Second order smooth trajectory generator with nonlinear constraints

A smooth trajectory generator useful in motion control systems is presented. The considered generator is a second order nonlinear system which receives as input a standard reference signal (step, ramp, etc.) and provides as output a smooth reference signal satisfying proper nonlinear constraints on the state variables as, for example, bounds on the first time-derivative x of the output x, or bounds expressed in the form |x| ≤ U(x). The imposed constraints can also be changed during system operation without modifying the system stability. Moreover, almost minimum time response is ensured with guaranteed no overshoot. Only the second order continuous-time case is considered. Finally, the performance of the the nonlinear generator is tested through simulation experiments.