Digital PID Controller Design Research Articles

Impact of the Sampling Period on the Design of Digital PID Controllers

The impact of the sampling period on the parameterization of a digital PID controller in the frequency domain is attempted using three different digital approximations of the integral action. The controller is implemented in the industrial process of regulation of the cement sulphates in the cement mill outlet. The maximum sensitivity, Ms, has been utilized as a main robustness criterion. For the same Ms, proportional and differential gain, a rise of the sampling period leads to a decrease of the integral gain ki for all the three approximations. For the same sampling period, the function between proportional and integral gain differs for the three approximations studied. If the design satisfies two criteria simultaneously, maximum sensitivity and phase margin in the current study, then the permissible PID gains zone becomes narrower.

Multi-Objective Digital PID Controller Design in Parameter Space and its Application to Automated Path Following

This paper presents a multi-objective digital PID controller design method using the parameter space approach of robust control. Absolute stability is treated first by finding the digital PID controller gain parameter space corresponding to closed loop poles being inside the unit circle. Additionally, phase margin, gain margin and a mixed sensitivity bound are treated as frequency domain constraints. Determination of digital PID controller parameter space regions satisfying these constraints is presented. All of these regions are superimposed to obtain a multi-objective digital PID controller gain parameter space solution region. The path following controller design of an automated driving vehicle is used as an example to illustrate the method. This multi-objective parameter space design approach can be extended to other digital controller forms also.

Optimal digital PID controller design for regulating blood glucose level of type-I diabetic patients

The main objective of this paper is the design and implementation of an optimised PID controller using Xilinx System Generator for the regulation of blood glucose level of type-I diabetic patients. In this work, the Bergman model is used to describe diabetic patient model. The particle swarm optimisation algorithm is used to find the optimal values of the PID controller parameters. To determine parameters that meet closed loop system of the blood glucose regulation performance specification and to show its effectiveness, the proposed PSO-PID controller is compared to the classical PID. Finally, Xilinx System Generator is used to implement the digital optimal PID controller and verify its capability.

Optimal digital PID controller design for regulating blood glucose level of type-I diabetic patients

Optimal digital PID controller design for regulating blood glucose level of type-I diabetic patients

Digital PI-PD controller design for arbitrary order systems: Dominant pole placement approach

In this paper, a digital PI-PD controller design method is proposed for arbitrary order systems with or without time-delay to achieve desired transient response in the closed-loop via dominant pole placement approach. The digital PI-PD controller design problem is solved by converting the original problem to the digital PID controller design problem. Firstly, parametrization of the digital PID controllers which assign dominant poles to desired location is done. After that the subset of digital PID controller parameters in which the remaining poles are located away from the dominant pole pair is found via Chebyshev polynomials. The obtained PID controller parameters are then transformed into the PI-PD controller parameters by considering the closed-loop controller zero and the design is completed. Success of the proposed design method is firstly demonstrated on an example transfer function and compared with the well-known PID controller methods from the literature through simulations. After that the design method is implemented on the fan and plate laboratory system in a real environment.

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.

Design of Digital PID Controllers using Particle Swarm Optimization: A Video Based Teaching Experiment

The use of videos is a valuable and powerful tool which may significantly contribute to change and improve teaching and learning methods. Lecturers can made their own videos addressing specific topics suitable to fulfill their student’s needs. These videos can address control engineering syllabus as well as complementary topics. This paper proposes using video as a tool to introduce the particle swarm optimization algorithm to students within a digital PID control simulation experiment. The experience preliminary results and feedback received from students are quite positive.

A New Approach for Calculation of PID Parameters with Model Based Compact Form Formulations

PID controller is a popular control method still widely used in process industry. In literature there are model/non-model based calculation methods for PID parameters. However, a model based analytic formulation in compact form in discrete time has not been come across yet. This study presents a new approach for calculation of PID parameters with model based analytic formulation (MBCF), which is presented uniquely in this paper, in compact form, in discrete time. Furthermore, a procedure for implementation of the proposed formulas is given in four stages. The formulations in related literature for PID parameter calculation are all derived for continuous time. Therefore, extra transformations are required for a discrete time design. The proposed MBCF formulation method reduces extra calculation burden and simplifies calculation complexity. Moreover, this method provides a direct calculation method for digital PID controller design in discrete time. The derived expressions in this study also provide a fast, easy-implemented, and practical PID parameter calculation method for all field researchers and application engineers. The validation of proposed MBCF formulations are comparatively proved with the simulations and the real time application results. DOI: http://dx.doi.org/10.5755/j01.eee.20.3.4415

Digital PID Controller Design of Electromagnetic Suspension (EMS) System

This paper presents the digital PID controller design of magnetic levitation application. The highly nonlinear of electromagnetic suspension (EMS) system is hardly and limited the system control subjected to prescribed stability of system. Due to the nonlinear dynamics of system, the linearization of the nonlinear EMS plant is described by linear model. An attraction force about the prescribed nominal operating point of current and air gap positioning is chosen for linearization at a nominal operating point. Such a linear system, digital PID controller is designed for controlling the EMS plant. The system stability is validated by experiment methods. From the results, the reference of air gap position can be tracked with the desired nominal operating air gap position control as shown in practical manner.

Decentralized Digital PID Controller Design for Performance

The paper deals with the frequency domain decentralized discrete-time controller design methodology to guarantee specified performance of the overall system. The underlying theory evolves from the stability conditions developed in the “Equivalent Subsystems Method” approach and applies closed-loop performance specification based on the relationship between phase margins of equivalent subsystems and maximum overshoot of the full system. To design local PI controllers for specified phase margin, Bode plots of discrete equivalent subsystems are used. Designed local continuous controllers are then converted to their discrete versions and implemented for the controlled plant. The design procedure is illustrated on the case study.

STATE‐SPACE DIGITAL PID CONTROLLER DESIGN FOR MULTIVARIABLE ANALOG SYSTEMS WITH MULTIPLE TIME DELAYS

ABSTRACTThis paper presents a discrete‐time state‐space methodology for optimal design of digital PID controllers for multivariable analog systems with multiple time delays. The multiple time‐delayed multivariable analog systems are formulated in a state‐space generic form so that the exact discrete‐time state‐space model can be constructed. Then, the optimal digital PID controller is designed via a state‐feedback and state‐feedforward LQR approach. The developed PID controller can be applied to a general time‐delayed multivariable analog system represented by a semi‐proper or strictly proper transfer function matrix. Illustrative examples are given to compare the performance of the proposed approach with alternative techniques.

Digital PID controller design for multivariable analogue systems with computational input-delay

Digital PID controller design for multivariable analogue systems with computational input-delay

A new approach to digital pid controller design

In this note, we present a new approach to the problem of designing a digital proportional-integral-derivative (PID) controller for a given but arbitrary linear time invariant plant. By using the Tchebyshev representation of a discrete-time transfer function and some new results on root counting with respect to the unit circle, we show how the digital PID stabilizing gains can be determined by solving sets of linear inequalities in two unknowns for a fixed value of the third parameter. By sweeping or gridding over this parameter, the entire set of stabilizing gains can be recovered. The precise admissible range of this parameter can be predetermined. This solution is attractive because it answers the question of whether there exists a stabilizing solution or not and in case stabilization is possible the entire set of gains is determined constructively. Using this characterization of the stabilizing set we present solutions to two design problems: 1) maximally deadbeat design, where we determine for the given plant, the smallest circle within the unit circle wherein the closed loop system characteristic roots may be placed by PID control and 2) maximal delay tolerance, where we determine, for the given plant the maximal-loop delay that can be tolerated under PID control. In each case, the set of controllers attaining the specifications is calculated. Illustrative examples are included.

Digital PID controller design via general discrete orthogonal polynomials

Based on the discrete orthogonal polynomials, a new computer-oriented algebraic method is proposed for designing a digital PID controller. The PID controller can approximately achieve an arbitrarily specified closed-loop response, and is determined by solving a linear equation using the least squares method. An example is given to demonstrate the availability of the proposed technique.