Mats F. Sågfors

State-space solution to the periodic multirate H/sub /spl infin// control problem: a lifting approach

A two-Riccati equation solution to the H/sub /spl infin// control problem for periodic multirate systems is derived via the lifting method. The solution is expressed in terms of two algebraic Riccati equations. The causality constraints are represented by a set of positive definiteness conditions and coupling criteria. As a by-product, the study shows that there is a close connection between the solution of the causally constrained lifted problem and the solution obtained by solving the problem directly as a periodic H/sub /spl infin// problem defined for the multirate system.

H ∞ and LGQ control of asynchronous sampled-data systems

A class of dual-rate sampled-data systems is considered, where the sampling rate is asynchronously related to the rate at which the hold element is operating. Such asynchronous sampled-data systems are aperiodic, and hence the lifting technique, which is used to represent synchronous sampled-data systems as single-rate discrete systems, cannot be applied to the asynchronous case. In this study, optimal H∞ and LQG controllers for asynchronous sampled-data systems are derived using a two-Riccati equation approach, which does not rely on the lifting method. A distribution theorem is used to evaluate the optimal stationary performance levels in the two cases.

H ∞ control of multirate sampled-data systems: a state-space approach

A state-space solution of the H∞ control problem for periodic multirate sampled-data systems is presented. The solution is characterized in terms of a pair of discrete algebraic Riccati equations with a set of associated matrix positive-definiteness conditions and coupling criteria. The solution is derived using two different approaches. In the first approach, the solution is obtained by discretizing two coupled periodic Riccati equations with jumps which characterize the H∞-optimal controller. The second approach is based on the lifting technique. The H∞-optimal controller for a lifted representation of the multirate system is characterized by a two-Riccati equation solution, in which the so-called causality constraint is represented by a set of positive-definiteness conditions and coupling criteria.

Multivariable control of ill-conditioned distillation columns utilizing process knowledge

Abstract In distillation, a reliable model of the column is generally considered as a prerequisite for the design of efficient two-product control by multivariable methods. However, such models are often very hard to obtain. In fact, even very small identification errors may introduce features which are in conflict with physical knowledge, and which make the model useless. Instead of focusing on the development of consistent models, this work is concerned with the utilization of physical process knowledge directly for multivariable control, even if a reliable input-output model is lacking. Such knowledge is, for example, the sign of the RGA-values and an estimate of the input-directionality. It is shown that such structural information of the process can form an entity of control-relevant knowledge that is sufficiently rich for the design of a multivariable SVD controller.

H/sub /spl infin// control of multirate sampled-data systems: a Riccati equation solution

A Riccati-equation based state-space solution to the H/sub /spl infin//-optimal control problem for periodic multirate sampled-data systems is presented. The solution is characterized by two standard discrete algebraic Riccati equations with a set of associated matrix positive definiteness conditions and coupling criteria. The equations are derived by discretizing a pair of coupled periodic Riccati differential equations with jumps, which characterize the H/sub /spl infin//-optimal controller. An important feature of the proposed solution is the fact that the so-called causality constraint, which is imposed on the controller structure in lifting-based solutions, is automatically satisfied. Instead, the solutions to the algebraic Riccati equations are required to satisfy a set of matrix positive definiteness and coupling conditions, which are easy to check.

ILL-CONDITIONEDNESS AND PROCESS DIRECTIONALITY - THE USE OF CONDITION NUMBERS IN PROCESS CONTROL

Abstract The concepts of process directionality and ill-conditionedness as commonly used in the literature might be confusing. Therefore, a refinement of the definition of process directionality is suggested. The refinement divides the concept of directionality into two parts, connected to stability and performance aspects, respectively. The refinement clarifies the connection between condition numbers and control difficulties and makes it possible to define general scaling methods for directionality analysis.

The sampled-data H/sub /spl infin// problem: the equivalence of discretization-based methods and a Riccati equation solution

For the solution of the sampled-data H/sub /spl infin// problem various approaches have been introduced. A commonly used method is the lifting procedure, in which the problem is transformed into an equivalent discrete-time H/sub /spl infin// problem, which can be solved by standard methods. An alternative approach is to consider the sampled-data system as a periodically time-varying system, and to solve the problem directly by applying H/sub /spl infin// control theory of time-varying systems. This method gives the solution in terms of two coupled Riccati differential equations with jumps. The purpose of this paper is to show that the two methods are indeed closely connected, and to show explicitly that the procedures give identical synthesis equations for the sampled-data H/sub /spl infin//-optimal controller.

Optimal H∞ and LQG Control of Asynchronous Sampled Data Systems

Abstract A class of dual-rate sampled-data systems is considered, where the sampling rate is asynchronously related to the rate at which the hold element is operating- Such asynchronous sampled-data systems are aperiodic, and hence the lifting technique, which is used to represent synchronous sampled-data systems as single-rate discrete systems, cannot be applied to the asynchronous case. In this study optimal H ∞ and LQG controllers for asynchronous sampled-data systems are derived using a two-Riccati equation approach which does not rely on the lifting method. A distribution theorem is used to evaluate the optimal stationary performance levels in the two cases.

THE IMPACT OF PROCESS DIRECTIONALITY ON ROBUST CONTROL IN NON-IDEAL DISTILLATION

Abstract The structure of the directionality in non-ideal (real) distillation is examined. The obtained knowledge of the directionality in distillation may be very useful when the two-point control problem is handled. A compensator structure to utilize this information is proposed.