Arvo Kaldmäe

Measurement feedback disturbance decoupling in discrete-time nonlinear systems

The paper studies the disturbance decoupling problem by the dynamic measurement feedback for discrete-time nonlinear control systems. To address the problem the algebraic approach, called the algebra of functions, is applied, which allows the system description also depend on non-differentiable functions. A necessary and sufficient condition is given in terms of controlled and (h,f)-invariant functions. Also, algorithms are derived, which find invariant functions and the required feedback. The algorithms are implemented in Mathematica software which is made available over the internet.

Dynamic measurement feedback in discrete-time nonlinear control systems

The problem of disturbance decoupling of discrete-time nonlinear control systems by dynamic measurement feedback is addressed in this paper. New input-output linearization conditions are derived to provide weaker sufficient conditions for disturbance decoupling problem than existing ones. Additionally, it is shown that these conditions are necessary if one assumes the certain form of the dynamic feedback.

On Flatness of Discrete-time Nonlinear Systems

Abstract The paper addresses the problem of dynamic feedback linearization of discrete-time nonlinear control systems. Analogously to the continuous-time case, necessary and sufficient conditions for flatness property are obtained and showed to be equivalent to previously known results on feedback linearizability by endogenous dynamic feedback. An example is added to illustrate the results.

Input-output Linearization of Discrete-time Systems by Dynamic Output Feedback

Abstract The paper addresses the input–output linearization problem by dynamic output feedback for multi-input multi-output nonlinear systems, described by a set of higher order difference equations. Necessary and sufficient solvability conditions are given together with the constructive procedure to check the conditions and compute the feedback.

On exact feedback linearization of HVAC systems

In this paper, we discuss the possible applications of algebraic framework, based on the theory of differential one-forms, to analysis of the real-life processes. The possibilities of this approach are illustrated on two common Heating, Ventilating, and Air Conditioning (HVAC) models. Algebraic formalism provides a unified framework to handle various problems for nonlinear control systems. It is briefly explained how to check the common properties in which engineer is usually interested in. The static and dynamic feedback linearization algorithms are discussed. Using algebraic tools it is possible to derive the appropriate change of coordinates in which the transformed system reads as a linear one. In addition, the specific scientific package NLControl based on Mathematica software is discussed.

Comparison of two methods for computing flat outputs

In this paper, the problem of linearization of discrete-time nonlinear control systems by dynamic state feedback is considered. Two different methods for finding certain polynomial matrix are compared. This polynomial matrix is necessary to compute linearizing (or flat) outputs of the system. Finally, a necessary and sufficient condition to check unimodularity of certain polynomial matrices, is given.

Comments on ‘A new kind of nonlinear disturbance observer for nonlinear systems with applications to cruise control of air-breathing hypersonic vehicles’

ABSTRACT In the comments we claim that the disturbance observer suggested in the commented paper is not applicable, since it depends implicitly on the disturbance it should estimate.

Realization of time-delay systems

Abstract The paper addresses the problem of transforming a single-input single-output nonlinear retarded time-delay system, described by an input–output equation, in the traditional observable state space form. The solution is generalized from the delay-free case and depends on integrability of certain submodule of differential 1-forms. The integrability conditions are improved to make them constructive. Finally, it is explained why one may obtain two realizations, which are not connected by bi-causal change of state coordinates.

Flatness Based Control of a HVAC System

This paper studies the flatness-based control of a nonlinear multi-input multi-output heating, ventilating and air conditioning (HVAC) system. First, a novel method for checking flatness property is used to verify that the given HVAC model is flat and that the flat outputs are the temperature and the humidity ratio of the thermal space. Since the flat outputs are also the variables, which one usually wants to control, it is relatively easy to construct a flatness-based feedforward control for the HVAC model. We define the appropriate trajectories for the flat outputs and then the controller is computed from the parametrization of system inputs in terms of flat outputs and their derivatives. The trajectories of flat outputs are chosen such that the temperature and the humidity ratio converge asymptotically from the initial values to the desired values. Simulations are made, which show the effectiveness of the approach. DOI: http://dx.doi.org/10.5755/j01.itc.46.4.17697

Input–output decoupling of discrete-time nonlinear systems by dynamic measurement feedback

Abstract The paper addresses the input–output decoupling problem for discrete-time nonlinear systems. The algebraic method based on difference algebra and differential forms is used to solve the problem by measurement feedback, i.e., by feedback depending only on some measured functions of state variables. Constructive necessary and sufficient solvability conditions are given separately for cases when the system is described by the state equations or by the input–output equations. By specifying the measured functions, one recovers the known conditions for the state feedback or obtains the conditions for the output feedback solution.