In this work, given a linear multivariable system, the problem of static state feedback realization of dynamic compensators is considered. Necessary and sufficient conditions for the existence of a static state feedback that realizes the dynamic compensator (square or full column rank compensator) are stated in structural terms, i. e., in terms of the zero-pole structure of the compensator, and the eigenvalues and the row image of the controllability matrix of the compensated system. Based on these...
J. C. Mathews and D. W. Curtis, [4], have introduced some structures which generalize structures of uniform types to the product of two sets, and they obtain a generalized version of Banach's contraction mapping theorem. In this note we prove that these structures are obtained from the usual analogues by means of a particular bijection; hence we do not have a meaningful generalization. For example, this bijection provides, from a result by A. S. Davies, [1], an analogue of Banach's well-known contraction...
The nonlinear control techniques are applied to the model of rotary inverted pendulum. The model has two degrees of freedom and is not exactly linearizable. The goal is to control output trajectory of the rotary inverted pendulum asymptotically along a desired reference. Moreover, the designed controller should be robust with respect to specified perturbations and parameters uncertainties. A combination of techniques based on nonlinear normal forms, output regulation and sliding mode approach is...
Considering a controllable, square, linear multivariable system, which is decouplable by static state feedback, we completely characterize in this paper the structure of the decoupled closed-loop system. The family of all attainable transfer function matrices for the decoupled closed-loop system is characterized, which also completely establishes all possible combinations of attainable finite pole and zero structures. The set of assignable poles as well as the set of fixed decoupling poles are determined,...
A mathematical model of the microalgal growth under various light regimes is required for the optimization of design parameters and operating conditions in a photobioreactor. As its modelling framework, bilinear system with single input is chosen in this paper. The earlier theoretical results on bilinear systems are adapted and applied to the special class of the so-called intermittent controls which are characterized by rapid switching of light and dark cycles. Based on such approach, the following...
In this paper we present a solution to the decoupling problem with stability of linear multivariable systems with 2 outputs, using nonregular static state feedback. The problem is tackled using an algebraic-polynomial approach, and the main idea is to test the conditions for a decoupling compensator with stability to be feedback realizable. It is shown that the problem has a solution if and only if Morse’s list is greater than or equal to the infinite and unstable structure of the proper and stable...
The regulator equation is the fundamental equation whose solution must be found in order to solve the output regulation problem. It is a system of first-order partial differential equations (PDE) combined with an algebraic equation. The classical approach to its solution is to use the Taylor series with undetermined coefficients. In this contribution, another path is followed: the equation is solved using the finite-element method which is, nevertheless, suitable to solve PDE part only. This paper...
The paper deals with the construction of the output feedback controllers for the systems that are transformable into a simpler form via coordinate change and static state feedback and, at the same time, via (possibly different) coordinate change and output injection. Illustrative examples are provided to stress the major obstacles in applying the above scheme, especially as far as its global aspects are concerned. The corresponding results are then applied to the problem of the real-time control...
This work is concerned with observability in Discrete Event Systems (DES) modeled by Interpreted Petri Nets (IPN). Three major contributions are presented. First, a novel geometric characterization of observability based on input-output equivalence relations on the marking sequences sets is presented. Later, to show that this characterization is well posed, it is applied to linear continuous systems, leading to classical characterizations of observability for continuous systems. Finally, this paper...
The simultaneous problem of consensus and trajectory tracking of linear multi-agent systems is considered in this paper, where the dynamics of each agent is represented by a single-input single-output linear system. In order to solve this problem, a distributed control strategy is proposed in this work, where the trajectory and the formation of the agents are achieved asymptotically even in the presence of switching communication topologies and smooth formation changes, and ensuring the closed-loop...
Most of the existing works in the literature related to greenhouse modeling treat the temperature within a greenhouse as homogeneous. However, experimental data show that there exists a temperature spatial distribution within a greenhouse, and this gradient can produce different negative effects on the crop. Thus, the modeling of this distribution will allow to study the influence of particular climate conditions on the crop and to propose new temperature control schemes that take into account the...
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