A Probabilistic Approach for Robust Input Shapers Design for Precise Point-to-Point Control

A probabilistic approach which exploits the domain and distribution of the uncertain model parameters has been developed for the design of robust input shapers. A Polynomial Chaos based expansion approach is used to approximate uncertain system states and cost functions in terms of finite-dimensional series expansion in the stochastic space. Residual energy of the system is used as cost function to design robust input shapers for precise restto-rest maneuvers. An optimization problem which minimizes any moment or combination of moments of the distribution function of the residual energy is formulated. Numerical examples are used to illustrate the benefit of using the Polynomial Chaos based probabilistic approach for the determination of robust Input Shapers for uncertain linear systems. The solution of Polynomial Chaos based approach is compared to the minimax optimization based robust input shaper design approach which emulates a Monte Carlo process.