Multivariable Control Design Research Articles

Design and implementation of robust multivariable PI-like fuzzy logic controller for aerodynamic plant

Most modern plants are multivariable, non-linear and time-variant. Therefore, they are difficult to model and control especially when measurements are insufficient or imprecise due to variables interactions, disturbances and noise impact. A perspective model-free approach is based on fuzzy logic, which has proved efficient in ensuring both robust and economic control, employing linguistic expert knowledge in production of simple and feasible non-linear controllers that outperform their linear counterparts. The aim of this investigation and the main contributions are related to the development of a method for the design of multivariable robust fuzzy logic controllers and its implementation for the control of a laboratory-scale aerodynamic plant in real time using MATLAB.

Multivariable fractional order PID controller design via LMI approach

AbstractIn this paper, we study the design problem of multivariable fractional-order (FO) PID controllers which guarantee the stability of the FO closed-loop systems. The idea is to transform the problem of FO PID controller design to that of static output feedback (SOF) controller design for an FO system in descriptor form. In terms of linear matrix inequalities, the PID gains can be found once the SOF matrix is obtained. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.

Heating, ventilation and air conditioning system modelling

Heating, ventilation and air conditioning modelling methods, for large scale, spatially dispersed systems are considered. Existing techniques are discussed and proposals for the application of novel analysis approaches are outlined. The use of distributed–lumped parameter procedures enabling the incorporation of the relatively concentrated and significantly dispersed, system element characteristics, is advocated. A dynamic model for a heating, ventilation and air conditioning system comprising inlet and exhaust fans, with air recirculation, heating/cooling and filtration units is presented. Pressure, airflow and temperature predictions within the system are computed following input, disturbance changes and purging operations. The generalised modelling advancements adopted and the applicability of the model for heating, ventilation and air conditioning system simulation, re-configuration and diagnostics is emphasised. The employment of the model for automatic, multivariable controller design purposes is commented upon.

Study of nonlinear control schemes for an automotive traction PEM fuel cell system

To be practical in automotive traction applications, fuel cell systems must provide power output levels of performance that rival that of typical internal combustion engines. In so doing, transient behavior is one of the keys for success of fuel cell systems in vehicles. The focus of this paper is on the air/fuel supply subsystem in tracking an optimum variable pressurization and air flow for maximum system efficiency during load transients. The control-oriented model developed for this study considers electrochemistry, thermodynamics, and fluid flow principles for a 13-state, nonlinear model of a pressurized fuel cell system. For control purposes, a model reduction is performed, and several multi-variable control designs are examined. The first technique uses an observer-based linear optimum control which combines a feed-forward approach based on the steady-state plant inverse response, coupled to a multi-variable LQR feedback control. An extension of that approach, for control in the full nonlinear range of operation, leads to the second technique, nonlinear gain-scheduled control. Some enhancements were applied to overcome the fast variations in the scheduling variable. Finally, a rule-based, output feedback control, implemented with fuzzy logic, is coupled with a nonlinear feed-forward approach, and is examined under the same conditions applied to the first two techniques. The control designs developed are compared in simulation studies to investigate robustness to disturbance, time delay, and actuator limitations.

Improved Performance for the Synchronization of the Angular Velocity in Hybrid Electric Vehicles using a Feedforward Strategy

In this paper a multivariable control design task in the field of parallel hybrid electric vehicles is discussed. The control design covers the speed synchronization of two propulsion aggregates using a controllable separation clutch. During the synchronization period the longitudinal vehicle motion of the vehicle should not be affected. The proposed control strategy is based on a feedforward controller and two decoupled feedback controllers. The performance and robustness properties of the closed-loop system are shown by nonlinear simulation results.

The dynamics of cyclic ventilation systems

Ventilation and air conditioning modelling methods, for large scale, spatially dispersed systems are considered. The limitations of existing techniques are discussed and proposals for the application of novel analysis approaches are outlined. The use of hybrid, distributed–lumped parameter procedures enabling the incorporation of the relatively concentrated and significantly dispersed, system elements, is advocated. A dynamic model for a ventilation arrangement comprising inlet and exhaust fans, with filtered air re-circulation and air conditioning units is presented. Pressure, flow and temperature predictions within the system are computed following input and disturbance changes. The employment of the model for automatic, multivariable controller design purposes is commented upon.

Covariance matrix adaptation evolution strategy based design of centralized PID controller

In this paper, design of centralized PID controller using Covariance Matrix Adaptation Evolution Strategy (CMAES) is presented. Binary distillation column plant described by Wood and Berry (WB) having two inputs and two outputs and by Ogunnike and Ray (OR) having three inputs and three outputs are considered for the design of multivariable PID controller. Optimal centralized PID controller is designed by minimizing IAE for servo response with unit step change. Simulations are carried out using SIMULINK-MATLAB software. The statistical performances of the designed controllers such as best, mean, standard deviations of IAE and average functional evaluations for 20 independent trials. For the purpose of comparison, recent version of real coded Genetic Algorithm (RGA) with simulated binary crossover (SBX) and conventional BLT method are used. In order to validate the performance of optimal PID controller for robustness against load disturbance rejection, load regulation experiment with step load disturbance is conducted. Also, to determine the performance of optimal PID controller for robustness against model uncertainty, servo and load response with +20% variations in gains and dead times is conducted. Simulation results reveal that for both OR and WB systems, CMAES designed centralized PID controller is better than other methods and also it is more robust against model uncertainty and load disturbance.

Design of Multivariable Neural Controllers Using a Classical Approach

In the present study, the neural network (NN) based multivariable controllers were designed as a series of single input-single output (SISO) controllers or multi variable SISO (MVSISO) controllers utilizing the classical decoupled process models. Multilayer feed forward networks (FFNN) were used as direct inverse neural network (DINN) controllers, which used the inverse dynamics of the decoupled process. To address the disturbance rejection problems, the IMC based neural control architecture was proposed with suitable choice of filter and disturbance transfer function. Multi input - multi output (MIMO) non-linear processes like interacting tank systems, temperature and level control of a mixing tank with hot and cold input streams & a (2×2) distillation process were considered as case studies for that purpose. Simplified as well as ideally decoupled process as well as disturbance transfer functions was used for neural controller design. DINN/IMC based NN controllers performed effectively well in comparison to conventional P/ PI/IMC based PI controllers for set-point tracking & regulator problems.

A unified method for the design of nonovershooting linear multivariable state-feedback tracking controllers

We consider the use of linear multivariable feedback control to achieve a nonovershooting step response. A method is given for designing a linear time invariant state feedback controller to asymptotically track a constant step reference with zero overshoot and arbitrarily small rise time, under some mild assumptions. We present a unified design method that can be applied to continuous and discrete time systems, square and non-square systems, minimum and nonminimum phase systems, and also strictly proper and nonstrictly proper systems.

A multivariable control scheme in a two-stage anaerobic digestion system described by partial differential equations

This paper deals with the design and application of a nonlinear multivariable controller in an anaerobic digestion system (AD) carried out in two interconnected fixed bed bioreactors. The proposed control scheme is derived from a mathematical model of the AD system described by a set of partial differential equations and consists of an estimator and two nonlinear control laws. The first law is developed to regulate the volatile fatty acids in the first bioreactor while the second aims at maintaining the chemical oxygen demand at predetermined set-points in the second bioreactor. The performance of the control algorithm is evaluated via numerical simulations in the face of load disturbances, parameter kinetic uncertainties and set-point changes. Stability and convergence properties of the proposed control scheme are also addressed in this paper.

Multivariable PID control design for activated sludge process with nitrification and denitrification

This paper investigates the application of multivariable PID (MPID) controllers to wastewater treatment plants (WWTPs) with pre-denitrifying process. WWTPs have usually a number of interacting control loops. The controller's parameters are often left unchanged since the plant commissioning and hence poor performance is often observed due to inevitable changes in the plant and its influent characteristics. The model-based MPID tuning methods are complicated, cumbersome and expensive, and require a high level of control expertise to design, and implement. In this paper, a simple and novel tuning method is proposed along with three existing methods, which require only step or frequency response tests. The performance of these methods is compared and the parameters are tuned using a proposed optimisation technique to meet standard quality effluent at a minimum cost. This is achieved using a nonlinear ASM1 model to determine the optimal values of the controller parameters. The results show that by effective and proper tuning of the MPID controllers, the closed-loop performance of WWTP improves and it could potentially lead to energy saving and improvement in the removal of nitrogen.

Nonlinear EGR and VGT Control with Integral Action for Diesel Engines

A non-linear multivariable control design with integral action is proposed and investigated for control of Exhaust Gas Recirculation (EGR) and Variable Geometry Turbocharger (VGT) in heavy duty diesel engines. The main control goal is to regulate oxygen/fuel ratio and intake manifold EGR-fraction, and they are specified in an outer loop. These are chosen as main performance variables since they are strongly coupled to the emissions. An existing non-linear control design based on feedback linearization is extended with integral action. In particular the control design method utilizes a control Lyapunov function, inverse optimal control, and a non-linear compensator. Comparisons between different control structures are performed in simulations showing the following four points. Firstly, integral action is necessary to handle model errors so that the controller can track the performance variables specified in the outer loop. Secondly, the proposed control design handles the non-linear effects in the diesel engine that results in less control errors compared to a control structure with PID controllers. Thirdly, it is important to use the non-linear compensator and it is sufficient to use a control structure with PID controllers and a non-linear compensator to handle the non-linear effects. Fourthly, the proposed control design is sensitive to model errors in the EGR and turbine flow model while a control structure with PID controllers and a non-linear compensator handles these model errors.

Evolutionary algorithms based design of multivariable PID controller

In this paper, performance comparison of evolutionary algorithms (EAs) such as real coded genetic algorithm (RGA), modified particle swarm optimization (MPSO), covariance matrix adaptation evolution strategy (CMAES) and differential evolution (DE) on optimal design of multivariable PID controller design is considered. Decoupled multivariable PI and PID controller structure for Binary distillation column plant described by Wood and Berry, having 2 inputs and 2 outputs is taken. EAs simulations are carried with minimization of IAE as objective using two types of stopping criteria, namely, maximum number of functional evaluations (Fevalmax) and Fevalmax along with tolerance of PID parameters and IAE. To compare the performances of various EAs, statistical measures like best, mean, standard deviation of results and average computation time, over 20 independent trials are considered. Results obtained by various EAs are compared with previously reported results using BLT and GA with multi-crossover approach. Results clearly indicate the better performance of CMAES and MPSO designed PI/PID controller on multivariable system. Simulations also reveal that all the four algorithms considered are suitable for off-line tuning of PID controller. However, only CMAES and MPSO algorithms are suitable for on-line tuning of PID due to their better consistency and minimum computation time.

EFFECTIVE DECENTRALIZED TITO PROCESS IDENTIFICATION FROM CLOSED-LOOP STEP RESPONSES

In this paper, a new identification method performed in the time domain based on the decentralized step-test is proposed for two inputs and two outputs (TITO) processes with significant interactions. In terms of parameter identification, the coupled closed-loop TITO system is decoupled to obtain four individual single open-loop systems with the same input signal. As in the SISO case, new linear regression equations are derived, from which the parameters of a first- or second-order plus dead-time model can be obtained directly. The proposed method outperforms the existing estimation methods for multivariable control systems that use step-test responses. Furthermore, the method is robust in the presence of high levels of measurement noise. Simulation examples are given to show both effectiveness and practicality of the identification method for a wide range of multivariable processes. The usefulness of the identified method in multivariable process modeling and controller design is demonstrated.

Efficient multivariable submarine depth-control system design

An efficient solution for the multivariable submarine control design at low-depth conditions under the influence of wave disturbances is presented. The analysis and control design process is carried out under the framework of individual channel analysis and design (ICAD), which is based on the multivariable structure function (MSF). Classical frequency-domain control techniques based on Bode and Nyquist plots are used. Robustness is stated in terms of gain and phase margins. The closed-loop system includes low-order diagonal controllers facilitating its implementation, assessment, and tuning. ICAD discloses new physical insights of the submarine dynamical behaviour. Previous designs based on diagonal controllers consider the input–output channels defined by pairing the bow hydroplane angle with the depth and the stern hydroplane angle with the pitch angle. The alternative input–output pairing leads to unstable closed-loop systems. This phenomenon is associated with hydroplane reverse control. Here it is shown that MSF-based diagonal controllers can be applied effectively for both sets of channel configurations. Emphasis is placed on satisfying design specifications aiming at maintaining the depth low. The solution presented is more feasible and clearer to apply in practice than those so far reported in the literature.

A closed-loop particle swarm optimizer for multivariable process controller design

Design of general multivariable process controllers is an attractive and practical alternative to optimizing design by evolutionary algorithms (EAs) since it can be formulated as an optimization problem. A closed-loop particle swarm optimization (CLPSO) algorithm is proposed by mapping PSO elements into the closed-loop system based on control theories. At each time step, a proportional integral (PI) controller is used to calculate an updated inertia weight for each particle in swarms from its last fitness. With this modification, limitations caused by a uniform inertia weight for the whole population are avoided, and the particles have enough diversity. After the effectiveness, efficiency and robustness are tested by benchmark functions, CLPSO is applied to design a multivariable proportional-integral-derivative (PID) controller for a solvent dehydration tower in a chemical plant and has improved its performances.

Robust Multivariable Pitch Control Design for Load Reduction on Large Wind Turbines

This paper deals with multivariable pitch control design for wind turbines, including load reducing control objectives. Different design approaches, including collective and cyclic pitch, and robustness aspects are discussed. A control design with decoupled controllers for collective and cyclic pitch is worked out in detail, based on the H∞ norm minimization approach. The control design is verified by simulations with a full nonlinear model of the wind turbine, showing the potential of multivariable pitch control to actively increase damping of the first axial tower bending mode and to reduce 1p fluctuations in blade root bending moments. Multivariable control design provides a convenient way of including additional load reducing objectives into the pitch controller of wind turbines. Fatigue loading of certain components, as tower and blades, could be reduced significantly.

Discrete-Time Control of Linear Time-Periodic Systems

A discrete-time control design approach for periodically time-varying systems is introduced. The method employs a period-to-period (point-mapping) formulation of the system’s dynamics and a parametrization of the control input to obtain an equivalent time-invariant discrete-time representation of the system. The representation is generalized to include sampling within the period and varying sampling rates in different feedback loops. The proposed formulation allows for the design of feedback control laws using established discrete-time control methodologies. In this paper, dead-beat and optimal control laws with state- or output-feedback control are presented. An example of a multivariable control design for double inverted pendulum with periodic forcing is used to illustrate the proposed approach.

Control-Oriented Modeling and Analysis of Air Management System for Fuel Reforming Fuel Cell Vehicle

With the purpose of meeting the specifically restrictive requirements of fuel reforming fuel cell vehicle, this paper brings into focus the issues of the transient operation of fuel cell systems and presents a control-oriented dynamic model of fuel cell air management system, suited for multivariable controller design, system optimization, and supervisory control strategy. In a first step, the dual analytical approach based on lumped and distributed parameter models is detailed: The partial differential equations deduced from mass/energy conservation laws and inertial dynamics are reduced to ordinary differential equations using spatial discretization and then combined with semiempirical actuator models to form the overall air system model. In a second step, a classical approach is followed to obtain a local linearization of the model. A validation of both nonlinear and linearized versions is performed by computational fluid dynamics simulations and experiments on a dedicated air system test bench. Thanks to dynamic analysis (pole/zero map), operating point impact and model order reduction are investigated. Finally, the multiinput multioutput state-space model—which balances model fidelity with model simplicity—can be coupled with reformer, stack, and thermal models to understand the system complexity and to develop model-based control methodologies.

Robust Nonlinear EGR and VGT Control with Integral Action for Diesel Engines

A robust non-linear multivariable control design with integral action is proposed and investigated for control of EGR valve and VGT position in heavy duty diesel engines. The main control goal is to regulate oxygen/fuel ratio and intake manifold EGR-fraction. These are chosen as main performance variables since they are strongly coupled to the emissions. A recently developed non-linear control design based on feedback linearization is extended with integral action. The nonlinear controller gives an inner loop with good stability and robustness properties. It is shown that integral action is necessary to handle model errors so that the controller can track the performance variables specified in the outer loop. In particular the control design method utilizes a control Lyapunov function and inverse optimal control, which results in a control law with robustness properties interpretable as gain and phase margins. Furthermore, comparisons by simulation also show that the proposed control design successfully handles non-linear effects.