Two-input Two-output Processes Research Articles

Design of decentralized proportional–integral proportional–retarded controllers in discrete-time domain for two-input two-output processes

In this paper, a decentralized proportional–integral proportional–retarded (PI-PR) controller design method is proposed for two-input two-output (TITO) systems in discrete-time domain. The well-known dominant pole assignment (DPA) approach is used as the basis of the proposed approach. The controller design starts with the decoupling of a given TITO system into two sub-systems and continues with the design of proportional–integral–retarded (PIR) controllers for each sub-system, respectively. The feasible discrete PIR controller parameter set is obtained through the Nyquist stability criterion by considering the desired closed-loop performance specifications. The obtained PIR controllers are then implemented using a PI-PR control structure to avoid poor performance of the closed-loop system (CLS) transient response, which can be caused by the controller zeros. Moreover, a case study is presented to show the performance of the PI-PR controller in a simulation environment. It is shown that the proposed control structure provides a satisfactory performance when compared with the other proportional–integral–derivative (PID) control methods from the literature.

System Identification and Design of Inverted Decoupling IMC PID Controller for Non-Minimum Phase Quadruple Tank Process

A systematic analytical and experimental method of identification of Two Input Two Output (TITO) Quadruple-Tank Process (QTP), operated at non-minimum phase condition has been presented. Parameters of the process transfer function matrix have been validated on an experimental laboratory-scale physical setup of the process. Appropriate input-output pairing and interaction among control loops have been studied based on the Relative Gain Array (RGA) analysis. Inverted Decoupling Internal Model Control (IMC) based Proportional Integral Derivative (PID) controller has been designed for the TITO process. The effect of changes in controller tuning parameters on the closed-loop response for servo problem has been reported in terms of quantitative performance indices such as Integral of Square of Error (ISE), Integral of Absolute Error (IAE), percentage overshoot and offset. The simulation results have been compared with the literature.

Proportional-Integral Controller with Decouplers for an interacting TITO Process

Proportional-Integral (PI) controllers are currently used in several industrial processes for controlling the process parameters. In this work a method has been formulated to design the controller for a multi input and multi-output (MIMO) unstable system by considering its effective transfer function (ETF). The approach mentioned, separates the unstable poles of the system into independent loops of the MIMO process with their own ETF’s. The process considered is First Order Process with Time Delay (FOPTD) and PI controllers are modelled for their diagonal components by using ETF synthesis method to counteract unstable characteristics. The design has a two-loop architecture in order to minimize the overshoot, as it is evident that the overshoot is maximum for unstable processes having a single control feedback structure. The controller design is tested for its efficacy on a Two Input Two Output (TITO) system and the results are highlighted for servo as well as regulatory response.

Evaluation and Redesign of Simplified Decouplers for TITO Processes Using Relay Experiments

Effective decoupling is not always achieved due to unavoidable model mismatch or change in the operating point. Thus, evaluation and redesign of the decoupler may improve performance. The redesign of decouplers is a subject that received little attention in the literature. In this paper, a methodology to evaluate and redesign simplified decouplers for two-input two-output (TITO) processes in open-loop using relay experiments is proposed. The decoupler redesign aims at achieving an effective decoupling at two frequencies of interest. The initial decoupler is evaluated by applying a relay-based excitation signal with two frequency components to the decoupled process. The initial decoupler is redesigned to eliminate the decoupler error at each one of the frequencies. Simulation and experimental results are used to illustrate the effectiveness of the methodology.

A single-step identification strategy for the coupled TITO process using fractional calculus

The reliable performance of a complete control system depends on accurate model information being used to represent each subsystem. The identification and modelling of multivariable systems are complex and challenging due to cross-coupling. Such a system may require multiple steps and decentralized testing to obtain full system models effectively. In this paper, a direct identification strategy is proposed for the coupled two-input two-output (TITO) system with measurable input–output signals. A well-known closed-loop relay test is utilized to generate a set of inputs–outputs data from a single run. Based on the collected data, four individual fractional-order transfer functions, two for main paths and two for cross-paths, are estimated from single-run test signals. The orthogonal series-based algebraic approach is adopted, namely the Haar wavelet operational matrix, to handle the fractional derivatives of the signal in a simple manner. A single-step strategy yields faster identification with accurate estimation. The simulation and experimental studies depict the efficiency and applicability of the proposed identification technique. The demonstrated results on the twin rotor multiple-input multiple-output (MIMO) system (TRMS) clearly reveal that the presented idea works well with the highly coupled system even in the presence of measurement noise.

Fractional-order two-input two-output process identification based on Haar operational matrix

The identification of multi-input-multi-output process is always challenging due to significant loop interactions. This article proposes an identification technique for two-input-two-output processes with fractional order models via Haar wavelet feature. The presented technique can estimate independent four fractional single-pole time delay models without additional steps to decouple processes during identification. The method uses a well-known relay feedback test to produce the input-output data for measurements. Then, the Haar wavelet operational matrix based algebraic approach is utilised to identify the unknown process models with reduced complexity. Numerical analysis on various examples show the efficacy even in presence of noise and without additional filter or preprocessing of measured signals. The comparative study proves advantages of the presented approach.

An FO–[PI]λ controller for inverted decoupled two-input two-output coupled tank system

ABSTRACTIn this paper, a new structured fractional order-[proportional integral] () controller design method is demonstrated. The designed controller is implemented in decoupled Two-Input Two-Output (TITO) Coupled Tank System (CTS) for liquid level control. An inverted decoupling technique is used to decouple the TITO process into two independent SISO (single-input single-output) processes. The designed controller is implemented for each SISO process. A frequency domain approach is used to tune the parameters of the controller. While designing, to approximate the fractional integral terms of the controller, Oustaloup's Recursive Approximation (ORA) method is used in the stable frequency bands. To validate the proposed approach, the performance of the controller is compared with the existing controllers designed based on the same specifications. From the simulation and experimental studies, it is shown that proposed gives better performance than , PI and PID controllers.

Auto-tuning of FOPI Controllers for TITO Processes with Experimental Validation

In this paper, the auto-tuning of a fractional order proportional and integral (FOPI) controller is proposed and experimentally validated for two-input two-output (TITO) processes. The proposed method first identifies an unknown TITO plant into fractional order TITO model with time delay. Furthermore, decoupling the TITO process into two fractional order single-input single-output (SISO) transfer function models makes it easier for designing the decentralized FOPI controllers. The proposed control method is a generalization of both integer order and fractional order TITO systems depending on the value of the order of the model. One advantage of this method is the non-requirement of a-priori information of gain and phase crossover frequencies of the system while tuning the controllers. The proposed algorithm is validated both by simulation of a class of TITO process models as well as by experimental analysis of a coupled tank system (CTS).

Fractional order IMC based PID controller design using Novel Bat optimization algorithm for TITO Process

An independent design of adaptive multiloop fractional order internal model control based PID (FOIMC-PID) controller for a two input two output process (TITO) is presented. The multivariable system is decomposed by ideal decoupler to develop effective open loop transfer function (EOTF) and then it is approximated into first order plus dead time (FOPDT) model. The multiloop FOIMC-PID controller is designed for TITO model and controller parameters are optimally tuned using Novel Bat Optimization Algorithm (NBOA). The simulation results are demonstrated to show the effectiveness of proposed controller and also some tuning procedure is suggested to get better FOIMC-PID controller performance.

Modified approach to distillation column control

This paper contains methodology research for forming the control algorithm for a distillation column, modeled as TITO (two-input two-output) process. Its modified form was obtained by connecting the two parts, and this combination hasn't been applied for such a industrial plant, until now. These parts include: a simplified decoupler which was first designed and decentralized PID controller obtained using D-decomposition method for such decoupled process. The decoupler was designed in order to make process become diagonal, and parameters of PID controllers are defined for the two SISO (single-input single-output) processes starting from relation between IE (integral error) criterion and integrator gain, taking into account desired response characteristics deriving from technological requirements of controlled plant. Their connecting provides centralized control. Analysis of the processes responses, obtained by the proposed algorithm and their comparison with the results from the literature, were performed after the completion of the simulations. The proposed approach to the centralized controller design, beside its simplicity of usage and flexibility in achieving diversity of process dynamic behavior, gives better response characteristics, in comparison with existing control algorithms for distillation column in the literature.

Decentralized PID controller design for TITO processes with experimental validation

In this paper, a design method of decentralized proportional–integral–derivative (PID) controller for two-input two-output processes based on pre-defined reference transfer function is proposed. An ideal decoupler is used to reduce the interaction among system variables. Free structure higher order diagonal controllers are computed for each decoupled subsystem by specifying closed-loop response in terms of dominant reference second order transfer function. Further, to obtain controllers in PID structure, the higher order diagonal controllers are truncated into first three terms of Maclaurin series. The stability of resulting PID controller is investigated. Two benchmark examples are illustrated to show the effectiveness of the proposed controller. An experimentation is performed on interacting coupled tank process to demonstrate the applicability in real life applications.

Mathematical modelling of the simplest fuzzy two-input two-output proportional integral or proportional derivative controller via Larsen product inference

In this paper, a mathematical model of the simplest Mamdani type fuzzy two-input two-output (TITO) proportional integral (PI) or proportional derivative (PD) controller using Larsen product inference is presented. Components of the fuzzy controller include two fuzzy sets on each input variable, five fuzzy sets on each output variable, five linear control rules, algebraic product AND operator, bounded sum OR operator, Larsen product inference, and Centre of Sums (CoS) defuzzification. Each output of the fuzzy controller is shown to be the sum of two nonlinear PI (or PD) controllers with variable gains that change continuously with TITO process outputs.

Decentralized discrete sliding mode controller for TITO processes with time delay with experimental application

Multiple input multiple output systems posses interaction among the variables and hence are difficult to control. In addition, if these systems have slow and non-linear dynamics with time delays; it becomes more difficult to control them under the effect of parametric uncertainty. This paper presents the decentralized discrete time sliding mode controller (DSMC) for the robust tracking of two input two output (TITO) chemical processes with time delay. The ideal decoupler is used to reduce interaction among the system variables by forming decentralized structure consisting decoupled subsystems. Then for each subsystem, DSMC is independently designed and the control signal is applied to the TITO system after passing it through the decoupler. In the design procedure, an optimal sliding surface is chosen as a linear function of the system’s state error and the coefficients of sliding surface are computed by minimizing the quadratic performance index. A delay ahead predictor–corrector is used to handle system’s time delay and plant-model uncertainties. The control law is derived from the discrete time state model and sliding surface. A variable gain switching control law is proposed which results into power rate reaching law with power equal to 1. The methodology integrates ideal decoupler, optimal sliding surface and delay ahead prediction–correction; and therefore results optimal performance of the systems with less interaction. The stability condition is derived using Lyapunov approach. The stability condition results into chatter free convergent quasi sliding mode. Two benchmark simulation examples are used to demonstrate effectiveness of the proposed controller and an experimentation is performed on interacting coupled tank level control system to show its applicability to real life non-linear TITO systems.

Identification of two‐input two‐output process using state‐space analysis

An analytical expression for the exact identification of two-input two-output (TITO) process using hysteresis relay is presented in this study. The identified transfer matrix consists of four independent first-order plus delay time (FOPDT) models and the time constants, delays and the gains of the FOPDT models are obtained from the limit cycle measurements. In this study, analytical expressions are derived using state-space analysis to identify the exact transfer matrix of the TITO process (TITO system). Problem of chattering and measurement noise is attenuated using relay with hysteresis. The simulation examples and real-time experiment show the effectiveness of the proposed method.

Static Decouplers with P-PI Dual Loop Controllers for Unstable System

The applicability of static decoupler followed by tuning of diagonal proportional integral controllers for unstable multivariable process is studied. The need of static decouplers for an unstable multivariable system where the conventional decouplers becomes unstable is brought about by using three examples of a two-input two-output processes. Further, dual loop controllers are tuned for the approximated decoupled system. Use of P-PI (Proportional – Proportional and Integral) dual loop control system reduces the overshoot significantly.

Adaptive integral filter for the identification of two-input two-output processes

Measurement noise and loop interaction introduce errors during the identification of a two-input two-output (TITO) process. This paper proposes a novel method for the identification of a TITO process in the presence of measurement noise and loop interaction. The proposed structure includes two preload relays (P_relays) in the forward paths and two adaptive integral filters in the feedback paths to induce the limit cycle outputs. The integral filters are designed adaptively during the identification. The integral filters in the feedback paths reduce the interaction between the loops and induce denoised limit cycle outputs. Then a pair of parametric transfer function models for the TITO process dynamics is obtained using the limit cycle information. Also, a new approach to estimate the steady state gains of the models is proposed. Simulation examples illustrate the effectiveness and the simplicity of the proposed identification and control method.

A graphical approach to computing loop gain margins for TITO systems

An effective method is presented to compute the loop gain margins exactly for two-input–two-output processes. The stable regions in parameter space are first obtained by determining the stability boundaries and the loop gain margins found within the stable regions. Examples are provided for illustration and comparison with other methods.

Self-Tuning Weighting Factor to Decoupling Control for Incubator System

This paper is focused on a design of an algorithm for decoupling multivariable systems based on generalized predictive control (DGPC) and its application to a control of an incubator system. Proposed control algorithm uses adaptive error weighting factor in cost function in order to reduce coupling between control loops. Two techniques are presented and compared for predictive control of TITO (Two-Input, Two-Output) processes. According to the first technique the weighting factor is tuned in synchronization to a reference signal change. According to the second method, the weighting factor is set dependent on the actual control error. The algorithm is applied to incubator climate control; obtained simulation results show its efficiency.

Decoupling Control Approach for Neonate Incubator System

This paper presents an adaptive decoupling temperature and humidity control for neonatal incubator process by exploiting an active humidification system. The neonatal incubator is a Two-Input Two-Output process (TITO) with characteristics of strong coupling and time variation. The coupling problem is treated by the weight adjustment of the output error to reduce the effect of coupling and to enhance control performance. In addition, an Adaptive Decoupling strategy based on Generalized Predictive Control (ADGPC) with Multivariable Recursive Extended Least-Squares (MVRELS) parameters estimator is used. The simulation and real results demonstrate that the decoupling by error dependent tuning of the weighting factor can eliminate the coupling influence with better control performance and can be easily generalized to the Multiple-Input – Multiple-Output (MIMO) systems. General Terms Incubator process, Multivariable system, Decoupling Predictive Control.

Decentralized PI/PID controllers based on gain and phase margin specifications for TITO processes

In this paper, a decentralized PI/PID controller design method based on gain and phase margin specifications for two-input–two-output (TITO) interactive processes is proposed. The decouplers are designed for systems to minimize the interaction between the loops, and the first order plus dead time (FOPDT) model is achieved for each decoupled subsystem based on the frequency response fitting. An independent PI/PID controller is designed for each reduced order decoupled subsystem to obtain the desired gain and phase margins, and the performance is verified on the original interactive system to show the effectiveness of the proposed design method for the general class of TITO systems. Simulation examples are incorporated to validate the usefulness of the presented algorithm. An experimentation is performed on the Level–Temperature reactor process to show the practical applicability of the proposed method for the interactive system.