Composite Nonlinear Feedback Controller For Robot Manipulators With Bounded Torques

Transient performance is an important measurement index for robot manipulators in trajectory tracking task. As is well known, the plant cannot achieve fast response without causing the response to large overshoot. A compromise is usually made between quicker response and smaller overshoot, so it is difficult to make the tracking process as fast and smooth as possible without large overshoot. Actuator saturation is an unavoidably nonlinear factor in robot systems, and every physical actuator has inherent constraints. When the input signals exceed such limits, the actuator saturates, causing the closed-loop performance to deteriorate and in the extreme case, to even lose stability. Another type of nonlinearity that deteriorates robot systems performance is friction, which leads to positions errors and oscillations.Starting from trajectory tracking in joint space, this dissertation studies the motion control for robot manipulators with bounded torques. First, a composite nonlinear feedback controller for high-order multivariable linear systems with actuator saturation is studied to track time-varying reference inputs. Then, the extended results are introduced to motion control for robot manipulators and a computed torque control based composite nonlinear feedback law is put forward. In a unified framework, the actuators with bounded torques and friction effects are solved. At the same time, the fast and smooth tracking performance is achieved. Afterwards, the stable region of robot systems is studied. Via the optimization techniques, a less conservative estimation of domain of attraction is attained. Finally, in order to enhance the ability to track reference inputs of higher amplitudes, a composite nonlinear feedback controller with tuning parameter for robot manipulators is introduced. The main work is summarized as follows:(1) For composite nonlinear feedback theory, the present design techniques are mainly developed for set-point tracking control and the time-varying trajectory tracking is only discussed in SISO linear systems with actuator saturation. However, it has not been deeply studied for high-order multivariable linear systems. So, for this more general task, the composite nonlinear feedback theory is extended to high-order multivariable linear systems subject to actuator saturation with state feedback, full order output feedback and reduced order output feedback. The theoretical basis is constructed for its application to motion control for robot manipulators with bounded torques.(2) Aiming at trajectory tracking for robot manipulators in joint space, in the presence of actuator saturation and friction effects, a computed torque control based composite nonlinear feedback law is put forward by embedding saturation function. The resulting controller consists of two loops. The inner loop is the full compensation for robot manipulators nonlinear dynamics and the outer loop is the composite nonlinear feedback for stabilization and performance enhancement. Stability analysis is carried out with the domain of attraction. In addition to the guaranteed stability properties, the controller takes advantage of a varying damping ratio induced by the composite nonlinear feedback control. The varying damping ratio allows fast transient response without overshoot and compensates the effects of friction.(3) The stable region for robot manipulators is studied. A Lyapunov function is used to construct ellipsoid invariant set to estimate domain of attraction. Two different"largest"ellipsoids are defined, the largest range of variation containing the initial configuration and the largest volume with desired shape. The solutions of"largest"ellipsoids are described as constrained optimization problems, which are solved by LMI after transformation. Via these optimization techniques, a less conservative ellipsoid invariant set is computed as an estimation of domain of attraction.(4) In order to enhance the ability to track reference inputs of higher amplitudes, a tuning parameter is embedded in the low gain term and high gain term of controller and a composite nonlinear feedback controller with tuning parameter for robot manipulators is studied. The theoretical analysis shows that with the tuning parameter, not only the domain of attraction is increased but also the stability and the ability to compensate the friction effects have no been influenced, and the transient response of systems is still smooth.