Flatness-based control in successive loops for mechatronic motion transmission systems

Mechatronic systems with nonlinear dynamics are met in motion transmission applications for vehicles and robots. In this article, the control problem for the nonlinear dynamics of mechatronic motion transmission systems is solved with the use of a flatness-based control approach which is implemented in successive loops. The state-space model of these systems is separated into a series of subsystems, which are connected between them in cascading loops. Each one of these subsystems can be viewed independently as a differentially flat system, and control about it can be performed with inversion of its dynamics as in the case of input–output linearized flat systems. In this chain of $i=1,2,\dots ,N$ subsystems, the state variables of the subsequent ( $i+1$)-th subsystem become virtual control inputs for the preceding $i$-th subsystem and so on. In turn, exogenous control inputs are applied to the last subsystem and are computed by tracing backwards the virtual control inputs of the preceding $N-1$ subsystems. The whole control method is implemented in successive loops, and its global stability properties are also proven through Lyapunov stability analysis. The validity of the control method is confirmed in the following two case studies: (a) control of a permanent magnet linear synchronous motor (PMLSM)-actuated vehicle's clutch and (ii) control of a multi-Degrees of Freedom (multi-DOF) flexible joint robot.