To simply and effectively realize the trajectory tracking control of a bionic joint actuated by a single pneumatic artificial muscle (PAM), a cascaded control strategy is proposed based on the robust modeling method. Firstly, the relationship between the input voltage of the proportional directional control valve and the inner driving pressure of PAM is expressed as a nonlinear model analytically. Secondly, the nonlinear relationship between the driving pressure input of PAM and the angular position output of the bionic joint is described as a second order linear time-invariant model (LTI) accompanied with parametric perturbations, equivalently, and then the parameters of the model are identified by the robust modeling method. Then, a hybrid model is established based on the two models (the nonlinear model and the LTI model), and corresponding to it, a cascaded controller is developed, the outer loop of which is an H∞ controller for the angular position tracking designed by loop-shaping design procedure (LSDP) and the inner loop is a nonlinear controller based on the feedback linearization theory for the PAM driving pressure control. Finally, the experiment is accomplished within the joint rotation range of 90° and with the work frequency upper bound of 1.25 rad/s. And the joint with the developed cascaded controller tracks given reference trajectories with steady-state errors smaller than 2%. Results show that the trajectory tracking control of a highly nonlinear system is highly efficient using the proposed strategy in the case of relatively low work frequency.
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