Analysis of robustness to gain variation in a fractional-order PI controller for knee joint motion

Studying knee biomechanics provides insight into injuries and possible treatments. As part of this general research, this papers discusses the design of a Fractional-Order Proportional-Integral (FOPI) controller for the movement of the shank around the knee joint. This system has applications in dynamical knee rigs and active orthoses. The control purpose is to regulate the angle of the shank by manipulating the torque applied to the knee joint. A mathematical model of the system is derived to design the controller using model-based techniques and to perform several simulations in the Simulink® environment. Implementation of the obtained FOPI controller is done by approximating the fractional-order controller by a finite-dimensional integer-order transfer function. A first set of simulations shows the robustness of the control system to large gain variations introduced by differences between several types of knees. Disturbance rejection of the controller is also investigated in a second set of simulation. Results suggest that the designed controller FOPI controller is more robust to gain variations compared to the integer-order PI controller. The second simulations show that the designed controller is able to reject input disturbances.