Equivalent Subsystems Method Research Articles

Decentralized QFT Controller Design Based on the Equivalent Subsystems Method

Since the 1970s various decentralized control methodologies have been developed to deal with the challenge of controlling complex and/or spatially distributed systems with multiple inputs and multiple outputs (MIMO), e.g., chemical plants, power systems, water systems, etc. In general, the use of distributed information and control structures requires the synthesis of control laws in a constrained (decentralized) information structure. The article presents a novel frequency domain robust decentralized controller design method that is appropriate for uncertain dynamic MIMO systems with equal numbers of input and output variables, which consist of interconnected physical subsystems and are given as a set of square transfer function matrices. The main framework of the proposed method provides the Equivalent Subsystems Method (ESM), whereby the overall closed-loop system under a decentralized controller is stable if, and only if, all the individual closed-loop equivalent subsystems are stable. By generating equivalent subsystems for all transfer matrices, which describe the uncertain MIMO system, the individual uncertain equivalent subsystems are obtained as sets of respective frequency responses. Such representation allows the application of the QFT (quantitative feedback theory) approach to independently design local single-input single-output (SISO) robust controllers which constitute the resulting decentralized controller implemented in real subsystems. The designed controller ensures robust stability of the overall closed-loop system and the required performance as specified by the standard QFT performance specification types in both the equivalent subsystems and the overall closed-loop system. Compared to the existing method and references therein, the proposed method reduces the conservatism of the robust stability conditions and enables the exploitation of the benefits by the SISO QFT approach in the independent design of the robust decentralized controller. The developed design procedure is verified and illustrated in a case study on the robust decentralized level controller design of the quadruple tank process.

Robust decentralized switched controller design for linear continuous-time systems

Abstract The paper is devoted to obtain original equivalent subsystem method to design of decentralized controller for linear large scale systems. On the theoretical example a new robust decentralized PID switched controller design procedure is obtained for linear time-varying (gain scheduled plant model) uncertain complex system with decentralized output and input structure. Controller design procedure to decentralized controller design performs on the subsystem level. The designed decentralized switched controller ensures the robust stability of closed-loop complex polytopic system with performance H 2 quadratic cost function (QSR). The proposed practical examples with ideal or non-ideal switch of switching parameters show the effectiveness of equivalent subsystem approach.

Robust decentralized controller design based on equivalent subsystems

A method for robust decentralized controller design of continuous and discrete-time controllers for SISO and MIMO systems is proposed. The uncertain MIMO system is given by a set of square transfer matrices of any dimension. The design procedure relies on the Equivalent Subsystems Method (ESM) – an independent design of local controllers for stability and required performance of the overall system. The ESM has been extended by integrating robust stability conditions directly in the independent design of local controllers to obtain a unified robust decentralized controller design method. To demonstrate the design procedure, a discrete-time robust decentralized PID controller for a minimum-phase system was designed.

Robust MIMO Control for Interconnected DC Motors

The paper deals with the robust controller design using conventional approaches (Small Gain Theory, Equivalent Subsystems Method), and advanced robust genetic method for uncertain MIMO systems. Decentralised robust controllers designed using the Small Gain Theory (SGT) ensure robust stability for additive, input/output multiplicative uncertainties; the Equivalent Subsystems Method (ESM) guarantees the required performance in terms of phase margin and settling time for input/output multiplicative uncertainties. The genetic algorithm is based on optimisation procedure, where the cost function to be minimized comprises the closed-loop simulation of the controlled MIMO process and evaluation of a selected performance index. Using this approach, the PID controller parameters were optimised to obtain the required behaviour of the controller process. Practical implementation and comparison of the proposed methods are verified and tested on a real process - two interconnected DC motors with varying parameters.

Robust Switched System Controller Design in the Frequency Domain

A new frequency domain switched controller design procedure is proposed applicable for both SISO and MIMO multi-model systems represented in an affine form. Robust theoretic approach based on the Small Gain Theorem is used to develop a frequency domain condition for closed-loop stability of the multi-model plant in all operation modes as well as stability during switching between individual controllers. Using this condition, a robust switched controller design procedure based the Equivalent Subsystems Method is developed to guarantee robust stability in individual operation modes in addition. The developed design procedure is demonstrated on a case study. The designed robust switched controller has been successfully verified by experiments on a TITO laboratory plant.

Multiloop control of a drum boiler

The Equivalent Subsystems Method (ESM) (Kozáková et al., 2011) is methodology of decentralized controller design in the frequency domain which allows designing local controllers using any SISO frequency domain method. The paper deals with the digital ESM version where digital local PID controllers guaranteeing required performance for the full system are designed for individual equivalent subsystems using the practice-oriented Sine-wave method (Bucz et al., 2012). The proposed decentralized controller design procedure was verified on the nonlinear benchmark drum boiler simulation model (Morilla, 2012).

Robust control system design in frequency domain

Abstract In this paper two robust control methods for hybrid system are presented. Both methods are usefull for SISO and MIMO systems. Controller design procedure is developed in frequency domain. Equivalent subsystem method is used for controller design in this paper. Stability condition of proposed methods bases on small gain theory and uses additive and inverse additive model type. Two tank water system is presented in the paper and serves as a numerical example to compare effectiveness of described methods

A Unified Frequency Domain Method for Designing Robust Decentralized Controllers

The paper presents a unified frequency-domain methodology for designing robust continuous-and discrete-time controllers for both MIMO and SISO uncertain systems. The generalized design procedure is based on the Equivalent Subsystems Method (ESM) – a frequency-domain decentralized controller design method guaranteeing required performance for the full system. Plant-wide performance specification in terms of maximum overshoot and settling time is translated into frequency domain performance measures (phase margin and bandwidth frequency). Generating equivalent subsystems allows applying independent design of the resulting decentralized controller for both SISO and MIMO systems. Robust stability conditions are integrated in the ESM. The design procedure is applied to design a discrete-time robust decentralized PID controller for a non-minimum phase system.

Robust Decentralized Controller Design: Laboratory Project-Based Learning

The paper presents an original Nyquist-based frequency domain robust decentralized controller design technique called Equivalent Subsystems Method (ESM) being developed at the Institute of Control and Industrial Informatics (ICII), and shows how it is included in education of control engineers in Cybernetics within laboratory project-based learning on real-world laboratory plants.

Direct Design of Robust Decentralized Controllers

AbstractThe paper introduces an important enhancement to the robust decentralized controller design for multi input/multi output uncertain systems within the setting of the Equivalent Subsystems Method (ESM). The class of design problems considered includes guaranteeing robust stability and nominal performance in terms of maximum overshoot of the full system achieved through specified phase margins in equivalent subsystems. The developed design procedure is illustrated by an example.

Decentralized Digital PID Controller Design for Performance

The paper deals with the frequency domain decentralized discrete-time controller design methodology to guarantee specified performance of the overall system. The underlying theory evolves from the stability conditions developed in the “Equivalent Subsystems Method” approach and applies closed-loop performance specification based on the relationship between phase margins of equivalent subsystems and maximum overshoot of the full system. To design local PI controllers for specified phase margin, Bode plots of discrete equivalent subsystems are used. Designed local continuous controllers are then converted to their discrete versions and implemented for the controlled plant. The design procedure is illustrated on the case study.