Multi-input Multi-output Processes Research Articles

Circular economy-based multi-objective decentralized controller for activated sludge wastewater treatment plant

Introduction: Water scarcity and water pollution are two major issues in India. Circular economy-based wastewater treatment technology provides the most sustainable solutions for solving these issues. In this paper, a novel multi-objective decentralized controller (MODC) is proposed for benchmarking a multi-input multi-output (MIMO) activated sludge wastewater treatment plant (WWTP) to achieve maximum effluent quality with minimum cost. WWTPs with conventional control schemes consume more energy to achieve the desired effluent quality.Methods: In this study, a MIMO model is developed for the activated sludge process (ASP) from a physics-based model, and relative gain array (RGA) analysis are carried out to determine the interaction between the loops to identify a suitable control scheme for the MIMO process. In addition, a multi-objective decentralized control problem is formulated to achieve the conflicting multiple objectives of improving effluent quality and minimizing operational costs by efficient usage of energy.Results and discussion: The desired quality and cost reduction are verified by comparing the integral square error (ISE) and control effort (CE) values of a closed-loop WWTP. A multi-objective evolutionary algorithm (MOEA), namely, the non-dominated sorting genetic algorithm (NSGA)-II, successfully solves the multi-objective control problem. NSGA-II provides several optimal solutions in the Pareto front. In order to demonstrate the feasibility of the proposed controller, three optimal solutions are selected from the Pareto-optimal front, and their closed-loop performances are evaluated qualitatively and quantitatively for both servo and regulatory operations. Improving the quality of effluent enhances active sludge production, which in turn increases the methane production in the anaerobic digester.

Bayesian Optimization for automatic tuning of digital multi-loop PID controllers

In recent years, the use of Bayesian optimization (BO) for efficient automatic tuning of general controller structures through iterative closed-loop experiments, has been attracting increasing interest. However, its potential for tuning interactive multi-loop PID controllers in Multi Input Multi Output (MIMO) processes remains largely unexplored. Even though the optimization domain greatly affects closed-loop performance and safety, it is usually defined manually, through expert knowledge or experimentation. This paper presents a novel systematic methodology for defining the optimization domain for automatic multi-loop PID tuning using BO. Sequential loop closing, system identification and tuning relations are used to constrain the bounds on controller parameters to meaningful ranges, including gains and sampling times. This provides an effective way to improve the convergence of BO and secure process safety during closed-loop experiments, without requiring a MIMO process model or extensive prior knowledge. The methodology can be applied ”as is” to single-loop PID controllers.

Demand response for flat nonlinear MIMO processes using dynamic ramping constraints

Volatile electricity prices make demand response attractive for processes that can modulate their production rate. However, if nonlinear dynamic processes must be scheduled simultaneously with their local multi-energy system, the resulting scheduling optimization problems often cannot be solved in real time. For single-input single-output processes, the problem can be simplified without sacrificing feasibility by dynamic ramping constraints that define a derivative of the production rate as the ramping degree of freedom. In this work, we extend dynamic ramping constraints to flat multi-input multi-output processes by a coordinate transformation that gives the true nonlinear ramping limits. Approximating these ramping limits by piecewise affine functions gives a mixed-integer linear formulation that guarantees feasible operation. As a case study, dynamic ramping constraints are derived for a heated reactor-separator process that is subsequently scheduled simultaneously with its multi-energy system. The dynamic ramping formulation bridges the gap between rigorous process models and simplified process representations for real-time scheduling.

Control of dead-time process: From the Smith predictor to general multi-input multi-output dead-time compensators

This review paper deals with the analysis, design, and tuning of dead-time compensators for stable and unstable multi-input multi-output (MIMO) processes with multiple time delays. It is well known that, even in the single-input single-output case, processes with significant dead times are difficult to control using standard feedback controllers. For MIMO systems, the study of processes with dead time is more involved, particularly when the process behavior exhibits different dead times in the different input-output relationships. Because of this, much research has been conducted in the last 50 years on this subject, with different approaches and proposals of controllers for covering a variety of objectives. Thus, this paper gives an overview of this important topic, focusing on the solutions derived from the Smith Predictor. First, a historical perspective of the different controllers proposed in the literature is presented. Then, the general solution of the problem is developed, paying particular attention to robustness and disturbance rejection properties, because of their importance and usefulness in industrial processes. All the development is done in the discrete-time case, which allows direct digital implementation. Two simulation case studies are presented to illustrate some of the ideas discussed in the paper, and an experimental case study is used to discuss aspects of practical implementation.

Anti-disturbance composite tracking control for a coupled two-tank MIMO process with experimental studies

Coupled multiple-tank systems are very important for a wide range of industrial applications due to their unique uses. However, the liquid level control for the coupled two-tank multi-input multi-output (MIMO) system is quite challenging because it has strong nonlinearity and coupling, and it is susceptible to multiple external disturbances. For this process, this paper proposes a novel anti-disturbance control strategy consisting on a nonlinear composite hierarchical anti-disturbance predictive control (CHADPC). First, a model-based explicit nonlinear model predictive controller (ENMPC) is designed assuming that all disturbances are measurable and its global exponential stability is proved. Then, a nonlinear disturbance observer (DO) is designed to estimate the lumped disturbances. The composite controller handling the estimated disturbances is then proposed. Finally, simulation and experimental tracking control tests under perturbations and comparisons with recently reported works have been carried out to highlight the promising performance of the proposed ENMPC and CHADPC schemes.

Weighted sensitivity design of multivariable PID controllers via a new iterative LMI approach

This paper addresses the weighted sensitivity design of multivariable proportional–integral–derivative (PID) controllers for multi-input multi-output (MIMO) processes. First, the PID reference tracking problem is formulated into an H∞ PID control problem by using the weighted sensitivity synthesis, and the problem is further casted into an H∞ SOF control problem. Second, based on the idea of T–K iteration, a new iterative LMI algorithm has been developed to locally solve the optimal H∞ SOF control problem. Then, a design procedure is presented for weighted sensitivity design of multivariable PID Controllers for MIMO processes. Finally, three application examples are provided to show the effectiveness and good performance of our method for practical industrial processes.

The optimal detuning approach based centralized control design for MIMO processes

This manuscript introduces an optimal detuning approach for designing a centralized PI control system for multi-input multi-output (MIMO) processes. Based on the approach, two multivariable PI controller designs are proposed in this manuscript. The proposed approach formulates the centralized PI controller design problem in an optimization framework and transforms it into an equivalent detuning parameter(s) design problem. While the centralized controller design with the proposed 1-Optimal Detuning Parameter (ODP) method is carried out as a multi-stage problem, the proposed 2-ODP method formulates the controller design as a single-stage optimization problem. An effective transfer function (ETF) parameterization followed by controller synthesis using the IMC theory and further the optimal detuning comprises the various stages in 1-ODP design. In this regard, a novel ETF parameterization procedure for large scale processes or systems with higher-order elements is presented in this manuscript. Contrary to the centralized controller design in the kp,ki space, where the dimensionality of the optimization problem blows at O(2n2), the proposed 1-ODP and 2-ODP design methods always aim at solving a uni- and bi-dimensional optimization problem, respectively, irrespective of the dimensionality of the MIMO process. Hence, the proposed method is easily applicable even to high-dimensional MIMO processes. Several illustrative industrial MIMO systems are considered to demonstrate the applicability of the proposed methods to highly interacting and large scale processes. The simulation studies show that the proposed methods performs better as compared to the other centralized PI controller designs. Even with parameter variations, the proposed methods give satisfactory closed-loop performance. Further, robust stability analysis for the proposed designs is performed by considering multiplicative input and output uncertainties.

Centralized PI controller design method for MIMO processes based on frequency response approximation

A simple method of controller design for multi-input multi-output (MIMO) processes have been proposed in frequency domain. The intensive calculation for the inverse of the process transfer function matrix is simplified to a great extent by evaluating the process transfer function matrix at a low frequency point. The desired closed loop transfer functions are derived for the process using a single tuning parameter for each diagonal element of the process transfer function matrix which represents the desired closed loop time constant. Centralized PI controllers are then designed using a model matching technique by evaluating the transfer functions at a low frequency point. The PI controllers provide acceptable performances for lag dominated as well as time-delay dominated processes and is also applicable to high-dimensional processes. The proposed method is extended for the non-square MIMO processes using two approaches one of which squares up the process transfer function matrix to apply the proposed technique while the other is based on pseudo-inverse evaluation of the process transfer function matrix at a low frequency point.

Modelling of the adsorption of Pb, Cu and Ni ions from single and multi-component aqueous solutions by date seed derived biochar: Comparison of six machine learning approaches

Biochar is an effective material for the removal of heavy metals from wastewater. Operational conditions, such as metal initial concentration, temperature, contact time as well as the presence of competing ions can impact the effectiveness of the treatment process. While several models have been proposed for modelling the adsorption process, no model currently exists that accounts for the mutual interactions of key process parameters on the adsorption capacity in multi-solute systems. The aim of this study is to address this gap in knowledge by formulating a multi-input multi-output (MIMO) model, which takes into account the effect of mutual interactions of key factors while predicting heavy metals adsorption capacity of the biochar in single and multi-solute systems. In this study, we use machine learning models, specifically several ANN models, radial basis and gradient boosting algorithms to model the MIMO process. The results of our models provide highly accurate predictions (R2 > 0.99). The generalized regression network provided the best match to the experimental data. This approach can allow operators to predict how the adsorption system will respond to changes in the operations and hence provide them with a tool for process optimization.

Direct Adaptive Controllers for a Multi Input Multi Output Process

Control of nonlinear dynamic systems is of great practical importance, since virtually all real world systems belong to this class. The prevalent approach is to use a model of the process linearized about the steady state operating point to design linear controllers. The Multi Input Multi Output (MIMO) process considered in this paper has varying system dynamics. This paper focuses on the performance evaluation of multi-loop Adaptive MIT(AMIT) controller and Adaptive PI(API) controller with vanishing adaptation technique for a laboratory interacting coupled tank MIMO process.

Model Predictive Control with a Relaxed Cost Function for Constrained Linear Systems

The Model Predictive Control technique is widely used for optimizing the performance of constrained multi-input multi-output processes. However, due to its mathematical complexity and heavy computation effort, it is mainly suitable in processes with slow dynamics. Based on the Exact Penalization Theorem, this paper presents a discrete-time state-space Model Predictive Control strategy with a relaxed performance index, where the constraints are implicitly defined in the weighting matrices, computed at each sampling time. The performance validation for the Model Predictive Control strategy with the proposed relaxed cost function uses the simulation of a tape transport system and a jet transport aircraft during cruise flight. Without affecting the tracking performance, numerical results show that the execution time is notably decreased compared with two well-known discrete-time state-space Model Predictive Control strategies. This makes the proposed Model Predictive Control mainly suitable for constrained multivariable processes with fast dynamics.

An Integrated Method for Multi-Objective Optimization of Multi-Pass Fe50/TiC Laser Cladding on AISI 1045 Steel based on Grey Relational Analysis and Principal Component Analysis

As an essentially multi-input multi-output process, determination of optimal conditions for laser cladding normally requires multi-objective optimization. To understand multi-response coupling, the effects of processing parameters on the morphology quality of multi-pass laser claddings of Fe50/TiC on medium carbon steel AISI 1045 were investigated based on composite central design using response surface methodology. Multiple responses, including clad width, flatness, and non-fusion area, were transformed into a single objective through grey relational analysis, with weights objectively identified by principal component analysis. The correlation between grey relational grade (GRG) and process parameters was established by regression analysis. The results show that the GRG response model has excellent goodness of fit and predictive performance. A validation experiment was conducted at the process condition optimized for maximum GRG. The relative error of the predicted optimal GRG is 4.87% whereas those of interested individual objectives, i.e. clad width, flatness, and non-fusion area, are 5.73%, 2.97%, and 6.73%, respectively, which verifies the accuracy of the established model. The investigation of mechanical properties suggests the hardness of substrate can be improved from 20 HRC to 60 HRC and wear resistance to over 8.14 times better.

A Central Composite Design Approach to Minimize HAZ of TIG Weldments

Welding is a multi-input multi-output fabrication process, which requires a multi-response optimization technique. In this present work, the effect of heat affected zone and percentage dilution on the quality of Tungsten Inert Gas welded joints was investigated using mild steel plates. The Central Composite Design matrix was adopted to perform the welding experiment and collect the data, thereafter Response Surface Methodology (RSM) models was employed to minimize heat affected zone and percentage dilution with very significant statistical results. The result shows that the quadratic model was the most suitable for the HAZ data and the percentage dilution data with a P-value < 0.05 and R2 value of 88% and 90% for the HAZ and percentage dilution respectively.

Routh-Hurwitz tuning method for stable/unstable time-delay MIMO processes

This paper presents a new method of tuning decentralized Proportional Integral Derivative (PID) control system for an n×n Multi Input Multi Output (MIMO) processes which can be either open-loop stable or unstable with time-delays. The tuning method has been established via the classical Routh-Hurwitz criteria with the aid of PID stability theorem. This new tuning method requires only 3 common tuning parameters, thus simplifying the conventional multi-loop PID tuning task to obtain the values for 3n PID parameters. Two numerical examples are presented to demonstrate the effectiveness of the proposed tuning procedure over some of the existing multi-loop PID tuning procedures. The proposed tuning procedure shows a good performance as well as able to simplify the tuning task as compare to the existing tuning method.

Online Validation of Relay based Identification and Controller Design with an Anti-Reset Windup for a Binary Distillation Column

Sequential auto-tuning based model identification is a closed loop approach, which has an extensive benefit compared to conventional methods because of user defined manipulated gain to the process within the verge of instability. Model parameters estimation of multi input multi output process is challenging because of existence of multivariable interaction among the variables. In this paper ideal relay is used as a sequential basis for binary distillation column in real time. Obtaining sustained oscillations in conventional methods is based on trial and error, benefit of relay is that oscillations can be generated as scaling of user defined gains. Predictive PI control algorithm is implemented. Results depicts the efficiency of methodology and importance of anti-reset term in the algorithm.

Online Validation of Relay based Identification and Controller Design with an Anti-Reset Windup for a Binary Distillation Column

Sequential auto-tuning based model identification is a closed loop approach, which has an extensive benefit compared to conventional methods because of user defined manipulated gain to the process within the verge of instability. Model parameters estimation of multi input multi output process is challenging because of existence of multivariable interaction among the variables. In this paper ideal relay is used as a sequential basis for binary distillation column in real time. Obtaining sustained oscillations in conventional methods is based on trial and error, benefit of relay is that oscillations can be generated as scaling of user defined gains. Predictive PI control algorithm is implemented. Results depicts the efficiency of methodology and importance of anti-reset term in the algorithm.

Application of RBFNNs Incorporating MIMO Processes for Simultaneous River Flow Forecasting

Simultaneous flow forecasting using multi-input multi-output (MIMO) processes is an efficient technique for accurate flow forecasting on river systems. The present study demonstrates the capability of radial basis function neural networks (RBFNN) incorporating MIMO processes in simultaneous river flow forecasting. The river system considered in the present study was the Barak river system, Assam, India. Hourly concurrent discharge data were collected from the Central Water Commission, Shillong, India from multiple sections of the Barak river system. The forecasts were tested for short-range time horizons, i.e. 1, 3, 6 and 12 hours in advance, and a comparative analysis was done using the popular Nonlinear Autoregressive with Exogenous Inputs (NARX) time series model. The result shows that MIMO-NARX provided higher prediction accuracy than MIMO-RBFNN, even at longer lead times when compared to following various statistical criterions.

An iterative LMI approach for H∞ synthesis of multivariable PI/PD controllers for stable and unstable processes

An iterative linear matrix inequality (LMI) approach for designing multi-input multi-output (MIMO) PI/PD controller for stable/unstable multivariable processes is proposed in this paper. For this purpose, the matrix gains of controller are calculated such that the closed-loop system be stable, and simultaneously, the infinity norm of the weighted sensitivity function is minimized. This problem is mathematically formulated using the well-known bounded real lemma (BRL). The matrix inequality of the BRL is nonlinear because of multiplication of the variable of Lyapunov equation and gains of controller. To remove this nonlinearity, first a solution to the Lyapunov LMI is calculated using some necessary-type LMIs developed for this purpose. Then, this solution is substituted in the BRL to arrive at an LMI whose solution determines the gains of a stabilizing MIMO PI/PD controller which also minimizes the infinity norm of the weighted sensitivity function. If the resulting controller was not satisfactory, one can use the proposed iterative algorithm to improve its performance. The proposed method is used for tuning MIMO PI/PD for four stable/unstable MIMO processes.

Kalman filter-based centralized controller design for non-square multi-input multi-output processes

In this paper, a simple and effective centralized controller is presented to control non-square multi-input multi-output industrial processes with heavy interactions and significant time-delays. The control objective is to achieve a good load disturbance rejection and set point tracking. The controller and process model equations are represented in a stochastic state-space. Also, the state and measurement equations respectively use general random walk model and finite impulse response model of the plant. To design the controller, a quadratic cost function including the control error vector as well as the input vector and its changes is introduced. A Kalman filter algorithm is used to solve the discrete algebraic Riccati equation and to estimate the state vector of the controller recursively. This novel use of Kalman filter combines the observer and controller in a block. No square down/up, pairing and pseudo-inversing, is required for the proposed control structure. This leads to the simplicity of controller design. To evaluate the performance of the proposed control strategy, it is applied to a simulation example and an industrial case study with heavy interactions and significant time delays, an atmospheric distillation column with 7 inputs and 4 outputs. Simulation results show that the proposed controller has a good performance in both load disturbance rejection and setpoint tracking.

Model-Free Fuzzy Adaptive Control for MIMO Systems

Control of multi-input multi-output (MIMO) plants poses a challenging control problem. The problem becomes much more complicated if the degree of interaction between the inputs and outputs is high. Most of the MIMO control schemes do not take into consideration the cross-coupling effect and are based on either decoupled or decentralized control schemes. These schemes can offer acceptable control performance if the degree of interaction is low. Ignoring the interaction is unrealistic for many plants and employing multiple MISO controllers results in degraded control performance. Almost all such strategies require a plant model a priori. In this work, an extension of SISO model-free fuzzy adaptive controller (MFFAC) is proposed for MIMO plants while taking into consideration the cross-coupling effect. No a priori knowledge about the plant is assumed, and the control scheme does not make use of any decoupler. SISO MFFAC is based on a special type of reinforcement learning, i.e., feedback error learning (FEL). The control architecture of SISO MFFAC is modified to work with MIMO plants by proposing a novel FEL scheme. The novel FEL mechanism incorporates the interaction between the input and output of a MIMO process by using relative gain array (RGA). Simulation results have demonstrated the efficacy of the proposed MIMO control scheme.