Robust Multi-Performances Control for Four-Link Manipulator Arm

The globally robust control of a four-link manipulator arm (FLMA) is an important subject for a wide range of industrial applications such as COVID-19 prevention robotics, lower limb rehabilitation robotics and underwater robotics. This article uses the feedback linearized approach to stabilize the complex nonlinear FLMA without applying a nonlinear approximator that includes the fuzzy approach and neural network optimal approach. This article proposes a new approach based on the “first” derived nonlinear convergence rate formula of the FLMA to control highly nonlinear dynamics. The linear quadratic regulator (LQR) method is often applied in the balance controlling space of the underactuated manipulator. This proposed approach takes the place of the LQR approach without the necessary trial and error operations. The implications of the proposed approach are “globally” effective, whereas the Jacobian linearized approach is “locally” valid. In addition, the main innovation of the proposed approach is to perform “simultaneously” additional performances including almost disturbance decoupling performance, which takes the place of the traditional posture–energy approach and avoids some torque chattering behaviour in the swing-up space, and globally exponential stable performance, without the need to solve the Hamilton–Jacobin equation. Simulations of comparative examples show that the proposed controller is superior to the singular perturbation and fuzzy approaches.