A sliding mode control (SMC) strategy using novel piecewise double power reaching law (PDPRL) for a class of fourth-order nonlinear underactuated systems (USs) is proposed to realize simultaneous control of the unactuated and the actuated part. A novel PDPRL is designed in the form of a piecewise function to reduce the chattering produced by SMC. The fixed-time convergence characteristic and the existence of maximum convergence time independent of the initial value of the sliding mode surface for the PDPRL are analyzed. Considering the uncertainties of model parameters and external disturbance in the USs, a supertwisting disturbance observer (STDO) is provided to accurately estimate the disturbance in real time, and the estimated value is compensated to the controller. The underactuated inverted pendulum system is taken to verify the effectiveness of the devised strategy, and the simulation results show that the proposed strategy can reduce chattering, suppress the disturbance, and enhance the robustness of the system.

It is difficult for a single control method to track the position quickly and accurately at the end of the robot. To solve this problem, a cooperative control strategy of backstepping adaptive neural network (BS-RBFNN) signal control and port controlled Hamiltonian (PCH) energy control is proposed. BS-RBFNN solves the problem of rapidity when the system is in dynamic state, PCH control solves the problem of accuracy when the system is in steady state. The cooperative function based on the error is designed, and the cooperative control of the robot joint system is realized by using this function. The robot joint position servo system can not only realize the rapid adjustment of the dynamic position, but also realize the high precision tracking control in the steady state. Simulation results show that the system achieves fast dynamic response and accurate steady-state position tracking by using cooperative control method.

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