Robust Fractional Adaptive Control Based on the Strictly Positive Realness Condition

Robust Fractional Adaptive Control Based on the Strictly Positive Realness ConditionThis paper presents a new approach to robust adaptive control, using fractional order systems as parallel feedforward in the adaptation loop. The problem is that adaptive control systems may diverge when confronted with finite sensor and actuator dynamics, or with parasitic disturbances. One of the classical robust adaptive control solutions to these problems makes use of parallel feedforward and simplified adaptive controllers based on the concept of positive realness. The proposed control scheme is based on the Almost Strictly Positive Realness (ASPR) property of the plant. We show that this condition implies also robust stability in the case of fractional order controllers. An application to Model Reference Adaptive Control (MRAC) with a fractional order adaptation rule is provided with an implementable algorithm. A simulation example of a SISO robust adaptive control system illustrates the advantages of the proposed method in the presence of disturbances and noise.

A Robust Controller for Second-Order Systems Using Acceleration Measurements

This paper presents a robust control design using strictly positive realness for second-order dynamic systems. A robust strictly positive real controller stabilizes second-order systems with only acceleration measurements. An important property of this design is that the stabilization is independent of the system plant parameters. The control design connects a virtual system to a given plant such that any strictly positive real controller can be used to achieve robust stability. A spring-mass system is used as an example to demonstrate the robust stability and robust performance of this design.