Discrete-time PID Research Articles

Stabilizing regions of dominant pole placement for second order lead processes with time delay using filtered PID controllers.

In order to handle second order lead processes with time delay, this paper provides a unique dominant pole placement based filtered PID controller design approach. This method does not require any finite term approximation like Pade to obtain the quasi-polynomial characteristic polynomial, arising due to the presence of the time delay term. The continuous time second order plus time delay systems with zero (SOPTDZ) are discretized using a pole-zero matching method with specified sampling time, where the transcendental exponential delay terms are converted into a finite number of poles. The pole-zero matching discretization approach with a predetermined sampling period is also used to discretize the continuous time filtered PID controller. As a result, it is not necessary to use any approximate discretization technique, such as Euler or Tustin, to derive the corresponding discrete time PID controller from its continuous time counterpart. The analytical expressions for discrete time dominant pole placement based filtered PID controllers are obtained using the coefficient matching approach, while two distinct kinds of non-dominant poles, namely all real and all complex conjugate, have been taken into consideration. The stabilizable region in the controller and design parameter space for the chosen class of linear second order time delay systems with lead is numerically approximated using the particle swarm optimization (PSO) based random search technique. The efficacy of the proposed method has been validated on a class of SOPTDZ systems including stable, integrating, unstable processes with minimum as well as non-minimum phase zeros.

Energy Minimization of New Robotic-Type Above-Knee Prosthesis for Higher Battery Lifetime

In this paper, an optimization problem for the energy minimization of a new robotic-type three-axes above-knee prosthesis is carried out based on the actuator power consumption. The optimization problem aims to find the optimal link masses with which to minimize the electrical energy drawn from the battery of the new prosthesis, subject to the kinematic and dynamic constraints. Particle swarm optimization (PSO) is used as the optimization algorithm. A discrete-time PID controller is used to represent the saved energy by means of mass optimization. Optimization illustrated that energy consumption in the batteries can be reduced 51% and provides 1.89 h of additional battery lifetime, according to the literature, by optimizing prosthetic link masses while providing acceptable prosthesis stiffness.

Discrete-Time Adaptive PID Current Controller for Wind Boost Converter

This paper proposes an adaptive controller for a dc-dc boost converter to regulate the output current levels of a 400 W small wind turbine based on a permanent magnet synchronous generator with a three-phase diode rectifier. Despite the stochastic nature of wind, this discrete-time adaptive PID controller regulates the current levels without large overshoots and oscillations to attain the maximum power point of the wind system. The adaptive mechanism algorithm operating with two electrical measurements adjusts the controller parameters, and is designed with an approach consisting of the integration of the variable operation point of the small wind turbine into the discrete-time model of the dc-dc boost converter and the Bode stability criteria. The mechanism algorithm features a low computational complexity for controller parameters estimation and therefor a practical implementation in a low-end microcontroller (small size, low cost, and low energy consumption) is possible. Furthermore, the results based on the processor-in-the-loop simulation approach show that controlling the current levels and the maximum power point of the wind system via the proposed adaptive controller is more effective than a controller tuned around a particular fixed operating point.

Multivariable generalized predictive control of reactive distillation column process for biodiesel production

Most industrial control systems consist of a significant number of control loops. Generally, large processes are divided into many interconnected subsystems affecting each other, thus creating multivariable systems known as multiple–input multiple–output (MIMO) process. Generalized Predictive Control (GPC) based control algorithm is most suitable for MIMO systems. In this study, multivariate nonlinear (NL) GPC and discrete–time PID control of calcium oxide catalyst–packed reactive distillation (RD) column used for biodiesel production from waste cooking oil were investigated. Temperatures of reaction and reboiler sections were controlled by using non–decoupled and decoupled MIMO NLGPC and discrete–time MIMO PID algorithms. Feed flow rate with constant molar ratio and reboiler heat duty parameters were selected as manipulating variables. All recommended control methods, except for non-decoupled MIMO NLGPC, have been found to perform satisfactorily reference tracking and disturbance rejection in RD column. Consequently, the best control results were obtained in the decoupled MIMO NLGPC.

Experimental performances of nonlinear GPC and discrete–time PID in multivariate process: NARIMAX and ARX models in temperature control of reactive distillation column in synthesis of biodiesel from waste cooking oil

Experimental performances of nonlinear GPC and discrete–time PID in multivariate process: NARIMAX and ARX models in temperature control of reactive distillation column in synthesis of biodiesel from waste cooking oil

Dominant pole region assignment with discrete time PI, PID and PIR controllers

Dominant pole region assignment with discrete time PI, PID and PIR controllers

A Tuning Method via Borges Derivative of a Neural Network-Based Discrete-Time Fractional-Order PID Controller with Hausdorff Difference and Hausdorff Sum

In this paper, the fractal derivative is introduced into a neural network-based discrete-time fractional-order PID controller in two areas, namely, in the controller’s structure and in the parameter optimization algorithm. The first use of the fractal derivative is to reconstruct the fractional-order PID controller by using the Hausdorff difference and Hausdorff sum derived from the Hausdorff derivative and Hausdorff integral. It can avoid the derivation of the Gamma function for the order updating to realize the parameter and order tuning based on neural networks. The other use is the optimization of order and parameters by using Borges derivative. Borges derivative is a kind of fractal derivative as a local fractional-order derivative. The chain rule of composite function is consistent with the integral-order derivative. It is suitable for updating the parameters and the order of the fractional-order PID controller based on neural networks. This paper improves the neural network-based PID controller in two aspects, which accelerates the response speed and improves the control accuracy. Two illustrative examples are given to verify the effectiveness of the proposed neural network-based discrete-time fractional-order PID control scheme with fractal derivatives.

Multivariable Unconstrained Pattern Search Method for Optimizing Digital PID Controllers Applied to Isolated Forward Converter

Most of the traditional PID tuning methods are heuristic in nature. The heuristic approach-based tuned PID controllers show only nominal performance. In addition, in the case of a digital redesign approach, mapping of the heuristically-designed continuous-time PID controllers into discrete-time PID controllers and in case of the direct digital design approach, mapping of the continuous-time plant (forward converter) into the discrete-time plant, results in frequency distortion (or warping). Besides this, nonlinear elements such as ADC and DAC, and delay in the digital control loop deteriorate the control performance. There is a need to tune conventionally-designed digital controllers to enhance performance. This paper proposes optimized discrete-time PID controllers for a forward DC–DC converter operating in continuous conduction mode (CCM). The considered conventional digital PID controllers designed on the basis of the digital redesign and direct digital approaches are tuned by one of the multivariable unconstrained pattern search methods named Hooke–Jeeves (H–J) search method to ensure excellent output voltage regulation performance against the changes in input voltage and load current. Numerical results show that the H–J-based optimized PID compensated forward converter system shows tremendous improvement in performance compared to its unoptimized counterpart and simulated annealing (SA)-based compensated system, thus justifying the applicability of the H–J method for enhancing the performance.

Discrete-time filter proportional–integral–derivative controller design for linear time-invariant systems

This paper introduces a new discrete-time filter proportional–integral–derivative (FPID) controller framework for linear time-invariant (LTI) systems. The discrete-time FPID controller plays an important role in both determining the dynamic response of the system and further improving the performance of the controller in itself. However, the introduction of the filter parameter brings more challenge for the design of discrete-time FPID controllers than that of discrete-time PID controllers. A novel result on the co-design of such a controller via dominant eigenvalue assignment is first provided, which enables us to tune the controller directly in accordance with the desired system performance indexes. Then, a further result on the discrete-time FPID controller design to improve the dynamic response of the closed-loop system is derived by placing the non-dominant eigenvalues in some assigned region. Compared with the discrete-time PID controller, on the one hand, the discrete-time FPID controller plays a significant role in improving the output of the controller in addition to guaranteeing the desired dynamic performance of the closed-loop system. On the other hand, a discrete-time FPID controller makes it possible to expand the effective parameter region and give a set of parameters which makes the controller achieve the objective of dominant eigenvalue assignment for the closed-loop system when a traditional discrete-time PID controller cannot do. Numerical examples have illustrated the effectiveness of the proposed results.

Optimal design of discrete-time fractional-order PID controller for idle speed control of an IC engine

This paper aims at proposing a discrete-time fractional-order PID (FOPID) controller, which can stabilise the variation of the idle speed of an internal combustion engine due to the occurrence of the external load disturbance. The nonlinear idle speed dynamics is linearised to be approximated by a first order plus dead time (FOPDT) model so that the FOPID controller can be initialised by a Ziegler-Nichols type tuning rule. The initialised FOPID controller can stabilise the linearised model, but it may lose its control capability in nonlinear idle speed dynamics. Therefore, an optimisation problem is solved through genetic algorithm (GA) to minimise a cost function within a small region around the FOPID's initial parameters. The optimal discrete-time FOPID controller are compared to a conventional discrete-time PID controller. The simulation study reveals that the optimal discrete-time FOPID controller secures an excellent control performance to the nonlinear idle speed model.

Optimal design of discrete-time fractional-order PID controller for idle speed control of an IC engine

This paper aims at proposing a discrete-time fractional-order PID (FOPID) controller, which can stabilise the variation of the idle speed of an internal combustion engine due to the occurrence of the external load disturbance. The nonlinear idle speed dynamics is linearised to be approximated by a first order plus dead time (FOPDT) model so that the FOPID controller can be initialised by a Ziegler-Nichols type tuning rule. The initialised FOPID controller can stabilise the linearised model, but it may lose its control capability in nonlinear idle speed dynamics. Therefore, an optimisation problem is solved through genetic algorithm (GA) to minimise a cost function within a small region around the FOPID's initial parameters. The optimal discrete-time FOPID controller are compared to a conventional discrete-time PID controller. The simulation study reveals that the optimal discrete-time FOPID controller secures an excellent control performance to the nonlinear idle speed model.

Real Time Performance Comparison of Buck Converter Circuit Controlled By Discrete Time PID, LQR and SMC Controllers in Continuous-Current Mode

In this study, a DC-DC buck converter circuit which is used to get direct voltage by decreasing the source voltage is researched. Firstly mathematical model for a DC-DC buck converter circuit is obtained and critical inductance value is calculated to make it work in continuous current mode. Then for controlling a DC-DC buck converter, three different controllers in discrete time (sliding mode control, proportional–integral–derivative controller and linear quadratic regulator) are designed. Finally, the performance of these controllers according to changing in the form of step function for input voltage, reference voltage and load conditions are examined and compared with real time studies. According to obtained results, a DC-DC buck converter circuit controlled by sliding mode controller has shown a better performance compared to the other controllers.

An adaptive PID controller with an online auto-tuning by a pretrained neural network

This paper describes an intelligent adaptive PID controller design procedure. The controller consists of a discrete time PID and an auto-tuning neural network unit. First system identification with a nonlinear autoregressive model (NARX) was performed. This model was then used to train the neural PID tuner. A special MATLAB toolbox “SmatPID Toolbox” was developed to automate the process of controller synthesis. The resulting controller was tested in a laboratory coal-gas furnace control system to track specified air flow rates.

Chatter Mitigation in Milling Process Using Discrete Time Sliding Mode Control with Type 2-Fuzzy Logic System

In order to achieve a high-quality machining process with superior productivity, it is very important to tackle the phenomenon of chatter in an effective manner. The problems like tool wear and improper surface finish affect the milling process and are caused by self-induced vibration termed as chatter. A strategy to control chatter vibration actively in the milling process is presented. The mathematical modeling of the process is carried out initially. In this paper, an innovative technique of discrete time sliding mode control (DSMC) is blended with the type-2 fuzzy logic system. The proposed active controller results in a significantly high mitigation of vibration. The DSMC is linked to the time-varying gain which is an innovative approach to mitigate chattering. The theorem is laid down which validates that the system states are bounded in the case of DSMC-type-2 fuzzy. Stability analysis is carried out using Lyapunov candidate. The nonlinearities linked with the cutting forces and damper friction are handled effectively by using the type-2 fuzzy logic system. The performance of the DSMC-type-2 fuzzy concept is compared with the discrete time PID (D-PID) and discrete time sliding mode control for validating the effectiveness of the controller. The better performance of DSMC-type-2 fuzzy over D-PID and DSMC-T1 fuzzy in the minimization of milling chatter are validated by a numerical analysis approach.

Optimal Setting and Control Strategy for Industrial Process Based on Discrete-Time Fractional-Order PI$^{\lambda}$ D$^{\mu}$

Generally, the main task of the optimal operation in the industrial process is to satisfy the process technical requirements, and the PID controller is a well-known controller in industrial control applications. Nevertheless, due to the complicated mechanisms and the dynamic characteristics of a complex industrial process, the conventional PID controller fails to provide effective control to such systems. In this paper, we develop a novel discrete-time fractional order PID (DFOPID) control strategy to achieve the technical requirements of the complex industrial process. The proposed work is conducted through a combination of three novel interdependent efforts. First, on the basis of the widely used Tustin operator and its Taylor series, a digital structure of the DFOPID is proposed. Second, in order to solve the stability problem of the complex industrial process, an optimal setting of the approximation function's order (N) and five parameters (λ, μ, K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> , K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> , K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> ) is necessary. Hence, an integral time absolute error (ITAE) criterion is applied to convert the optimal setting problem to a nonconvex optimization problem. Finally, a novel intelligent optimization search algorithm called state transition algorithm is employed to carry out the aforementioned design procedure. Furthermore, the performance of the DFOPID control strategy in some practical industrial control systems, including the copper removal process and the electrochemical process of zinc are also investigated.

Introduction to the Discrete Time PIDmn Control for the IPDT Plant

The aims of this paper are: (a) to extend the discrete time 2DOF PI and PID controller for the integral plus dead time (IPDT) models to the 2DOF PIDmn mn control with an mth order derivative action (m = 0,1, 2) tuned by the multiple real dominant pole method, (b) to introduce simple integrated tuning procedures of all the considered controllers augmented with the n ≥ mth order series binomial filters required for the derivative action implementation and measurement noise attenuation and (c) to compare the filtered controllers as for the performance limits expressed in terms of the integral of absolute error (IAE) and the relative total variance.

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.

Optimal trajectory generation algorithm for serial and parallel manipulators

In this paper, an Optimal Trajectory Generation Algorithm (OTGA) is developed for generating minimum-time smooth motion trajectories for serial and parallel manipulators. OTGA is divided into two phases. The first phase encompasses derivation of minimum-time optimal trajectory using cubic spline due to its less vibration and overshoot characteristics. Although cubic splines are widely used in robotics, velocity and acceleration ripples in the first & last knots can worsen manipulator trajectory. The second phase includes changing cubic spline interpolation in the first and last knots of optimized trajectory with 7th order polynomial for having zero jerk at the beginning and end points of trajectory. Performing this modification eliminate undesired worsening in the trajectory and provide smoother start and stop of joint motions. Particle Swarm Optimization (PSO) is chosen as optimization algorithm because of its easy implementation and successful optimization performance. OTGA has been tested in simulation for PUMA robot and results are compared with algorithms proposed by earlier authors. In addition, a discrete-time PID control scheme for PUMA robot is designed for comparing energy consumption of OTGA with algorithms developed by previous authors. Comparison results illustrated that OTGA is the better trajectory generation algorithm than the others.

Identification and Nonlinear PID Control of Hammerstein Model using Polynomial Structures

In this paper, a new nonlinear discrete-time PID is proposed to control Hammerstein model. This model is composed by a static nonlinearity gain associated to a linear dynamic sub-system. Nonlinear polynomial structures are used to identify and to control this class of systems. The determination of parameters is based on the use of RLS algorithm. A coupled two-tank process is given to illustrate the effectiveness of the proposed approach.

PSO and DE Based Model Order Reduction and Discrete Time Structure Specified Controller Design

Background/Objectives: The objective is to reduce the order of the plant and design discrete time PID controller using Particle Swarm Optimization (PSO) and Differential Evolution. Methods/Statistical analysis: Two popular optimization techniques – PSO and Differential Evolution (DE) are used to obtain the reduced order model of the physical plant and its discrete time structure specified PID controller. The objective function used for model order reduction is an integral square error between outputs of original and reduced order model. Whereas, the controller designs, integral square error between output and reference signal is chosen for tracking purpose. Findings: Nominal models for physical systems are highly complex and their order is usually very high. Designing controllers for such models in industries require huge amount of cost and large number of hardware components. The optimization techniques will prevent this issue, as shown in this paper. The optimal reduced model and optimal controllers are extremely useful for the industrial applications. Application/Improvements: In this paper, this methodology is proposed to design discrete time controller for a process of eight orders. But, this approach can be effectively applied to the complex plants for implementation of controller.