Multivariable Control Design Research Articles

Robust grid-oriented control of high voltage DC links embedded in an AC transmission system

Several studies have shown that the way to design controllers for the HVDC links impacts the transient behavior of the electric system in which the latter are inserted. This can be exploited to improve the performances of the stability of the power system. In this paper, a robust multivariable control design for the converters of an HVDC link is proposed. It is based on the coordination of the control actions of the HVDC converters and the use of a control model. The latter takes into consideration, in addition to the dynamics that mostly impact stability of the neighbor zone of the HVDC link, several cases of faulted situations modeled as uncertainties. An H∞ controller allowed us to achieve robustness against such uncertainties. The new controller is tested in comparison with the standard vector control and an optimal LQ controller using the Eurostag simulation software on both academic and realistic large-scale power systems.

Trajectory Tracking Control of a Mobile Robot Through a Flatness-Based Exact Feedforward Linearization Scheme

In this article, a multivariable control design scheme is proposed for the reference trajectory tracking task in a kinematic model of a mobile robot. The control scheme leads to time-varying linear controllers accomplishing the reference trajectory tracking task. The proposed controller design is crucially based on the flatness property of the system leading to controlling an asymptotically decoupled set of chains of integrators by means of a linear output feedback control scheme. The feedforward linearizing control scheme is invoked and complemented with the, so called, generalized proportional integral (GPI) control scheme. Numerical simulations, as well as laboratory experimental tests, are presented for the assessment of the proposed design methodology.

Robust decentralised control of a hydrodynamic human circulatory system simulator

A novel feedback controlled hydrodynamic human circulatory system simulator, well-suited for in-vitro validation of cardiac assist devices, is presented in this paper. The cardiovascular system simulator consists of high-bandwidth actuators allowing a high precision hardware-in-the-loop hydrodynamic interface in connection with physiological circulatory models calculated in real-time. The hydrodynamically coupled process dynamics consist of several actuator loops and demand a multivariable control design approach in the face of system nonlinearities and uncertainties. Based on a detailed model employing the Lagrange formalism, a robust decentralised controller is designed. Fixed structural constraints and the minimisation of the H∞-norm necessitate the application of nonsmooth optimisation techniques. The robust decentralised norm-optimal controller is tested in extensive in-vitro experiments and shows good performance with regard to reference tracking and system coupling. In-vitro experiments include multivariable reference step tests and frequency analysis tests of the vascular impedance transfer function.

Multivariable control with grid objectives of an HVDC link embedded in a large-scale AC grid

Abstract The HVDC links are increasingly used not only to interconnect asynchronous AC systems but are also embedded into a same meshed AC power system. Thanks to its speed and flexibility, the HVDC technology is able to provide transmission system advantages as transfer capacity enhancement and power flow control. In addition, studies have shown that the way of controlling the HVDC converters impacts the stability of the AC system. This can be particularly exploited to enhance the dynamic power system performances during transients. In this paper a robust multivariable control design for HVDC link converters is proposed. It is based on the coordination of the control actions of the HVDC converters and the use of a control model which takes into account the dynamics that mostly impact stability of the neighbor zone of the HVDC link. This new methodology was used to synthesize the controller for an actual grid 1000 MW HVDC link reinforcement project called “Midi-Provence” in the southern part of the French grid. The synthesis, implementation and validation processes are presented in detail. The new controller is tested in comparison with the standard vector control. A large-scale dynamic model of the whole European power system, currently used and updated by the European TSO’s for the interconnection studies has been used with Eurostag simulation software.

Adaptive fuzzy multivariable controller design based on genetic algorithm for an air handling unit

In HVAC (Heating, Ventilation and Air Conditioning systems, effective thermal management is required because energy and operation costs of buildings are directly influenced by how well an air-conditioning system performs. HVAC systems are typically nonlinear time varying with disturbances, where conventional PID controllers may trade-off between stability and rise time. To overcome this limitation, a Genetic Algorithm based AFLC (Adaptive Fuzzy Logic Controller design has been proposed for the multivariable control of temperature and humidity of a typical AHU (air handling unit by manipulating valve positions to adjust the water and steam flow rates. Modulating equal percentage Globe valves for chilled water and steam have been modeled according to exact flow rates of water and steam. A novel method for the adaptation of FLC (Fuzzy Logic Controller by modifying FRM (Fuzzy Rule Matrix based on GA (genetic algorithm) has been proposed. This requires re-designing the complete FLC in MATLAB/Simulink whose procedure has also been proposed. The proposed adaptive controller outperforms the existing fuzzy controller in terms of steady state error, rise time and settling time.

Design of multivariable PID controller using DE-PSO

This paper presents design of multivariable PID controller using a novel method differential evolution (DE)-based particle swarm optimisation (PSO) for two-input two-output (TITO) processes and its performance compare with evolutionary algorithms (EAs) like DE and modified PSO methods. In the proposed DE-PSO method, preliminary DE is applied on the random generated population then PSO is used to update the position and velocity of the particles. To validate the effectiveness of the proposed DE-PSO method, two different industrial processes and real time experiment on four tank level control system is considered. Simulation results show that DE-based PSO is better than both MPSO and DE in terms of getting global optimum in less iterations and avoiding premature convergence.

MIMO Tracking PI/PID Controller Design for Nonlinear Systems based on Singular Perturbation Technique

Problem of the tracking PI/PID multivariable controller design based on time-scale separation technique (singular perturbation technique) for MIMO nonlinear systems is discussed. The presented design methodology guarantees almost perfect rejection of nonlinearities, unknown external disturbances, and interactions between loops due to increase of time-scale separation degree between the fast and slow modes that are artificially forced in the closedloop system. Simulation results for trajectory tracking control of two-link robot manipulator are presented as an example of the proposed design methodology application.

Design of multivariable PID controllers using real-coded population-based extremal optimization

The issue of designing and tuning an effective and efficient multivariable PID controller for a multivariable control system to obtain high-quality performance is of great theoretical importance and practical significance. As a novel evolutionary algorithm inspired from statistical physics and co-evolution, extremal optimization (EO) has successfully applied to a variety of optimization problems while the applications of EO into the design of multivariable PID and PI controllers are relatively rare. This paper presents a novel real-coded population-based EO (RPEO) method for the design of multivariable PID and PI controllers. The basic idea behind RPEO is based on population-based iterated optimization process consisting of the following key operations including generation of a real-coded random initial population by encoding the parameters of a multivariable PID or PI controller into a set of real values, evaluation of the individual fitness by using a novel and reasonable control performance index, generation of new population based on multi-non-uniform mutation and updating the population by accepting the new population unconditionally. From the perspectives of simplicity and accuracy, the proposed RPEO algorithm is demonstrated to outperform other reported popular evolutionary algorithms, such as real-coded genetic algorithm (RGA) with multi-crossover or simulated binary crossover, differential evolution (DE), modified particle swarm optimization (MPSO), probability based discrete binary PSO (PBPSO), and covariance matrix adaptation evolution strategy (CMAES) by the experimental results on the benchmark multivariable binary distillation column plant.

Multivariable adaptive control: A survey

Adaptive control is a control methodology capable of dealing with uncertain systems to ensure desired control performance. This paper provides an overview of some fundamental theoretical aspects and technical issues of multivariable adaptive control, and a thorough presentation of various adaptive control schemes for multi-input–multi-output systems, literature reviews on adaptive control foundations and multivariable adaptive control methods, and related technical problems. It covers some basic concepts and issues such as certainty equivalence, stability, tracking, robustness, and parameter convergence. It discusses some of the most important topics of adaptive control: plant uncertainty parametrization, stable controller adaptation, and design conditions for different adaptive control schemes. The paper also presents a detailed study of well-developed multivariable model reference adaptive control theory and design techniques. It provides an introduction to multivariable adaptive pole placement and adaptive nonlinear control, and it concludes by identifying some open research problems.

Design Of Multivariable Fractional Order Pid Controller Using Covariance Matrix Adaptation Evolution Strategy

Abstract This paper presents an automatic tuning of multivariable Fractional-Order Proportional, Integral and Derivative controller (FO-PID) parameters using Covariance Matrix Adaptation Evolution Strategy (CMAES) algorithm. Decoupled multivariable FO-PI and FO-PID controller structures are considered. Oustaloup integer order approximation is used for the fractional integrals and derivatives. For validation, two Multi-Input Multi- Output (MIMO) distillation columns described byWood and Berry and Ogunnaike and Ray are considered for the design of multivariable FO-PID controller. Optimal FO-PID controller is designed by minimizing Integral Absolute Error (IAE) as objective function. The results of previously reported PI/PID controller are considered for comparison purposes. Simulation results reveal that the performance of FOPI and FO-PID controller is better than integer order PI/PID controller in terms of IAE. Also, CMAES algorithm is suitable for the design of FO-PI / FO-PID controller.

The Modified Quadruple-Tanks Process: A Flexible Mathematical Model with an Adjustable Simulink Block

This paper presents the modified quadruple-tanks process, a flexible laboratory process with an adjustable Simulink block, which is multivariable system consisting of four interconnected water tanks included with lower interacting valve. The new general form of modified quadruple-tanks mathematic model and Simulink block is developed for the advantage of control system analysis and design which can make practical use for many styles of multivariable process by adjusting the value of connected valve resistance, inlet and outlet valve ratio. In this paper described clearly about physical properties of modified quadruple-tanks process, mathematical modeling, transformation of modified quadruple-tanks process, analysis of right half-plane zeros characteristic and controller design for multivariable system. By the several models of transformed modified quadruple-tanks, they can be used to teach students in the skills of multivariable control system analysis and design, understanding control limitation due to interactions, model uncertainties, non-minimum phase behavior, and unpredictable time variations, design decentralized controllers, Implementing decouples to reduce the effect of interactions, and understanding their limitations.

System Identification for Low-cost Small-scale Helicopters

The preliminary platform design for a twin-helicopter slung load transportation system is presented. The framework is intended for testing robust multivariable control design methods and nonlinear state-estimation algorithms. An avionics unit is designed for on-board sensing and control. A low-cost visual tracking system is designed for estimating the helicopter pose within a flying volume. Using flight data logged by the avionics and visual tracking system, an uncertain set of parameters are estimated which completely define the plant dynamics for hover flight condition.

Controller Design for Multivariable Linear Time-Invariant Unknown Systems

This paper deals with the design of multivariable controllers for stable linear time-invariant multi-input multi-output systems, with an unknown mathematical model, subject to constant reference/disturbance signals. We propose a new controller parameter optimization approach, which can be carried out experimentally without knowledge of the plant model or the order of the system. The approach has the advantages that controllers can be tuned by perturbing only the initial conditions of the servocompensator, and that the order of the resulting controller can be specified by the designer. Implementation of the proposed controller design approach is described, and an experimental application study of the proposed method applied to a multivariable system with industrial sensor/actuator components is presented to illustrate the feasibility of the design method in an industrial environment.

Multivariable Control and Optimization of a Compact 6-DOF Precision Positioner With Hybrid ${\cal H}_{2}/{\cal H}_{\infty}$ and Digital Filtering

In this paper, we present multivariable controller design and implementation of a high-precision 6-DOF magnetically levitated (maglev) positioner. To achieve high-precision positioning, two discrete-time integrator-augmented controllers based on the linear quadratic Gaussian multivariable control are applied. A novel discrete hybrid H2/H∞ filter is used as the observer to obtain the optimal estimates of position and orientation, as well as additional estimates of linear and angular velocities for all six axes. The positioner has a single moving part that carries three 3-phase permanent-magnet linear-levitation-motor armatures. The positioner moves over a Halbach magnet matrix using three sets of two-axis Hall-effect sensors to measure the planar motion and three laser distance sensors for the vertical motion. The Hall-effect sensor signals are found to generate a considerable amount of noise and are centered at 50 Hz. A second-order digital notch filter is implemented to optimize the sensor readings and attenuate the noise. Experimental results show a position resolution, which is the smallest noticeable step of 1.5 μm with a position noise of 0.545 μm rms in the x- and y-directions, and a position resolution of 110 nm with a position noise of 49.3 nm rms in the z-direction.

A Multivariable Design Methodology for Voltage Control of a Single-DG-Unit Microgrid

This paper proposes a multivariable digital control design methodology for the voltage regulation of an islanded single distributed generation (DG) unit microgrid and its dedicated load. The controller design methodology is based on a family of spectral Multi-Input Multi-Output (MIMO) models of the microgrid system and performs open-loop shaping and system decoupling simultaneously by a convex optimization approach. The control design procedure includes: (i) the determination of a family of nonparametric models of the system at various operating points, (ii) the determination of the class of the controller, and (iii) system open-loop shaping by convex minimization of the summation of the square second norm of the errors between the system open-loop transfer functions and a desired open-loop transfer function. Based on the proposed design methodology, two dq -augmented voltage controllers are proposed to regulate the load voltages of a single-DG-unit microgrid. The proposed controllers guarantee the robust stability and satisfactory dynamic response of the system in spite of load parametric uncertainties and also the presence of nonlinear load. This paper describes the theoretical aspects involved in the design procedure of the controllers and evaluates the performance of the controllers based on simulation studies and experiments.

Oversizing analysis in plant-wide control design for industrial processes

In this work, an alternative plant-wide control design approach based on oversizing analysis is presented. The overall strategy can be divided in two main sequential tasks: 1 – defining the optimal decentralized control structure, and 2 – setting the controller interaction degree and its implementation. Both problems represent combinatorial optimizations based on multi-objective functional costs and were solved efficiently by genetic algorithms. The first task defines the optimal selection of controlled and manipulated variables simultaneously, the input–output pairing, and the overall controller dimension in a sum of square deviations context. The second task analyzes the potential improvements by defining the controller interaction degree via the net load evaluation approach. In addition, some insights are given about the feasibility (implementation load) of these control structures for a decentralized or centralized framework. The well-known Tennessee Eastman (TE) process is selected here for sake of comparison with other multivariable control designs.

A multivariable IMC-PID method for non-square large time delay systems using NPSO algorithm

Multiple time delays and strong interactions among different loops are the main problems in the design of multivariable controller for non-square systems. In this paper, the concept of effective open-loop transfer function (EOTF) is extended to non-square systems. By applying the internal model control (IMC) method, the controllers with equivalent models are designed. For practical applications, the NPSO algorithm is used to obtain the parameters of the incremental PID with first-order lag filter. This new method does not only avoid the complex computation caused by the procedure of decoupling first and then designing controllers but also employs the advantages of IMC-PID's suitable for large time delay systems and strong robustness. Simulation is carried out to demonstrate the effectiveness of the proposed method; also significant performance improvement has been achieved with the proposed method compared with other methods.

Multivariable output feedback robust adaptive tracking control design for a class of delayed systems

In this paper, we develop a model reference adaptive control scheme for a class of multi-input multi-output nonlinearly perturbed dynamic systems with unknown time-varying state delays which is also robust with respect to an external disturbance with unknown bounds. The output feedback adaptive control scheme uses feedback actions only, and thus does not require a direct measurement of the command or disturbance signals. A suitable Lyapunov–Krasovskii type functional is introduced to design the adaptation algorithms and to prove stability.

Robust nonlinear multivariable tracking control design to a manipulator with unknown uncertainties using operator-based robust right coprime factorization

In this paper, an operator-based robust nonlinear multivariable tracking control for a manipulator with uncertainties is proposed by using a robust right coprime factorization approach. In general, there exist unknown modelling errors in measuring structural parameters of the manipulator and external disturbances in real situations. In the present control system design, the effect of the modelling errors and disturbance on system performance is considered to be uncertainties in the manipulator dynamics. Considering the uncertainties, an operator-based robust nonlinear multivariable tracking control using robust right coprime factorization is studied. That is, firstly a robustly stable control based on robust right coprime factorization is designed. Secondly, a robust nonlinear multivariable tracking system is proposed for improving the trajectory of the manipulator, and the output tracking performance is evaluated based on the exponential iteration theorem. Finally, the effectiveness of the designed system is confirmed by simulation results.

Diagonal control design for atomic force microscope piezoelectric tube nanopositioners

Atomic Force Microscopes (AFM) are used for generating surface topography of samples at micro to atomic resolutions. Many commercial AFMs use piezoelectric tube nanopositioners for scanning. Scanning rates of these microscopes are hampered by the presence of low frequency resonant modes. When inadvertently excited, these modes lead to high amplitude mechanical vibrations causing the loss of accuracy, while scanning, and eventually to break down of the tube. Feedback control has been used to damp these resonant modes. Thereby, enabling higher scanning rates. Here, a multivariable controller is designed to damp the first resonant mode along both the x and y axis. Exploiting the inherent symmetry in the piezoelectric tube, the multivariable control design problem is recast as independent single-input single-output (SISO) designs. This in conjunction with integral resonant control is used for damping the first resonant mode.