On the simulation of RFPT-based adaptive control of systems of 4th order response

As an alternative of Lyapunov functions based design methods the “Robust Fixed Point Transformations (RFPT)”-based adaptive control design was developed in the past years. The traditional approaches emphasize the global stability of the controlled phenomena while leaving the details of the trajectory tracking develop as a not very clear consequence of the control settings the novel design directly concentrates on the observable response of the controlled system therefore it can concentrate on the tracking details as a primary design intent. Whenever a Classical Mechanical system that normally produces 2nd order response (i.e. acceleration) is forced through an elastic component its immediate response becomes 4th order one. Practical observation of the 4th order derivatives of a variable may suffer from measurement noises. Furthermore, when in simulation studies the higher order derivatives are numerically integrated and later numerically differentiated to provide the appropriate feedback signals the non-smooth jumps in the numerical integrator can destroy the simulation results. By the use of a simple 4th order model in this paper it is shown that the chained use of the built-in differentiators of the simulation package SCILAB is inappropriate for simulation purposes. It is also shown that by the use of a simple 4th order polynomial differentiator this problem can be solved. This statement is substantiated by simulation results.