Multivariable Control Systems Research Articles

Control strategy for power factor correction circuits based on model predictive control

Power factor correction circuits are being used more extensively, and with that, the requirements and standards have become increasingly stringent. To improve the power factor of the circuit, thereby improving its operational efficiency and mitigating the load effects in boost power factor correction circuits, reducing Total Harmonics Distortion is crucial for improving the quality of the current. An improvement upon the conventional dual-loop PID control algorithm has been proposed. It involves integrating Model Predictive Control into the current loop design and incorporates a Luenberger observer. Model Predictive Control methods can be applied for the control of multivariable systems, especially in complex multivariable systems, as they exhibit strong robustness. Finally, by performing both simulation and experimental validations and analyzing the data results, it is shown that under full load conditions, the power factor λ is 0.968, the efficiency η is 91.11%, the voltage total harmonic distortion Uthd is 1.88%, and the current total harmonic distortion Ithd is 7.04%. These data results strongly confirm the performance of the control mechanism proposed in this paper.

Grey-Box Modeling and Decoupling Control of a Lab Setup of the Quadruple-Tank System

The quadruple-tank system (QTS) is a popular educational resource in universities for studying multivariable control systems. It enables the analysis of the interaction between variables and the limitations imposed by multivariable non-minimum phase zeros, as well as the evaluation of new multivariable control methodologies. The works utilizing this system present a theoretical model that may be too idealistic and based on erroneous assumptions in real-world implementations, such as the linear behavior of the actuators. In other cases, an identified linear model is directly provided. This study outlines the practical grey-box modeling procedure conducted for the QTS at the University of Cordoba and provides guidance for its implementation. A configurable nonlinear model was developed and controlled in a closed loop using different controllers. Specifically, decentralized control, static decoupling control, and simplified decoupling control were compared. The simulation designs were experimentally validated with high accuracy, demonstrating that the conclusions reached with the developed model can be extrapolated to the real system. The comparison of these three control designs illustrates the advantages and disadvantages of decoupling in certain situations, especially in the presence of non-minimum phase zeros.

Design of Multivariable PID Control Using Iterative Linear Programming and Decoupling

The design of multivariable process control systems is specially complicated when there are strong interactions between the different control loops, and even more with multiple time delays. This paper proposes an iterative design method of centralized proportional-integral-derivative (PID) controllers for stable linear systems. The methodology is based on the linear parameterization of equivalent loop transfer functions (ELTFs) for centralized control. These functions capture the dynamics of the other loops and, from a prior design, allow solving the design problem at each iteration with linear programming that shapes the Nyquist plot of the ELTFs in the frequency domain, which also avoids the need for approximations. Two optimizations are proposed: (I) maximizing integral gains by fulfilling linear robustness margins in each ELTF and (II) maximizing linear robustness margins by fulfilling minimum bandwidths in each loop. In both optimizations, static decoupling and decoupling at a frequency close to the bandwidth of each loop are included as constraints, which improves the decoupling performance and the procedure convergence. The effectiveness of the method is verified in three simulation examples (square and non-square) and a lab experimental process. The proposed designs achieve a similar or better response when compared to that achieved by other authors.

Sir Alistair G. J. MacFarlane. 9 May 1931—2 November 2021

Sir Alistair MacFarlane was a gifted engineer with a fascination for feedback control systems from his industrial experience on radar systems through to his university research on multivariable control system design. He managed to excel in both practical design and mathematical analysis. He was also exceptionally effective, charismatic and visionary in leadership positions at both Cambridge and Heriot-Watt universities.

Multivariable Fractional-Order Controller Design for a Nonlinear Dual-Tank Device

Fractional calculus is defined by expanded integer order integration and differentiation. In this paper, multiple mathematical models of a nonlinear dual-tank device are precisely formulated by fractional calculus. Using the accurate model, a multivariable fractional-order controller is designed for nonlinear devices. The merits of the fractional-order design include: (1) control of multivariable nonlinearities, (2) compensation of uncertainties, and (3) elimination of coupling effects. Simulations and experiments are conducted to verify the precision of the fractional order models and the effectiveness of the multivariable fractional-order control system design.

Non-classical method of calculating the integral component in regulators of multivariable discrete time control systems

Non-classical method of calculating the integral component in regulators of multivariable discrete time control systems

Simultaneous tuning of multiple PID controllers for multivariable systems using deep reinforcement learning

Traditionally, tuning of PID controllers is based on linear approximation of the dynamics between the manipulated input and the controlled output. The tuning is performed one loop at a time and interaction effects between the multiple single-input-single-output (SISO) feedback control loops is ignored. It is also well-known that if the plant operates over a wide operating range, the dynamic behaviour changes thereby rendering the performance of an initially tuned PID controller unacceptable. The design of PID controllers, in general, is based on linear models that are obtained by linearizing a nonlinear system around a steady state operating point. For example, in peak seeking control, the sign of the process gain changes around the peak value, thereby invalidating the linear model obtained at the other side of the peak. Similarly, at other operating points, the multivariable plant may exhibit new dynamic features such as inverse response. This work proposes to use deep reinforcement learning (DRL) strategies to simultaneously tune multiple SISO PID controllers using a single DRL agent while enforcing interval constraints on the tuning parameter values. This ensures that interaction effects between the loops are directly factored in the tuning. Interval constraints also ensure safety of the plant during training by ensuring that the tuning parameter values are bounded in a stable region. Moreover, a trained agent when deployed, provides operating condition based PID parameters on the fly ensuring nonlinear compensation in the PID design. The methodology is demonstrated on a quadruple tank benchmark system via simulations by simultaneously tuning two PI level controllers. The same methodology is then adopted to tune PI controllers for the operating condition under which the plant exhibits a right half plane multivariable direction zero. Comparisons with PI controllers tuned with standard methods suggest that the proposed method is a viable approach, particularly when simulators are available for the plant dynamics.

The Influence of Competition Rules on the Difficulty Groups of Aerobics

The competition rules are the directional indicators of competitive sports, which not only restrict the direction of sports technology, but also promote the development of sports events. Difficulty movements are an important component of aerobics, determining the level of athletes' competition results, and also one of the important judgments of judges. The selection and use of difficulty action groups for participating athletes should comply with the requirements of the rules. There are a total of four difficulty groups in aerobics. In competition statistics, Group C has the highest usage rate of nearly 50% among the four groups, while Group B has the least number of difficulty choices and a relatively single difficulty type. Considering the adjustment of one's own set of difficulty groups based on the opponent's strength, the athlete's performance system during the competition exhibits a three-dimensional, open, fluctuating, and multivariate complex control system.

Hybrid Optimization of Controller for Multi-variable System

Hybrid Optimization of Controller for Multi-variable System

Stability by assigning structures by applying the multivariable subspace identification algorithm for a wind system with a DFIG

In this paper, a controller for a doubly fed induction generator (DFIG) connected to a wind system is proposed. This control assigning its own structures as an optimal control method, the electric model in the DFIG state space is also shown, for which it is expected to estimate a linear model through the subspace technique and thus to design the controller. It will be possible to show that a structure assignment controller is undoubtedly a good option for the control of multivariable systems. The results of the output signals will be analyzed when applying the controller, assigning their own structures, which will allow us to observe that the response and disturbance times are below two tenths of a second.

Stability Augmentation in Lateral Directional Dynamics: A Multivariable Approach

This paper delves into the concept of stability augmentation in lateral-directional dynamics, focusing on a multivariable approach. In aircraft control systems, ensuring lateral-directional stability is crucial for safe and efficient flight. The primary objective is to examine the feedback control system's role in enhancing stability and how it interacts with the aircraft's inherent dynamics. We begin by exploring the basic augmentation system for lateraldirectional dynamics, which includes the feedback of body-axis roll rate to ailerons and yaw rate to the rudder, commonly referred to as the yaw damper. One of the key challenges addressed in this paper is the need to overcome the interference caused by the yaw damper when coordinating turns. This interference results from the constant nonzero yaw rate present during coordinated turns. To address this issue, the concept of "transient rate feedback" is introduced, which uses a washout filter to differentiate the feedback signal and minimize its effect during steady-state conditions. The paper presents mathematical models and transfer functions that describe the behavior of the lateral-directional augmentation system. It discusses the impact of different parameters, such as the time constants of actuators and washout filters, on the system's performance. The design of the feedback loops for roll and yaw control is elaborated upon, emphasizing the trade-offs between roll response, dutch roll damping, and roll-yaw coupling. Simulation results are used to evaluate the effectiveness of the stability augmentation system in improving the aircraft's roll response and dutch roll damping under varying flight conditions. The paper concludes with insights into the challenges and benefits of multivariable control system design for lateral-directional stability augmentation in aircraf

A bivariate CUSUM control chart based on exceedance statistics

AbstractIn manufacturing systems, statistical process control (SPC) is used to detect unusual observations in the process. Most control charts are composed based on the normality assumptions of the observations. However, checking the normality assumption in multivariate control systems cannot be practical in real‐life applications. As a result, we propose a nonparametric bivariate cumulative sum control chart (CUSUM) based on exceedance statistics for detecting the shifts in location parameters. Since the proposed chart (BCUSUM‐EX) relied on exceedance statistics and is nonparametric, the use of the chart is straightforward and practical for users. Moreover, due to the nature of CUSUM charts, the proposed chart contains information about historical and current observations. The performance of the BCUSUM‐EX chart is compared with the spatial sign CUSUM (SS‐CUSUM) control chart under some well‐known bivariate distributions such as bivariate normal, t, and gamma. The BCUSUM‐EX chart's performance is better than the SS‐CUSUM control chart regarding run length characteristics. Lastly, to show the importance of the proposed control chart, the BCUSUM‐EX chart has been applied to the aluminium electrolytic capacitor manufacturing process.

Evolutionary design of marginally robust multivariable PID controller

Two Margin-based design methods for tuning of decentralized PI controllers for multivariable systems are presented. The first method is predefined marginally robust controller (PMR) which is based on solving a constrained optimization problem to satisfy the desired values of the multivariable phase and gain margins that are set based on the designer’s knowledge of the working condition of the plant. The second method is self-setting marginally robust (SMR) that is an automatic controller design procedure. This method, by solving a many-objective optimization problem (MaOP), sets controller coefficients and finds optimum gain and phase margins. It offers a trade-off between tracking, interaction, and robustness. Evolutionary algorithm is applied to solve the problems and disk margin to define the multivariable stability margins. Proposed methods by combining the simplicity of margin-based design and effectiveness of optimization problems offer a practical solution in tuning the industrial multivariable controllers. Simulation results show that these methods are simple, practical, and at the same time, comparable with other robust multivariable controllers.

Machine learning-based ethylene and carbon monoxide estimation, real-time optimization, and multivariable feedback control of an experimental electrochemical reactor

Electrochemical reduction of CO2 gas is a novel CO2 utilization technique that has the potential to mitigate the global climate crisis caused by anthropogenic CO2 emissions, and enable the large-scale storage of energy generated from renewable sources in the form of carbon-based chemicals and fuels. However, due to the complexity of the electrochemical reactions, the explicit first-principles models for CO2 reduction are not available yet, and there has been a limited effort to develop process modeling, optimization and control of CO2 electrochemical reactors. To this end, a rotating cylinder electrode (RCE) reactor has been constructed at UCLA to understand the mass transfer and reaction kinetics effects separately on the productivity. In the RCE reactor, the applied potential strongly influences the reaction energetics and the electrode rotation speed affects the hydrodynamic boundary layer and modifies the film mass transfer coefficient, which involves convective and diffusive transport. The present work aims to develop a multi-input multi-output (MIMO) control scheme for the RCE reactor that integrates techniques from artificial and recurrent neural network modeling, nonlinear optimization, and process controller design. Specifically, production rates of two products from the experimental reactor, ethylene and carbon monoxide, are controlled by manipulating two inputs, applied potential and catalyst rotation speed. Process dynamics and controllability are analyzed, a feedback control strategy is designed and the controllers are tuned accordingly. The experimental electrochemical cell is employed to gather data for process modeling and implement the multivariable control system. Finally, the experimental results are presented which demonstrate excellent closed-loop performance by the control system and regulation of the outputs at three different set-points including an economically-optimal set-point.

Performance-Seeking Control of Aero-Propulsion System Based on Intelligent Optimization and Active Disturbance Rejection Fusion Controller

To investigate the performance potential of the aero-propulsion system and the problem of control mode conversion, this paper takes the inlet/engine integrated component-level model as the research object, and a performance-seeking control (PSC) scheme based on the neighborhood-based speciation differential evolution–grey wolf optimization (NSDE-GWO) algorithm is designed and combined with an active disturbance rejection control (ADRC) to establish a multivariable fusion closed-loop control system. The analysis reveals that the NSDE-GWO hybrid algorithm, which takes advantages of the two algorithms, significantly improves the computing efficiency and optimization accuracy, achieving better optimization solutions in three different modes. The intelligent fusion controller is able to achieve a smooth transition of performance modes to ensure that the engine is provided with a stable thrust during operation under supersonic conditions, and the potential for performance optimization is maintained at a reasonable level. Maximum installed thrust mode capable of achieving no thrust loss and a maximum fluctuation rate within 2000 N/s, with the largest variation in thrust during the conversion being less than 0.9% under the minimum turbine temperature mode and the minimum specific fuel consumption mode. This study presents a theoretical foundation and engineering applications for the design of supersonic propulsion system controllers.

Computation of the phase and gain margins of MIMO control systems

This paper solves the problem of exact computation of the phase and gain margins of multivariable control systems. These stability margins are studied using the concept of the Davis–Wielandt shell of complex matrices. Calculation of the phase and gain margins requires solving a quadratically constrained quadratic program (QCQP) and a parametrized quadratically constrained problem, respectively, which are known to be difficult in general. The semidefinite relaxation (SDR) technique is often used as a computationally efficient approximation technique to solve QCQPs. It turns out that the QCQPs formulated from the phase and gain margin problems in this paper fall under the class of quadratic optimization problem, for which the SDR is exact. This is so in the sense that optimal values of the QCQP and its SDR are equal, and an optimal solution for the original QCQP problem can be obtained from an optimal solution of its SDR. Thus, we are able to propose computationally efficient algorithms to compute the phase and gain margins with an arbitrarily high precision. Numerical examples are given to illustrate the effectiveness of the proposed algorithms.

Gain-Phase Margin of MIMO Control Systems

This paper defines the gain-phase margin of multivariable control systems. This stability margin is studied using the concept of the Davis-Wielandt shell of complex matrices. The lower bound of the gain-phase margin is obtained using the semidefinite relaxation of a parametrized quadratically constrained quadratic program. Numerical examples are given to illustrate the effectiveness of the proposed algorithm.

Minimal-norm state-feedback globally non-overshooting/ undershooting tracking control of multivariable systems

The non-overshooting/undershooting (NOUS) tracking control objective in the output response of the closed-loop system has several practical applications in “positioning” control problems. Recently, a state-feedback gain matrix based on Moore’s eigenstructure assignment technique to achieve the above control objective with a desired convergence rate in the output error from any initial condition is designed, referred to as globally monotonic tracking control, which is a convex optimization problem. From a practical viewpoint, a feedback gain matrix of a minimal norm is often required to install low-cost actuators in the overall closed-loop system. However, there is always a trade-off between the control objectives of achieving a NOUS tracking response with the desired convergence rate and a minimal norm of the feedback gain matrix. Besides, the latter control requirement renders the globally NOUS control optimization problem nonconvex. In this paper, a convex optimization-based iterative algorithm is developed to synthesize a minimal-norm state-feedback globally NOUS tracking controller. An upper bound on the achievable settling time in all output responses for the closed-loop eigenvalues lying in a prespecified region of the complex plane is also provided. The effectiveness of the proposed algorithm is demonstrated through a numerical example, followed by experimental validation on a multitank system.

A Novel Generalized Predictive Control Strategy With Improved Time Domain Performance

Abstract Due to the ability of handling the coupling property of multivariable control system, generalized predictive control (GPC) has been widely employed in process industry. However, the existing GPC method normally utilizes the frequency domain indices in the design procedure, which is not intuitive to the industrial end users. Therefore, a new GPC method with improved time domain performance is proposed for multiple-input-multiple-output system. First, the slope and rate of change of the slope of the system outputs are considered as two new weighting terms in the cost function of GPC such that the dynamic characteristics of the system can be better considered in the optimal control problem of the controller. Second, given the modified cost function, the resultant GPC algorithm is developed to improve the time domain performance of the system. Third, the convergence and stability of the closed-loop system under the proposed method are theoretically proved. Finally, the experimental results based on the variable air volume (VAV) air conditioning system show that the time domain performance indices, including overshoot and settling time, of the proposed method, have been improved by 68.75% and 66.67%, compared with the traditional GPC, showing the advantages of the new GPC method.

Decoupling Control Applied to the Smart Grid Power Dispatching Problem

This paper presents controller designs of the decoupling issue dedicated to renewable decentralized generators or new generation grids known as smart grids. The control methods were based on a three-phase voltage source grid representation that integrated wind and photovoltaic generators. The utilized decoupling strategies (Boksenbom and Hood, Zilkind and Luyben, and inverted decoupling) allowed the optimization of energy transfers and costs through the routing grid distribution path. Simulations were conducted in Matlab/Simulink. The trustworthiness of the multivariable control system design in addition to the tuning method was established using three test batches, totally decoupled and stable from input dependencies.