A comprehensive performance comparison of linear quadratic regulator (LQR) controller, model predictive controller (MPC), $$H_{\infty }$$ H ∞ loop shaping and $$\mu $$ μ -synthesis on spatial compliant link-manipulators

Position control and mechanical vibration suppression are still open problems in compliant link mechanisms. Operation and accuracy improvements of manipulators can be made by finding solutions for these problems. This paper presents a comprehensive performance comparison between controllers (two of them robust controllers) to control position and reduce mechanical vibration over a compliant link-manipulator in a three-dimensional environment: (i) linear quadratic regulator, (ii) model predictive controller, (iii) $$H_{\infty }$$ loop shaping, and (iv) $$\mu $$-synthesis. The comparisons of controllers are made based on position tracking, vibration damping and control effort in the simulation environment by taking the gravity effect into account. Finally, the paper makes a conclusion by providing some information about main purpose, advantages and disadvantages of each controller in compliant link-manipulator applications.