Euler implicit time-discretization of multivariable sliding-mode controllers.

This paper aims to develop the Euler implicit time-discretization of multivariable sliding-mode controllers to solve the numerical chattering problem without modifying the continuous-time control law. To this end, a continuous-time multi-input plant under a multivariable sliding-mode control is studied, and it is shown that the implicit discretization of the continuous-time sliding-mode controller leads to a multivariable generalized equation with several set-valued terms which is not possible to be solved using the graphical interpretations. Subsequently, an algorithm is proposed to solve such a multivariable generalized equation required to synthesize the implicit sliding-mode control signal at each time step. The proposed algorithm is explained through a simple example accompanied by numerical simulations. The properties of the implicit multivariable sliding-mode controller, e.g., finite-time convergence, gain insensitivity, and chattering suppression, are studied analytically. Afterwards, a multivariable sliding-mode controller is implemented on a digital processor based on the developed algorithm to control a six-input six-output system, i.e., six-component thrust generator, and the results are compared with the case where the continuous-time sliding-mode controller is implemented using the conventional Euler explicit discretization. In the end, the related issues and drawbacks are addressed to be considered in future works.

Distribution of forces between synergistics and antagonistics muscles using an optimization criterion depending on muscle contraction behavior.

In this paper, a new neuromusculoskeletal simulation strategy is proposed. It is based on a cascade control approach with an inner muscular-force control loop and an outer joint-position control loop. The originality of the work is located in the optimization criterion used to distribute forces between synergistic and antagonistic muscles. The cost function and the inequality constraints depend on an estimation of the muscle fiber length and its time derivative. The advantages of a such criterion are exposed by theoretical analysis and numerical tests. The simulation model used in the numerical tests consists in an anthropomorphic arm model composed by two joints and six muscles. Each muscle is modeled as a second-order dynamical system including activation and contraction dynamics. Contraction dynamics is represented using a classical Hill's model.