Gives a comprehensive treatment of several important aspects of the discrete-time periodic Riccati equation (DPRE) arising from the prediction problem for linear discrete-time periodic systems. The authors analyze the symmetric periodic positive semidefinite (SPPS) solution of the DPRE under appropriate assumptions of stabilizability and detectability of the periodic system. Among the results obtained are necessary and sufficient conditions for the existence and uniqueness of the SPPS solution and the stability of the resulting closed-loop system. Some of these results can be seen as extensions of the corresponding results for the time-invariant case; however, a number of them contain contributions to the time-invariant case as well. The paper also gives a numerical algorithm based on an iterative linearization procedure for computing the SPPS solution. The algorithm is a periodic version of Kleinman's algorithm for the time-invariant case. >

The difference periodic Ricati equation for the periodic prediction problem

The history of the time-varying Riccati equation can be traced back to Riccati’s original manuscripts of 1715–1725. Indeed, the major concern of Count Riccati was to study the problem of the separation of variables in quadratic and time-varying scalar differential equations [1]. The equation has been the subject of several contributions in the subsequent centuries. In recent times, the importance of the Riccati equation in Control, Systems, and Signals has led to the development of a considerable research activity on the subject, see e.g., [2], [3], [4] for the time-varying matrix Riccati equation.

The Periodic Riccati Equation

Deterministic and stochastic linear periodic systems

This paper presents the application of dynamic matrix control (DMC) to a drum-type boiler-turbine system. Two types of step-response models for DMC are investigated in designing the DMC; one is developed with the linearization of the nonlinear plant model and the other is developed with the process step-response data. Then, the control performances of the DMC based on both types of models are evaluated. Because of severe nonlinearity of drum water-level dynamics, it is observed that the simulation with the step-response model based on the test data shows satisfactory results, while the linearized model is not suitable for controller design of the drum-type boiler-turbine system.

/pdf/step-response-model-development-for-dynamic-matrix-control-4jd0d1p5tq.pdf

Step-Response Model Development for Dynamic Matrix Control of a Drum-Type Boiler–Turbine System

In an industrial boiler system, multiloop (decentralized) proportional-integral (PI) control is used because of its implementational advantages. We show that such control schemes sacrifice robustness and performance of the overall system. In particular, under normal boiler operating conditions, we design a robust multivariable controller using H/sub /spl infin// loop-shaping techniques; for consideration in implementation, we then reduce this controller to a multivariable PI controller. Both the H/sub /spl infin// controller and its PI approximation are tested extensively in letdown the frequency domain as well as in the time domain, using a valve complex nonlinear simulation software; the results show that the designed controllers are superior in robustness and performance to the existing multiloop controller.

http://www.ece.ualberta.ca/~marquez/journal_publications_files/papers/tan_tcst02.pdf

Multivariable robust controller design for a boiler system

Practical-optimal control of a drum boiler power plant

Referring to recently published results, a few problems apparently playing a basic role in periodic control theory are discussed in this paper. Specifically, the problems dealt with are the controllability of linear periodic systems and the existence of periodic solutions for periodic matrix Riccati equations.

Periodic Systems: Controllability and the Matrix Riccati Equation

Practical-Optimal Control of a drum boiler Power Plant

Parameter Optimization in Decentralized Process Control: A Unified Setting for Multivariable Industrial Regulator Design

The first part of this paper considers the computer-aided design of multivariable structurally constrained regulators for linear time-invariant plants. Two relevant control problems which can be effectively solved by a parameter optimisation approach, are introduced; the basic role played by the internal model principle is then specifically pointed out, and the reformulation of the resulting optimisation problems as mathematical programs are given. The most relevant aspects of the computational algorithms developed to solve these problems are finally outlined, along with the main features of the program package developed to solve, among others, the two cases presented in Part 2

C. Maffezzoni

Papers

Practical-optimal control of a drum boiler power plant

Periodic Systems: Controllability and the Matrix Riccati Equation

Practical-Optimal Control of a drum boiler Power Plant

Parameter Optimization in Decentralized Process Control: A Unified Setting for Multivariable Industrial Regulator Design

Computer-aided design of structurally constrained multivariable regulators. Part 1: Problem statement, analysis and solution