Discrete Proportional Integral Derivative Controller Research Articles

Dissipative Discrete PID Load Frequency Control for Restructured Wind Power Systems via Non-Fragile Design Approach

This article proposes a discrete proportional-integral-derivative (PID) load frequency control (LFC) scheme to investigate the dissipative analysis issue of restructured wind power systems via a non-fragile design approach. Firstly, by taking the different power-sharing rates of governors into full consideration, a unified model is constructed for interconnected power systems containing multiple governors. Secondly, unlike existing LFC schemes, a non-fragile discrete PID control scheme is designed, which has the performance of tolerating control gain fluctuation and relieving the huge computational burden. Further, by constructing a discrete-type Lyapunov–Krasovskii functional, improved stability criteria with a strict dissipative performance index are established. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed control method.

Active Fault-Tolerant Control Applied to a Pressure Swing Adsorption Process for the Production of Bio-Hydrogen

Pressure swing adsorption (PSA) technology is used in various applications. PSA is a cost-effective process with the ability to produce high-purity bio-hydrogen (99.99%) with high recovery rates. In this article, a PSA process for the production of bio-hydrogen is proposed; it uses two columns packed with type 5A zeolite, and it has a four-step configuration (adsorption, depressurization, purge, and repressurization) for bio-hydrogen production and regeneration of the beds. The aim of this work is to design and use an active fault-tolerant control (FTC) controller to raise and maintain a stable purity of 0.9999 in molar fraction (99.99%), even with the occurrence of actuator faults. To validate the robustness and performance of the proposed discrete FTC, it has been compared with a discrete PID (proportional–integral–derivative) controller in the presence of actuator faults and trajectory changes. Both controllers achieve to maintain stable purity by reducing the effect of faults; however, the discrete PID controller is not robust to multiple faults since the desired purity is lost and fails to meet international standards to be used as bio-fuel. On the other hand, the FTC scheme reduces the effects of individual and multiple faults by striving to maintain a purity of 0.9999 in molar fraction and complying with international standards to be used as bio-fuel.

Stabilizing region in dominant pole placement based discrete time PID control of delayed lead processes using random sampling

Handling time delays in industrial process control is a major challenge in the dominant pole placement based design of proportional-integral-derivative (PID) controllers due to variable number of zeros and poles which may arise from the Pade approximation of the exponential delay terms in the characteristic polynomials used for stability analysis. This paper proposes a new concept for designing PID controllers with a derivative filter using dominant pole placement method mapped onto the discrete time domain with a suitable choice of the sampling time to convert the continuous time time-delays into finite number of discrete time poles. Here, the continuous-time plant and the filtered PID controller have been discretized using the pole-zero matching method for handling linear dynamical systems, represented by the first order plus time delay with zero (FOPTDZ) transfer function models of the open-loop system under control. We use a swarm intelligence based global optimization method as a sampler to discover the approximate the pattern of the stabilizable region in the controller parameter as well as the design specification space while also satisfying the analytical conditions for pole placement given as higher order polynomials. Simulations on test-bench plants with open-loop stable, unstable, integrating, low-pass, high-pass characteristics have been presented in order to demonstrate the validity and effectiveness of the proposed control design method.

Компаративна анализа на различни алгоритми за управување на поле од хелиостати

This study presents the use of various algorithms for control of a field of heliostats, through which a thermal power plant with concentrated solar energy is controlled. The design of the control algorithms consists of several steps. First, the Sun tracking alghorithm is presented for a specific location with an accuracy of ± 0.0003°. In order to obtain the mathematical model of the system, the real system is identified according to the gray box and the least-square method. The data used to identify the system is generated by step excitation on the real system, for a specific sampling period. The resulting mathematical model is used to design and simulate a continuous and discrete Proportional-Integral-Derivative (PID) controller, Mamdani and Sugeno fuzzy logic controllers, as well as ANFIS based fuzzy logic controller. The results of the applied controllers are analyzed and compared, based on the output overshoot, the rise and settling time. It can be concluded that we got best results (least settling time and the least overshoot) when fuzzy logic controller with ANFIS was used, while in terms of speed and rise time, the best results were obtained when discrete PID control algorithm was used. The study is extension of the work given in [23].

Load Frequency Control in a Multi-Area Deregulated Power System with BBBC-based Discrete Fractional Order Control Scheme

Load frequency control (LFC) for multi-area restructured power system using discrete controlscheme has been suggested in this paper. The proposed LFC scheme utilizes synchronously measured dataof frequency and tie-line power to calculate area control error (ACE). A discrete non-integer proportionalintegral derivative controller (D-FOPID) has been used to derive frequency error to zero. Two-area thermaland four-area hydro thermal deregulated power system has been used to investigate various LFC issues. Theoptimal factors of D-FOPID have been obtained using big bang big crunch (BBBC) algorithm. The systemresults under MATLAB/Simulink validate that D-FOPID effectively work under different types of contractscenarios. D-FOPID performance has also been compared to discrete proportional integral derivativecontroller (D-PID). Further the compliance with control standards of North American electric reliabilitycouncil (NERC) has also been ensured for both the controller.

Transformation of LQR Weights for Discretization Invariant Performance of PI/PID Dominant Pole Placement Controllers

SummaryLinear quadratic regulator (LQR), a popular technique for designing optimal state feedback controller, is used to derive a mapping between continuous and discrete time inverse optimal equivalence of proportional integral derivative (PID) control problem via dominant pole placement. The aim is to derive transformation of the LQR weighting matrix for fixed weighting factor, using the discrete algebraic Riccati equation (DARE) to design a discrete time optimal PID controller producing similar time response to its continuous time counterpart. Continuous time LQR-based PID controller can be transformed to discrete time by establishing a relation between the respective LQR weighting matrices that will produce similar closed loop response, independent of the chosen sampling time. Simulation examples of first/second order and first-order integrating processes exhibiting stable/unstable and marginally stable open loop dynamics are provided, using the transformation of LQR weights. Time responses for set-point and disturbance inputs are compared for different sampling times as fraction of the desired closed loop time constant.

Control of force during rapid visuomotor force-matching tasks can be described by discrete time PID control algorithms.

Force trajectories during isometric force-matching tasks involving isometric contractions vary substantially across individuals. In this study, we investigated if this variability can be explained by discrete time proportional, integral, derivative (PID) control algorithms with varying model parameters. To this end, we analyzed the pinch force trajectories of 24 subjects performing two rapid force-matching tasks with visual feedback. Both tasks involved isometric contractions to a target force of 10% maximal voluntary contraction. One task involved a single action (pinch) and the other required a double action (concurrent pinch and wrist extension). 50,000 force trajectories were simulated with a computational neuromuscular model whose input was determined by a PID controller with different PID gains and frequencies at which the controller adjusted muscle commands. The goal was to find the best match between each experimental force trajectory and all simulated trajectories. It was possible to identify one realization of the PID controller that matched the experimental force produced during each task for most subjects (average index of similarity: 0.87±0.12; 1=perfect similarity). The similarities for both tasks were significantly greater than that would be expected by chance (single action: p=0.01; double action: p=0.04). Furthermore, the identified control frequencies in the simulated PID controller with the greatest similarities decreased as task difficulty increased (single action: 4.0±1.8Hz; double action: 3.1±1.3Hz). Overall, the results indicate that discrete time PID controllers are realistic models for the neural control of force in rapid force-matching tasks involving isometric contractions.

Fuzzy PID controller design using time-delay estimation

A fuzzy proportional-integral-derivative (PID) controller is designed using time-delay estimation (TDE). In this paper, we show that, in a discrete-time domain, the fuzzy PID controller is a superset of a time-delay controller (TDC). In other words, with certain fuzzy parameter conditions, the discrete fuzzy PID controller is equivalent to the discrete TDC. Tuning the fuzzy PID controller can be started by exploiting the TDC: a simple, efficient and effective controller. The initial fuzzy parameters can be obtained with equivalence relationships between the fuzzy PID controller and the TDC. Furthermore, the performance of the fuzzy PID controller can be enhanced by using the non-linear control surface described by various fuzzy parameters. To this end, a fuzzy TDC is proposed using the TDE and the desired fuzzy error dynamics, and a conversion formula from the fuzzy TDC to the fuzzy PID controller is derived in a discrete-time domain. The effectiveness of the proposed method is verified through experiments on a PUMA-type robot manipulator.

Dynamic Stability Improvement of a Smart Grid Using Neural Network Based STATCOM

Objectives: A micro grid is a cluster of loads and distributed resource units serviced by a distribution grid and capable of operation in a grid –connected mode, in an autonomous mode or a ride-through between the above two modes. Methods: Micro grids are significant for local reliability, considerable reduction of losses, different costs and continuity of service. Smart Grid is formed with the interconnection of different generating resources and loads, the characteristics of the grid can be modified according to the requirements. The major challenges are fault clearing, voltage regulation, islanding, and power quality and interfacing with the utility system in terms of its stability. Findings: This paper describes improvement of dynamic stability in interconnected on and off shore wind turbines with Proposed Artificial Neural Network Controller compared with the discrete Proportional–Integral–Derivative (PID) controller. As per the references indicated, the generators driven by OWF may be modeled as the parallel connection of several Doubly -Fed Induction Generators (DFIGs) and the generators driven by MCFs can be modeled by means of Squirrel Cage Induction Generators (SCIGs) well efficiently. Normally, STATCOMs or different combinations of Flexible AC Transmission System (FACTS) devices are used as large scale control devices in many applications. In the present work, Artificial Neural Network (ANN) based PID controller is used instead of Discrete PID controller for providing control pulses to the STATCOM connected to the grid system. Keywords: Artificial Neural Network, Converter, Power System Stability, Smart Grid, Static Var Compensators

Design and implementation of discrete PID control applied to Bitumen tank based on new approach of pole placement technique

This paper develops a novel approach for pole placement method of discrete proportional-integral-derivative (PID) control with industrial application of Bitumen system. The approach utilizes first order discrete-time transfer function (TF) with samples time delay more than unity for tuning the PID compensators, in order to achieve a priori set point of Bitumen mixing temperature. The work also introduces the well established Ziegler Nichols (ZN) and Chien-Hrones-Reswick (CHR) tuning techniques of discrete PID control, when applied to the same TF of Bitumen system, as benchmark. Bitumen system, sited at INSUMAT Company, is considered as a demonstrator for which the discrete PID control with the novel discrete pole placement approach is applied. Here, it is required to achieve a certain temperature for the Bitumen prior to the mixing process with the additives (polymers and fillers) in order to achieve a certain properties for insulation purposes. The key factor for the mixing process is the temperature of Bitumen which should not exceed \(\pm 5\,\%\) of the specified temperature, which ranges from 90 to \(180\,^{\circ }\hbox {C}\), to avoid reaching self-ignition state for the vapor inside the tank (\(\sim \)220\(\,^{\circ }\hbox {C}\)). This explains the avoidance of using conventional online tuning for PID compensators. Simulation results verify the applicability of the new approach and show satisfactory steady state response with very good control action when compared to the noisy control action of the ZN and CHR techniques. Finally, the paper shows successful implementation ‘onsite’ for the discrete PID control using the new approach for pole placement technique, for which all the control design criteria are verified.

Variable PID Gain Tuning Method Using Backstepping Control With Time-Delay Estimation and Nonlinear Damping

Proportional-integral-derivative (PID) controllers with constant gains seldom meet desired performance when system dynamics rapidly changes due to unknown disturbances. A gain tuning method for variable PID controllers is presented in this paper. First, the equivalence relationship between a discrete PID control and a discrete backstepping control with time-delay estimation and nonlinear damping is clarified, and the variable gains of the PID controller are automatically tuned with a nonlinear damping component. The nonlinear damping terms directly affect system performance and make PID gains vary. The system performance of a variable PID controller with the proposed method is compared with that of a constant PID controller. The experimental results show that the proposed method is adaptive, robust, and effective.

An experimental–numerical method for estimating heat transfer in a Bridgman furnace

Direct measurement of heat flux and heat transfer coefficients in a Bridgman furnace is not always possible using traditional methods. This study characterised a vertical tubular Bridgman furnace using experimental data so that the estimated heat flux and heat transfer coefficients may be used in simulations of future experiments using the same furnace. An experimental–numerical method is presented where a discrete proportional integral derivative controller manipulates the radial heat flux in a front tracking solidification model so that the output temperature profile matches experimental data. The method is applicable for other experimentalists and modellers and its usefulness is demonstrated by example.

Networked Control of a Large Pressurized Heavy Water Reactor (PHWR) With Discrete Proportional-Integral-Derivative (PID) Controllers

Networked control has been attempted for a wide variety of plants using memory-less State Feedback controllers. Networked Control Systems (NCSs) have also been mooted for PHWRs and implemented in practical systems e.g. a Reactor Regulating System (RRS) of the Indian PHWRs. While existing approaches using State Feedback controllers guarantee stability under data loss and variable delay which are inherent in real time communications, they cannot be extended to discrete PID controllers which involve a memory element. In this paper, a switched system formulation has been used to analyze the stability of a nuclear reactor with networked discrete PID controllers in the RRS under specified data loss and variable delay. The results have been verified using MATLAB xPC target based Real-time Simulation involving multiple simulation nodes integrated over switched Ethernet. A Distributed Network Analyzer (DNA) has been used to log actual network traffic to establish the credibility of the assumptions related to data loss and variable delay in communication.

A Systematic Method for Gain Selection of Robust PID Control for Nonlinear Plants of Second-Order Controller Canonical Form

A systematic method to select gains of a discrete proportional-integral-derivative (PID) controller is presented. The PID controller with the gains obtained by the proposed method can robustly control nonlinear multiple-input-multiple-output (MIMO) plants in a second-order controller canonical form, such as robot dynamics. This method has been made possible by the finding that the discrete PID control is equivalent to the discrete form of time-delay control (TDC), a robust control method for nonlinear plants with uncertainty. By using this equivalence relationships are obtained between PID gains and parameters of TDC, which enable a systematic method for the select PID gains. In addition, based on the systematic method, a simple and effective method is proposed to tune PID gains applicable to nonlinear plants with inaccurate models. This method incorporates a set of independent tuning parameters that is far less than those for conventional methods for PID gain selection. The usefulness of the proposed methods is verified through the ease and simplicity of determining PID gains for six degrees-of-freedom (DOF) programmable universal machine for assembly (PUMA)-type robot manipulator; the effectiveness of these PID gains is confirmed by the adequate and robust performance through experimentation on the robot.

Predictive PID

A new stochastic, predictive, proportional-integral-derivative (PID) control law is proposed which is mathematically equivalent to generalized predictive control (GPC) with a steady state weighting term. The main motivation of this paper is the extension of the classical PID algorithm on industrial computers to do advanced control without employing specialized software. The predictive PID constants and the internal model are chosen by equating the discrete PID control law with the linear form of GPC. The result is a long range predictive control law with a model based PID structure. Use of a first order model yields a PI controller while a second order plant results in a PID structure. The process model order is restricted to a maximum of two although there is no restriction on the choice of GPC tuning parameters. Performance of the predictive PID scheme is shown, via simulation, to be identical to GPC. Results from the use of the predictive PID algorithm for the control of an industrial heat exchanger are also presented.