori. In order to broaden the existing control schemes to more applications,a generic upper bound condition of inertia matrix is investigated so that the presented control can be used in prismatic joint manipulator. By using backstepping-like technique, a virtual control is implanted and the real control can then be formulated via state equivalent transformation. The control, which is only based on the possible upper bound of uncertainty, renders the system uniform boundedness and uniform ultimate boundedness.Since the information of uncertainty is usually poorly known or totally unknown, we then propose an adaptive robust control for flexible joint manipulator whose uncertainty bound is un-known. This unknown bound is assumed to be in a known manner on an unknown parameter. That is, the bound may be governed by a function with known structure, but some arguments of the function are unknown. An adaptive law is then proposed to obtain the estimation of these unknown arguments such that the actual value of uncertainty bound is obtained accordingly. No knowledge of uncertainty bound is required other than its existence. The adaptive law here is of leakage type which means the adaptive parameter does not always grow with time, since once the system per-formance is satisfactory or the gradients of the boundary function are small. Furthermore, not only the stability of transformed system, containing adaptive laws, is proved, but also the stability of original system is proved theoretically. This part of work is neglected in many other studies.Then, a novel fuzzy dynamical system approach to the control design of flexible joint ma-nipulator with fuzzy uncertainty bound is proposed. Fuzzy set theory is employed to describe the information of uncertainty and system state rather than probability theory. The performance of system is assured by the proposed control which is deterministic and is not Takagi-Sugeno nor Mamdani type nor other IF-THEN heuristic fuzzy control. The optimal control problem is equiv-alent to a performance index minimization problem in the consideration of the average control cost. The performance index is a combination of initial condition, deterministic performance and average fuzzy control effort. It is proved that the extreme solution to this minimization problem,which is obtained by the first-order necessary condition, is indeed the minimum solution,which is verified by the second-order sufficient condition,to the optimal problem.For the constraint force servo control of uncertain flexible joint manipulator system, we firstly introduce a new modeling approach based on Udwadia-Kalaba theory. The fundamental equation of motion can be established via Newtonian or Lagrangian mechanics. The Moore-Penrose gen-eralized inverse is employed to reveal the relation between impressed force and constraint force.Then the constraint force,by using Udwadia-Kalaba equation,is obtained in the closed-form so that it can be applied in the servo control. This method is feasible of dealing with both holonomic and nonholonomic constraints since they are utilized in second-order form (we also show that sta-bilization problem, trajectory following problem, optimization problem, etc., can be cast into this form). Under these, an adaptive robust control is proposed to generate appropriate constraint force such that the controlled system (maybe only a part of the system) approximately follows the given constraints. The uncertainty is regarded as fuzzy and there is no restriction on the initial condition.Meanwhile, the tracking error (and maybe also the rest of system) is guaranteed to be uniformly bounded and uniformly ultimately bounded.Experimental results of a two-link flexible joint manipulator, in Chapter 2 and Chapter 3,are used to verify the theoretical contributions of this work. In Chapter 4 and Chapter 6, the contributions are verified by numerical simulations.