P.N. Paraskevopoulos

Multirate adaptive temperature control of greenhouses

Abstract A new adaptive technique is proposed for the control of the temperature in a greenhouse whose parameters vary with operating conditions. The proposed adaptive controllers are derived by solving either the pole-placement or the linear quadratic regulation (LQR) problem and use multirate controllers in which the greenhouse temperature is sampled many times over a fundamental sampling period. On the basis of the proposed control scheme, the problem is reduced to an associated discrete-time problem for which constant state feedback controllers are derived. Thus, the proposed technique essentially becomes one of computing a constant gain controller rather than one of deriving state observers or output feedback controllers, as in other indirect adaptive control techniques. As a consequence, the exogenous dynamics introduced in the control loop is of low order. Furthermore, the proposed adaptive controllers can be designed to possess any degree of stability, since their transition matrices can be chosen arbitrarily. The proposed scheme estimates the unknown parameters of the greenhouse on-line from sequential data on the greenhouse temperature and the heating power, which are recursively updated. Persistency of excitation of the controlled system is assured without making assumptions on the system under control, other than controllability, observability and known order. Simulation results of the greenhouse dynamics illustrate the effectiveness of the proposed scheme.

Observer design for generalized state space systems with unknown inputs

Abstract The following four major aspects for the observer design problem for generalized state space systems with unknown inputs are resolved: Necessary and sufficient conditions for the problem to have a solution, the order of the minimal observer, the properties of the closed-loop system (separation principle) and general analytical expressions of the minimal order observer matrices. All above results are first in the field.

The operational matrix of integration for Bessel functions

Abstract A general expression for the operational matrix of integration P for the case of Bessel functions is derived. Using this P, several problems such as identification, analysis and optimal control may be studied. Examples are included to illustrate the theoretical results.

A new approach to the decoupling problem of linear time-invariant systems

Abstract A new approach to the input-output decoupling problem of linear time-invariant systems via proportional state and output feedback is presented. A major feature of the proposed approach is that it reduces the solution of the decoupling problem to that of solving a linear algebraic system of equations. This system of equations greatly facilitates the solution of the following four major aspects of the decoupling problem: necessary and sufficient conditions, general analytical expressions for the controller matrices, general analytical expressions for the diagonal elements of the closed-loop system, and the structural properties of the closed-loop system.

Disturbance rejection of left-invertible systems

Abstract A new approach is presented for the study of the disturbance rejection of left-invertible systems via proportional state feedback, reducing the problem to that of solving a linear algebraic system of equations. On the basis of this system of equations, the necessary and sufficient conditions for the existence of a solution to the disturbance rejection problem are established in a form of simple algebraic criteria (thus reducing the computational effort over known results) and the general analytical expressions of all solutions of the controller matrices are derived. These solutions are parameterized only by an arbitrary matrix.

Exact model matching of generalized state space systems

The problem of exact model matching for generalized state space (GSS) systems via pure proportional state and output feedback is studied. The following two major issues are resolved here for the first time: The necessary and sufficient conditions for the problem to have a solution and the general analytical expressions for the exact modelmatching controller matrices. The important case of left invertible systems is treated separately wherein simple solutions are established for the above two major issues and results on structural properties of the closed-loop system are reported. Known results on model matching of regular systems are derived as a special case of the GSS systems results, thus unifying the solution of the exact model-matching problem of regular and singular systems.

Exact model matching of linear systems using generalized sampled-data hold functions

A new technique is presented for the solution of the exact model matching problem of linear time-invariant systems using generalized sampled-data hold functions. This technique reduces the problem to that of solving a nonhomogeneous algebraic system of equations. On the basis of this system of equations, the necessary and sufficient conditions are established and the expressions of the controller matrices are derived.

Disturbance Rejection of Left-Invertible Neutral Time-Delay Systems

The problem of disturbance rejection (DR) for general left-invertible neutral multi-delay systems, via proportional realizable state feedback, is extensively solved. The necessary and sufficient conditions for the problem to have a realizable solution are established. The general analytical expression of the proportional realizable controller matrix is derived. The conditions and the general expression of the controller are computed using a finite number of explicit algebraic manipulations

Sampled-data minimum H ∞ -norm regulation of linear continuous-time systems using multirate-output controllers

This paper deals with the problem of designing multirate-output contrlleers for sampled-dataH∞-optimal control of linear continuous-time systems. Two formulations of the problem are studied. In the first, the intersample behavior of the disturbance and the controlled output signals is not considered, whereas in the second the continuous-time nature of these signals is taken into account. It is shown that, in both cases and unter appropriate conditions, it is plausible to reduce the repective initial problem to an associated discrete-timeH∞-optimization problem for which a fictitious static state feedback controller is to be designed. This fact has a beneficial influence on the theoretical and numerical complexity of the problem, since only one algebraic Riccati equation is to be solved here, as compared to two algebraic Riccati equations needed in known techniques concerning theH∞-optimization problem with dynamic measurement feedback.

Exact model matching of left invertible neutral time delay systems

The problem of exact model matching (EMM) for general left invertible neutral multi-delay systems, via proportional realizable state and output feedback, is extensively solved. The necessary and sufficient conditions for the problem to have a realizable solution are established. The general analytical expression of the controllers, solving the problem, is derived for this system category with realizable proportional state and output feedback controllers. The present results are rather useful to adaptive control of distributed industrial processes described by neutral time delay models