Robust control of compliant actuators using positive real ℋ2-controller synthesis

Series elastic actuation in rehabilitation robotics was introduced to elastically decouple the actuator from the joint in order to improve safety and guarantee a compliant actuator behaviour. Classical control approaches of series elastic actuation usually consist of a number of cascaded control structures, where the force or torque control problem is rearranged to a translational or rotational displacement control problem. Considering the parameter tuning of PID-type cascaded control-loops, passivity of the patient-actuator interaction dynamics should be of concern and imposes parameter bounds for the controller. In order to overcome these limitations, guarantee robust stability, minimise load impedance and reduce the complexity of the classical cascaded control structure, a new control strategy is presented in this paper. The controlled plant is down-squared to yield a positive real system and augmented with frequency dependent weightings to shape the sensitivity functions. Consequently, a new ℋ₂-optimal controller is designed using an additional constraint to guarantee the strict positive realness of the controller. The resulting controller is obtained by solving a LMI-system, which is of a new form for the proposed loop-shaping procedure. Additionally, orthogonality constraints of the ℋ₂-problem are relaxed in the new procedure by a loop-shifting approach. The resulting controller inherently guarantees the patient-actuator interaction transfer function to be positive real, minimises the load impedance and robustly stabilises the actuator due to the dissipative controller properties.