Control of a Multivariable System Using Optimal Control Pairs: A Quadruple-Tank Process

Pavel Navratil,Radek Matusu,Libor Pekar

doi:10.1109/access.2019.2962302

Pavel Navratil, Radek Matusu + Show 1 more

Open Access

https://doi.org/10.1109/access.2019.2962302

Copy DOI

Abstract

This paper deals with one of the possible ways to control multivariable (MIMO) control loops. The suggested control design procedure uses the so-called primary controllers, auxiliary controllers, and also correction members. Parameters of the primary controllers are determined for the optimal control pairs using arbitrary single-variable synthesis methods; namely, the modulus optimum method, the balanced tuning method, and the desired model method. The optimal control pairs are determined using the so-called relative gain array tool or the relative normalized gain array tool combined with other tools, as the condition number or the Niederlinski index. The auxiliary feedback controllers serve for ensuring a control loop decoupling. Invariance to load disturbance of a control loop is realized by using the correction members. The novelty lies especially in the combination of the original inverted decoupling with disturbance rejection and provided tuning methods. The proposed control design for a MIMO loop is verified by simulation for the two-variable controlled plant of a quadruple-tank process and evaluated by using various criteria. Moreover, a numerical comparison to some other methods is given to the reader.

Highlights

Controlled plants with one input variable and one output variable are classified as single-input single-output (SISO), or single-variable, ones
For a huge number of controlled plants, more than one output variable is controlled simultaneously via several input variables, i.e., input variables influence their corresponding output variables. These controlled plants are known as multi-input multioutput (MMO), or multivariable, ones and can be found in various areas of human activities, e.g. an air-condition system [1], [2], a tubular chemical reactor [3], [4], a military aircraft turbofan engine [5], a heating plant [6], a balance platform [7], an autopilot system [8], a quadcopter [9], [10], etc
1) RELATIVE GAIN ARRAY (RGA) The relative gain array (RGA) represents the most common tool to determine the optimal control pairs for MIMO controlled plants; it serves for the analysis of interactions between inputs and outputs [18], [19], [26]

Summary

INTRODUCTION

Controlled plants with one input variable and one output variable are classified as single-input single-output (SISO), or single-variable, ones. This study is aimed at the design of an inverted decentralized decoupling MIMO control strategy that, provides the ideal or a partial disturbance rejection. The main contribution of this research lies in the unique combination of the optimal control configuration selection based on three indicators (which gives a sufficient optimal solution in most cases), the use of a novel inverted decoupler, the ideal (or a simplified) measurable disturbance elimination, and the used SISO controller tuning techniques. The presented comprehensive numerical example of the four-tank process model control can highly be beneficial for the reader since it includes even a non-minimum phase case and disturbances rejection, and presents results for various control design principles.

BASIC DESCRIPTION OF THE MULTI-VARIABLE CONTROL LOOP

DETERMINATION OF OPTIMAL CONTROL PAIRS

CONCLUSION