Krister Forsman

Construction of Lyapunov functions using Grobner bases

The author shows how Grobner bases can be used when choosing parameters in Lyapunov functions for nonlinear dynamic systems in an optimal way. The method requires the nonlinearities of the system and the Lyapunov function to be of a polynomial type. Some concrete examples of how to apply the method are provided.<<ETX>>

Constructive algebraic geometry in nonlinear control

It is shown how Grobner bases can be used to solve some common problems in nonlinear systems theory efficiently. These problems include finding critical levels of local Lyapunov functions and solving the equations that arise in the harmonic balancing method. The methods proposed are illustrated by some concrete examples in which the computer algebra system Maple is used for performing the necessary calculations.<<ETX>>

Hierarchical scheduling and utility disturbance management in the process industry

The integration of scheduling and control in the process industry is a topic that has been frequently discussed during the recent years, but many challenges remain in order to achieve integrated solutions that can be implemented for large-scale industrial sites. In this paper we consider production control under disturbances in the supply of utilities at integrated sites together with the integration towards production scheduling. Utilities, such as steam and cooling water, are often shared between the production areas of a site, which enables formulation of an optimization problem for determining the optimal supply of utilities to each area at the occurrence of a disturbance. Optimization in two timescales is suggested to handle the scheduling and disturbance management problems in a hierarchical fashion. The suggested structure has been discussed with companies within the chemical process industry. A simple example is provided to show how the structure may be used.

POLYCON-computer algebra software for polynomial control systems

This paper describes the features and implementation of the Maple software package POLYCON which is intended to assist the control theorist in the analysis of nonlinear dynamical systems, in continuous and discrete time. POLYCON handles systems where all nonlinearities are polynomial or rational functions. It is supposed to be accessible to non-experts and those that are not familiar with computer algebra, commutative algebra or differential algebra. POLYCON is included in the Maple Share Library.<<ETX>>

On Rational State Space Realizations

Abstract It is investigated when a polynomial input- output differential equation can be realized in rational, explicit state space form, i.e. so that all components of the right hand side are rational functions of the states. In the case where there are no inputs the problem is showed to be equivalent to a famous problem in algebraic geometry, which is solved only in various special cases. For systems with inputs the problem is more complicated, as is the discrete time case. An interpretation of the Luroth problem in terms of observability is made.

A constructive approach to algebraic observability

The authors address the problem of observability of polynomial discrete-time systems. The ideal theoretic definition is translated to effective computations in terms of Grobner bases. Linear system observability is a special case, and for general polynomial systems n samples are needed to determine observability, where n is the state dimension. The formulation yields a decision criterion as well as an implicit form of an observer.<<ETX>>

Hybrid control systems and comprehensive Grobner bases

A class of hybrid systems that can be modeled by polynomial differential equations is investigated. By a hybrid system we mean a system which mixes continuous and discrete variables. All variables in the system have the same time scale. The polynomial models have the advantage that constructive methods are available for system analysis. One such method that occurs naturally in this context is so called comprehensive Grobner bases.<<ETX>>

Solving the ARE symbolically

Methods from computer algebra, mostly so called Grobner bases (gb) from commutative algebra, are used to solve the algebraic Riccati equation (ARE) symbolically. The methods suggested allow us to track the influence of parameters in the system or penalty matrices on the solution. Some nontrivial aspects arise when addressing the problem from the point of view commutative algebra, for example the original equations are rational, not polynomial. We explain how this can be dealt with rather easily. Some methods for lowering the computational complexity are suggested and different methods are compared regarding efficiency. Preprocessing of the equations before applying gb can make computations more efficient.<<ETX>>

Practical control of surge tanks suffering from frequent inlet flow upsets

In the presence of frequent inlet flow upsets, tuning of averaging level controllers is typically quite complicated since not only the size of the individual steps but also the time in between the subsequent steps need to considered. One structured way to achieve optimal filtering for such a case is to use Robust Model Predictive Control. The robust MPC controller is, however, quite computationally demanding and not easy to implement. In this paper two linear controllers, which mimic the behavior of the robust MPC, are proposed. Tuning guidelines to avoid violation of the tank level constraints as well as to achieve optimal filtering are presented.

A general method for defining and structuring buffer management problems

In an industrial plant, availability is an important factor since increased availability often gives an increase of final production, which in many cases means an increased profit for the company. The purpose of using buffer tanks is to increase the availability either by separating production units from each other or by minimizing flow variations. However, the methods for achieving this goal is not trivial, and depend on the specific characteristics of the problem. This paper contributes to structuring the general buffer management problem for continuous chemical plants and suggests methods for solving some specific problems, presented as a case study at Perstorp AB, Sweden.