Model predictive control of a CSTR: A comparative study among linear and nonlinear model approaches

© 2017 IEEE. This paper presents a comparative study of two widely accepted model predictive control schemes based on mixed logical dynamical (MLD) and nonlinear modeling approaches with application to a continuous stirred tank reactor (CSTR) system. Specifically, we approximate the nonlinear behavior of a CSTR system with multiple local linear models in a MLD framework. The main benefit of such a scheme is the significant improvement in model accuracy when compared with a single linearized model. The benefits and trade-offs associated with predictive control laws synthesized using MLD and nonlinear modeling approaches are also compared.National Research Foundation, Singapore

Robust multivariable feedback design for an extractive distillation column

In this paper, multivariable quantitative feedback theory (QFT) techniques are used to synthesize a robust feedback system for an extractive distillation column with a vaporous sidestream. The simplified state space model of Gilles and Retzbach (1983) for an extractive distillation column exhibiting sharp temperature profiles is adopted here. Large uncertainty of +20% is assumed in three key matrix elements of this model. The feedback design problem is to find the controller and prefilter matrices such that the stated tracking specifications are met, over the entire range of model parametric uncertainty. The fourth MIMO QFT technique of Yaniv and Horowitz (1986) is used to solve the design problem. The design is verified through extensive simulations in both frequency and time domains, for several plants picked from the plant uncertainty set. In all cases, the results obtained are quite satisfactory.© IEE

Reliable computation of rectangular system templates to prescribed accuracy

An algorithm is proposed for reliable computation of rectangular template enclosures for transfer functions of linear systems with uncertain parameters. The algorithm is developed using tools of interval mathematics. The main feature of the algorithm is its applicability to any transfer function whose magnitude and phase values over the given parameter ranges are (i) bounded, and (ii) can be found using a digital computer. It is shown that a machine interval arithmetic Implementation of the algorithm accounts for all kinds of computational errors, and generates reliable values for the magnitude and phase Intervals of the template. The algorithm is demonstrated on a seven parameter non-rational nuclear reactor example having multiple transport lags and highly correlated nonlinear parameter dependencies

Interval QFT: a mathematical and computational enhancement of QFT

The paper presents an overview of a mathematical and computational enhancement of Horowitz's QFT design procedure. The enhancement uses methods of interval analysis and is called as interval QFT, or IQFT. IQFT addresses and solves some of the fundamental issues in QFT, concerning selection of design frequencies, selection of controller phases in bound generation, approximation of plant templates with finite plant sets, and generation of plant templates and controller bounds with reliability and to a prescribed accuracy. An example is presented to illustrate the key features of IQFT. Copyright (C) 2002 John Wiley Sons, Ltd

Computation of QFT bounds for robust tracking specifications

An algorithm is proposed for generation of QFT controller bounds to achieve robust tracking specifications. The proposed algorithm uses quadratic constraints and interval plant templates to compute the bounds, and presents several improvements over existing QFT tracking bound generation algorithms. The proposed algorithm (1) guarantees robustness against template inaccuracies, (2) guarantees robustness against phase discretization, (3) provides a posteriori error estimates, (4) is computationally efficient, achieving a reduction in flops and execution time, typically by 1-2 orders of magnitude. The algorithm is demonstrated on an aircraft example having five uncertain parameters. (C) 2001 .

A MATLAB toolbox for QFT-based synthesis of linear / nonlinear lumped and linear distributed systems

We present QFT IIT, a MATLAB toolbox for quantitative feedback theory (QFT)-based synthesis of robust feedback systems. QFT IIT can handle several system classes including linear and nonlinear, single input-output and multi input-output, output and internal variable feedback, and linear distributed with distributed or point feedback types. We used QFT IIT to successfully solve a large number of robust control problems at The Indian Institute of Technology (IIT) Bombay.© IEE

On fractional-order QFT controllers

We propose the synthesis of robust fractional-order controllers using the principles of quantitative feedback theory (QFT). The resulting controllers are called as fractional-order QFT controllers. To demonstrate the synthesis method, we synthesize proportional-integral-derivative (PID) and more general types of fractional-order QFT controllers for a fractional-order plant, a DC motor and a multistage flash desalination process

Adaptive QFT control using hybrid global optimization and constraint propagation techniques

We propose a procedure for the online design of adaptive quantitative feedback theory (QFT) control system. The proposed procedure uses hybrid global optimization and interval constraint propagation techniques to automatically design online an adaptive QFT controller and prefilter as and when required. While the hybrid global optimization combines interval global optimization and nonlinear local optimization methods, the interval constraint propagation techniques accelerate the optimization search by very effectively discarding infeasible controller parameter regions. The proposed adaptive QFT control is experimentally demonstrated on a coupled tanks system in the laboratory. Experimental results show the superiority of the proposed adaptive QFT control over standard QFT control, in terms of both reduced error and reduced control effort.© IEE

An improved algorithm for set inversion using interval analysis with application to control system

We present an algorithm to characterize the set S = {x is an element of R-l : f(x) > 0} = f(-1)(]0, infinity[(m)) in the frame work of set inversion using interval analysis. The proposed algorithm improves on the algorithm of Jaulin et. al. The improvement exploits powerful Hansen's method for solving systems of nonlinear inequalities. We test and compare the performance of the proposed and existing algorithms in characterizing the domain for the robust stability. The results of the testing show that the proposed algorithm is computationally efficient and encloses the solution more sharply than the existing algorithm, requires less memory space and iterations

The extrapolated interval global optimization algorithm

This paper presents a new approach based on extrapolation to accelerate the linear convergence process of Vectorized Moore-Skelboe (VMS) algorithm. The VMS is a modified version of basic Moore-Skelboe (MS) algorithm, where the vectorization is used as a means to speed up the basic MS algorithm. We propose to further accelerate the converging process of VMS from linear to quadratic by combining the Richardson extrapolation technique with VMS. The effectiveness of the proposed algorithm is tested on various multivariate examples and compared with the unaccelerated conventional method, i.e., MS and well-known optimization software GlobSol. The test results show that the proposed extrapolation-based VMS offer considerable speed improvements over both the existing algorithms