Multivariable Control of Not Almost Strictly Positive Real Systems (ASPR).

Abstract

Simple Adaptive Control (SAC) is one of the main configurations used in passivity-basedadaptive systems. Since the problems of stability and robustness have been partiallysolved, several researchers have set the goal of improving performance on one hand andsimplifying design and implementation on the other. The SAC finds its application indeterministic systems as well as in disturbed systems. SAC of non-Almost Strictly PositiveReal (ASPR) SISO/MIMO systems is well studied. In the last decades, some applicationsof the SAC technique presented a design complexity issue arising from a large number ofparameters and coefficients to select. This issue was recently decreased by the idea of theDecentralized Simple Adaptive Controller (DSAC), which considers only the diagonal ofthe time-varying gain matrices. Therefore, the decreased computational requirements ofthe DSAC facilitated real-time implementation.In the first part of this thesis, we further improve the flexibility of the DSAC byconsidering the fractional derivative of the adaptive gains. The proposed new controller iscalled Fractional Order DSAC (FO-DSAC). Firstly, the ASPR conditions for the design ofa stable fractional adaptive system are established. A fractional Order parallel feedforwardcompensator (FO-PFC) to realize an augmented ASPR system is then provided and anew ASPR-based FODSAC controller is proposed. The stability analysis of the proposedcontrol scheme is presented and simulation example comparing the standard DSAC withthe new FODSAC is provided, showing the performance of the proposed method.In the seconde part of this thesis, a new Adaptive Synergetic Controller (ASC) isproposed as a solution for the problem of the design of the standard Synergetic Control lawwhen the system parameters and dynamics are unknown. It is well known that the designof the SC law requires a thorough knowledge of the system parameters and dynamics.Such problem obstructs the synthesis of the SC law and the designer is prompted topass through the estimation methods, which, in turn, poses a problem of increasing thecomputation time of the control algorithm. To cope with this problem, a solution isproposed by modifying the original SC law to develop an SAC-like adaptive SC lawwithout the need of prior knowledge of the system. The stability of the proposed adaptivecontroller is formally proven via the Lyapunov approach. Experimental application to aquadrotor system is given to validate the theoretical results.