Discrete Controller Design Research Articles

LMI-based discrete LPV controller design for systems with inherent couplings in the scheduling vector: Improved robustness and performance

This work presents the design of controllers for discrete-time linear parameter-varying systems, particularly in scenarios where uncontrollable regions emerge within the polytope obtained by convex rewriting of a certain bounded region. Two fundamental aspects are addressed: the stability of the system and the enhancement of the controller performance and robustness. The most significant results include the proposal of a strategy to isolate the regions that are not reached by the trajectories of the system due to inherent couplings in the scheduling vector. The resulting control law ensures asymptotic stability under specific conditions, along with improved performance and robustness against perturbations through the use of H∞ and linear matrix inequalities regions. A numerical example illustrates the applicability and performance of the proposal.

Frequency Adaptive Discrete Repetitive Controller Design for Electric Vehicle Charger

Frequency Adaptive Discrete Repetitive Controller Design for Electric Vehicle Charger

Design of discrete PID controllers for maximizing stability margins

AbstractThe objective of this paper is to provide a discrete PID controller design procedure for maximizing stability margins. First, a new and complete characterization of the entire set of stabilizing discrete PID controllers for a given plant is presented. Then, based on this characterization, an efficient algorithm is developed for testing if, for a given plant, there exists a digital PID controller gain parameter space corresponding to closed‐loop poles being inside the circle of radius centered at the origin. The developed algorithm is finally applied along with a bisection strategy to determine, for a specified small positive number , a minimum value and the corresponding discrete PID controller set for achieving at least of stability margin. To illustrate the features of our new characterization of stabilizing digital PID controller sets and the effectiveness of the presented algorithms to the maximum stability‐margin discrete PID controller design, two numerical examples are provided.

Discrete State-Feedback Control Design with D-Stability and Genetic Algorithm for LED Driver Using a Buck Converter

In this paper, a discrete state-feedback controller is applied to control the current in power LEDs by using a buck converter. Sufficient conditions for the existence of the controller are given in terms of linear matrix inequalities (LMIs) with D-stability theory. In order to consider the specific closed-loop dynamics of the closed-loop LED driver, the genetic algorithm (GA) technique is applied, as a complement of the D-stability theory. Therefore, the proposed GA technique is used to search offline the optimal closed-loop eigenvalues to have a desired response of the closed-loop system, subject to a proposed cost function equation. The main contribution of this work is the design and the experimental validation of both the state-feedback controller and the GA to achieve the desired closed-loop dynamics of the LED-driver system. Finally, simulations and experimental results are done in order to illustrate the effectiveness of the proposed methodology.

Model‐based periodic event‐triggered stabilization for continuous‐time stochastic nonlinear systems

AbstractIn this paper, we investigate a model‐based periodic event‐triggered control framework for continuous‐time stochastic nonlinear systems. In this framework, an auxiliary approximate discrete‐time model of stochastic nonlinear systems is constructed in the controller module, which is utilized not only to design a discrete‐time controller but also as a state predictor within trigger intervals. This discrete controller design approach, the strategy of state prediction, and the periodic detection strategy for the trigger rule not only provide a manner of more direct and easier implementation on the digital platform but also effectively reduce the communication load while a satisfactory control performance is maintained. Additionally, the mean‐square exponentially stabilization for continuous‐time stochastic nonlinear systems is achieved, in which a guideline for determining the maximum admissible sampling period is provided and the periodic event trigger rule is designed. The final numerical simulation also supports the effectiveness of our proposed framework.

Tube-Based Discrete Controller Design for Vehicle Platoons Subject to Disturbances and Saturation Constraints

Cooperative adaptive cruise control (CACC) is a promising intelligent vehicle technology for improving traffic flow stability, throughput, and safety. One major control objective of CACC is to guarantee $\mathcal {L}_{p}$ string stability, i.e., $\mathcal {L}_{p}$ -norm measured disturbance is uniformly bounded along the vehicle string. Most existing methods for string stability are laborious for implementation without considering either heterogeneous disturbances (e.g., tracking errors and unmodeled dynamics) or saturation constraints (e.g., input saturation). The decentralized model predictive control (MPC) method, which is a widely used feedforward control for string stability, suffers the burdens of computation cost and intervehicular communication. To fill these gaps, we distinguish different types of disturbances and use different ways to handle them. We use feedforward control for large yet infrequent disturbances and feedback control for small yet frequent disturbances. Different from MPC, our feedforward control is event-triggered so that the intervehicle communication and planning costs can be significantly reduced. Different from pure robust feedback control, our combination of feedback and feedforward control could reduce the conservation of the controller. Theoretical analysis and simulations show that the proposed method guarantees $\mathcal {L}_{p}$ string stability of vehicle platoons considering heterogeneous disturbances and saturation constraints.

Full Discrete Modeling, Controller Design, and Sensitivity Analysis for High-Performance Grid-Forming Converters in Islanded Microgrids

Recent works have shown that the state-feedback decoupling of capacitor voltage allows for drastic bandwidth enlarging of current controllers for grid-forming converters in islanded microgrids. Furthermore, Smith predictor and lead compensation have been also proved as very effective implementations for compensating the controller delays. These features are key to fulfill demanding requirements in terms of voltage regulation in islanded applications. This work deepens in the discrete-time domain modeling and implementation issues of the above-mentioned techniques. A full discrete-time and sensitivity analyses reveal phenomena not properly modeled in previous works, which limits the performance: the presence of high-frequency oscillations due to discrete poles with negative real part. Subsequently, proper design countermeasures (i.e., limit bandwidth) are proposed. Discrete implementation of the voltage controller is also addressed, and design guidelines are provided. Experimental tests in accordance with the high demanding standards for uninterruptible power supply systems verify the theoretical analysis.

PLC-based Discrete Fractional-order Control Design for an Industrial-Oriented Water Tank Volume System with Input Delay

Abstract We present PLC-based fractional-order controller design for an industrial-oriented water tank volume control application. The system comprises input delay which is a typified characteristic in such industrial process control applications. The particular contribution of this work is on discrete fractional-order PID implementation via PLC and its application to the aforementioned realistic water tank test bed. Stability and robustness properties of fractional-order discrete PID feedback-loops for different approximation methods and orders are also shown. Fractional-order controllers are obtained for a variety of stability margin choices, and benefits of the non-integer-order controllers compared to the integer-order PID control are illustrated via simulation and experimental runs on a realistic test-bed.

Model Predictive Control of Mineral Column Flotation Process

Column flotation is an efficient method commonly used in the mineral industry to separate useful minerals from ores of low grade and complex mineral composition. Its main purpose is to achieve maximum recovery while ensuring desired product grade. This work addresses a model predictive control design for a mineral column flotation process modeled by a set of nonlinear coupled heterodirectional hyperbolic partial differential equations (PDEs) and ordinary differential equations (ODEs), which accounts for the interconnection of well-stirred regions represented by continuous stirred tank reactors (CSTRs) and transport systems given by heterodirectional hyperbolic PDEs, with these two regions combined through the PDEs’ boundaries. The model predictive control considers both optimality of the process operations and naturally present input and state/output constraints. For the discrete controller design, spatially varying steady-state profiles are obtained by linearizing the coupled ODE–PDE model, and then the discrete system is obtained by using the Cayley–Tustin time discretization transformation without any spatial discretization and/or without model reduction. The model predictive controller is designed by solving an optimization problem with input and state/output constraints as well as input disturbance to minimize the objective function, which leads to an online-solvable finite constrained quadratic regulator problem. Finally, the controller performance to keep the output at the steady state within the constraint range is demonstrated by simulation studies, and it is concluded that the optimal control scheme presented in this work makes this flotation process more efficient.

Design of Digital PID Controllers Relying on FPGA-based Techniques

A major challenge of higher education institutions is to prepare professionals capable of learning by building effective solutions that are able to integrate different disciplines and knowledge areas. With this in mind, academics and researchers from ESPOL university in Ecuador, have designed laboratory experiments for a digital control class that introduces students to a modular design of embedded feedback controllers using Field Programmable Gate Array (FPGA) technologies. The proposed experiment includes the design of direct discrete time PID controllers, for an existing speed control system with three different sampling times, to test and compare their performance. The obtained controllers are implemented using a prototyping strategy that relies on FPGA development boards. The prototype controller is tested using the experimental plant, and the system performance is contrasted with results from simulations under realistic conditions.

Emulation of Cyber-Physical Systems Using IEC-61499

Automation systems used in smart grids, transportation, and medical electronics are cyber physical in nature. Automation standards, such as IEC-61499, while well suited to the design of discrete controllers, are not ideally suited to model the dynamics of the plant. Such modeling is essential for emulation-based validation of the controllers in the cyber-physical systems (CPS) domain. We use a well-known formal model for CPS, called hybrid input output automata (HIOA), as the main vehicle in the proposed formulation. A physical process (the plant) may be described as a synchronous composition of a network of such HIOA. We provide an approach to transform such a network to a composite function block (CFB) in IEC-61499. This transformation is shown to be semantics preserving. Code generated from such plant models can be executed on a computer chip to provide real-time response to their adjoining controllers. Through practical examples, we illustrate the scalability and practicability of the proposed approach. The developed approach enables the emulation of physical processes in industrial automation without using the actual plant.

Bandwidth Assessment for MultiRotor UAVs

AbstractThis paper is a technical note about the theoretical evaluation of the bandwidth of multirotor helicopters. Starting from a mathematical linear model of the dynamics of a multirotor aircraft, the transfer functions of the state variables that deeply affect the stability characteristics of the aircraft are obtained. From these transfer functions, the frequency response analysis of the system is effected. After this analysis, the bandwidth of the system is defined. This result is immediately utilized for the design of discrete PID controllers for hovering flight stabilization. Numeric simulations are shown to demonstrate that the knowledge of the bandwidth is a valid aid in the design of flight control systems of these machines.

Real time implementation of H-infinity and RST motion control of rotary traveling wave ultrasonic motor

ABSTRACT This paper deals with design, performances comparison and experimental validation of H-infinity (H∞) and discrete time RST position controllers for a Traveling Wave Ultrasonic Motor (TWUM) which is dedicated to robotic applications. The proposed positioning system shows high precision levels of piezoelectric motor without additional hysteresis and dead zone compensation systems. Moreover, the perturbation rejection capability and the robustness to motor parameters variation are guaranteed. The synthesis procedure of robust H∞ and RST position controllers is detailed. The performances of the proposed controllers are validated by simulation and experimental results.

On the Design of Discrete Time Repetitive Controllers in Closed Loop Configuration

This paper deals with a discrete time repetitive control synthesis for non minimum phase plants. Two parts can be distinguished. The main design features of the repetitive controllers are discussed in the first part. More precisely one shows that one can realize two objectives; tracking with zero error and tracking with nonzero error. In the second part, a suitable plant model identification procedure for the repetitive control is proposed. An adequate input-output identification filter is designed such that the difference between the nominal and the actual repetitive control convergence conditions is minimized. Some illustrative examples are given to highlight the main features of the proposed approach.

Component-Based Design by Solving Language Equations

An important step in the design of a complex system is its decomposition into a number of interacting components, of which some are given (known) and some need to be synthesized (unknown). Then a basic task in the design flow is to synthesize an unknown component that when combined with the known part of the system (the context) satisfies a given specification. This problem arises in several applications ranging from sequential synthesis to the design of discrete controllers. There are different formulations of the problem, depending on the formal models to specify the system and its components, the composition operators, and the conformance relations of the composed system versus the specification. Various behavioral models have been studied in the literature, e.g., finite state machines and automata, omega-automata, process algebras; various forms of synchronous and asynchronous (interleaving/parallel) composition have been considered; the conformance relations include language containment and equality, and notions of simulation. In this paper we give an overview of the problem (a.k.a., the unkown component problem, or submodule construction, etc.), and we focus on its reduction to solving equations over languages, as a key technology for supporting synthesis of compositional systems. We survey the state-of-art and highlight open problems requiring further investigation.

Design of observer-based discrete repetitive-control system based on 2D model

A discrete observer-based repetitive control (RC) design method for a linear system with uncertainties was presented based on two-dimensional (2D) system theory. Firstly, a 2D discrete model was established to describe both the control behavior within a repetition period and the learning process taking place between periods. Next, by converting the designing problem of repetitive controller into one of the feedback gains of reconstructed variables, the stable condition was obtained through linear matrix inequality (LMI) and also the gain coefficient of repetitive system. Numerical simulation shows an exceptional feasibility of this proposal with remarkable robustness and tracking speed.

Проектування робастних тривісних систем стабілізації бортової апаратури спостереження

Присвячено дослідженню особливостей проектування робастних тривісних систем стабілізації бортової апаратури спостереження. Подано математичну модель у просторі станів об’єкта стабілізації, який являє собою платформу з апаратурою спостереження та вимірювальними пристроями, встановлену у тривісному кардановому підвісі. Розглянуто підхід до робастного структурного синтезу на підставі методу змішаної чутливості. Показано алгоритм проектування робастного дискретного регулятора. Описано структуру синтезованого регулятора у вигляді четвірки матриць у просторі станів. Наведено результати моделювання. Зазначено, що результати дослідження становлять інтерес для галузі систем стабілізації інформаційно-вимірювальних пристроїв, призначених для експлуатації на рухомих об’єктах широкого класа.

A discrete time-varying internal model-based approach for high precision tracking of a multi-axis servo gantry

In this paper, we consider the discrete time-varying internal model-based control design for high precision tracking of complicated reference trajectories generated by time-varying systems. Based on a novel parallel time-varying internal model structure, asymptotic tracking conditions for the design of internal model units are developed, and a low order robust time-varying stabilizer is further synthesized. In a discrete time setting, the high precision tracking control architecture is deployed on a Voice Coil Motor (VCM) actuated servo gantry system, where numerical simulations and real time experimental results are provided, achieving the tracking errors around 3.5‰ for frequency-varying signals.

Features of computer-aided design of robust discrete controllers for information-measuring devices stabilization systems

Features of computer-aided design of robust discrete controllers for information-measuring devices stabilization systems

Evolutionary design of discrete controllers for hybrid mechatronic systems

This paper investigates the issue of evolutionary design of controllers for hybrid mechatronic systems. Finite State Automaton (FSA) is selected as the representation for a discrete controller due to its interpretability, fast execution speed and natural extension to a statechart, which is very popular in industrial applications. A case study of a two-tank system is used to demonstrate that the proposed evolutionary approach can lead to a successful design of an FSA controller for the hybrid mechatronic system, represented by a hybrid bond graph. Generalisation of the evolved FSA controller to unknown control targets is also tested. Further, a comparison with another type of controller, a lookahead controller, is conducted, with advantages and disadvantages of each discussed. The comparison sheds light on which type of controller representation is a better choice to use in various stages of the evolutionary design of controllers for hybrid mechatronic systems. Finally, some important future research directions are pointed out, leading to the major work of the succeeding part of the research.