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Abstract The two degree of freedom ball balancing table (BBT) is a well-known didactic tool used to evaluate the effectiveness and performances of many control algorithms for dynamic systems. The present paper proposes to control the ball position of the BBT system via a linear feedback controller based on a functional observer. The parameters of the linear functional observer are determined by applying the direct method which requires neither a Sylvester equation resolution nor canonical transformations. The use of a digital controller has motivated the elaboration of the equations in the discrete time case. In this work, the BBT is tested in real-time to evaluate the proposed controller performances when stabilizing a ball on a reference point. This paper is a continuity of the previous work [12], in which only simulation results have been carried out.

This paper deals with the problem of functional observer design for systems with non-commensurate time varying delays. The main procedure of three types of functional observers are presented in this article, more precisely, observers with delays dependent, observers without internal delays and delay-free functional observers. A necessary condition for the existence of these observers is given as rank equality. The design conditions for functional observers are presented in terms of linear matrix inequalities (LMIs). The solution of these LMIs is used to determine the observers parameters. Finally, some numerical examples are given at the end of the paper to show the feasibility of the proposed approach. [ABSTRACT FROM AUTHOR]

A discrete-time sliding mode control is one of the most prominent robust control techniques for stabilising systems. However, the assumption of full state feedback being available is seldom satisfied in practice. This chapter presents the functional observer-based sliding mode controller (SMC) design for discrete-time stochastic systems with unmatched uncertainty. A disturbance-dependent sliding function method is proposed such that the effect of unmatched uncertainty of the system is minimised. Furthermore, SMC is calculated using the functional observer method. Finally, a simulation example is given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This chapter presents a new approach to designing a functional observerbased sliding mode control for discrete-time stochastic systems. The functional observer is based on theKronecker product approach. Existence conditions and stability analysis of the proposed observer are given. The control input is estimated by a novel linear functional observer. This approach leads to a nonswitching type of control, thereby eliminating the fundamental cause of chatter. Furthermore, the functional observer is designed in such a way that the effect of the process and measurement noise is minimised. A simulation example is given to illustrate and validate the proposed design method. [ABSTRACT FROM AUTHOR]

Sliding mode control (SMC) is one of the most popular techniques to stabilise linear discrete-time stochastic systems. However, application of SMC becomes difficult when the system states are not available for feedback. This paper presents a new approach to design a SMC-based functional observer for discrete-time stochastic systems. The functional observer is based on the Kronecker product approach. Existence conditions and stability analysis of the proposed observer are given. The control input is estimated by a novel linear functional observer. This approach leads to a non-switching type of control, thereby eliminating the fundamental cause of chatter. Furthermore, the functional observer is designed in such a way that the effect of process and measurement noise is minimised. Simulation example is given to illustrate and validate the proposed design method. [ABSTRACT FROM AUTHOR]

In this paper a straightforward procedure, to obtain a linear functional observer with order equal to the dimension of the vector to be estimated, is proposed. Inspired by [3], we have developed a procedure to construct this type of observer in which some significant simplifications have been made and allow computational burden reduction. The procedure developed in this work has the originality and the great advantage that all required matrices are obtained without calculating any generalized inverse. A novel approach which constitutes the coupling of a coordinates transformation and the use of the {1}-inverse property requires only the inversion of a nonsingular matrix. A procedure where all steps are clearly identified is written and a numerical example is provided to illustrate the effectiveness of the observer. [ABSTRACT FROM AUTHOR]

This paper considers a class of uncertain, nonlinear differential state delayed control systems and presents a reduced-order observer design procedure to asymptotically estimate any vector state functionals. The method proposed involves decomposition of the delayed portion of the system into two parts: a matched and mismatched part. Provided that the rank of the mismatched part is less than the number of the outputs, a reduced-order linear functional observer, with any prescribed stability margin, can be constructed by using a simple procedure. A numerical example is given to illustrate the new design procedure and its features. [Copyright &y& Elsevier]