Cristina I. Muresan

A novel auto-tuning method for fractional order PI/PD controllers

Fractional order PID controllers benefit from an increasing amount of interest from the research community due to their proven advantages. The classical tuning approach for these controllers is based on specifying a certain gain crossover frequency, a phase margin and a robustness to gain variations. To tune the fractional order controllers, the modulus, phase and phase slope of the process at the imposed gain crossover frequency are required. Usually these values are obtained from a mathematical model of the process, e.g. a transfer function. In the absence of such model, an auto-tuning method that is able to estimate these values is a valuable alternative. Auto-tuning methods are among the least discussed design methods for fractional order PID controllers. This paper proposes a novel approach for the auto-tuning of fractional order controllers. The method is based on a simple experiment that is able to determine the modulus, phase and phase slope of the process required in the computation of the controller parameters. The proposed design technique is simple and efficient in ensuring the robustness of the closed loop system. Several simulation examples are presented, including the control of processes exhibiting integer and fractional order dynamics.

Theoretical Analysis and Experimental Validation of a Simplified Fractional Order Controller for a Magnetic Levitation System

Fractional order (FO) controllers are among the emerging solutions for increasing closed-loop performance and robustness. However, they have been applied mostly to stable processes. When applied to unstable systems, the tuning technique uses the well-known frequency-domain procedures or complex genetic algorithms. This brief proposes a special type of an FO controller, as well as a novel tuning procedure, which is simple and does not involve any optimization routines. The controller parameters may be determined directly using overshoot requirements and the study of the stability of FO systems. The tuning procedure is given for the general case of a class of unstable systems with pole multiplicity. The advantage of the proposed FO controller consists in the simplicity of the tuning approach. The case study considered in this brief consists in a magnetic levitation system. The experimental results provided show that the designed controller can indeed stabilize the magnetic levitation system, as well as provide robustness to modeling uncertainties and supplementary loading conditions. For comparison purposes, a simple PID controller is also designed to point out the advantages of using the proposed FO controller.

A fractional order controller for seismic mitigation of structures equipped with viscoelastic mass dampers

In this paper a fractional order (FO) controller is proposed for solving the vibration suppression problem in civil structures. A laboratory scaled steel structure, with one floor, modeled as a single degree-of-freedom system is used as a case study. Two passive control solutions are proposed: a tuned mass damper (TMD) and a viscoelastic damper (VED), the latter being modeled using fractional derivatives. The simulation results show that the VED is able to further reduce the vibrations induced as forced oscillations or due to seismic excitation inputs, as compared to the passive TMD. The FO controller is then tuned using a new approach based on imposing a magnitude condition for the closed-loop system at the structural resonance frequency. The resulting FO active control strategy, together with the VED, ensures an increased seismic mitigation. Structural modeling errors are also considered, with the proposed active FO control strategy behaving robustly in terms of vibration suppression. The novelty of the paper resides in the tuning approach, as well as in the proposed active control strategy that is based upon combing VEDs, described using an FO model, and an FO controller.

Tuning algorithms for fractional order internal model controllers for time delay processes

ABSTRACT This paper presents two tuning algorithms for fractional-order internal model control (IMC) controllers for time delay processes. The two tuning algorithms are based on two specific closed-loop control configurations: the IMC control structure and the Smith predictor structure. In the latter, the equivalency between IMC and Smith predictor control structures is used to tune a fractional-order IMC controller as the primary controller of the Smith predictor structure. Fractional-order IMC controllers are designed in both cases in order to enhance the closed-loop performance and robustness of classical integer order IMC controllers. The tuning procedures are exemplified for both single-input-single-output as well as multivariable processes, described by first-order and second-order transfer functions with time delays. Different numerical examples are provided, including a general multivariable time delay process. Integer order IMC controllers are designed in each case, as well as fractional-order IMC controllers. The simulation results show that the proposed fractional-order IMC controller ensures an increased robustness to modelling uncertainties. Experimental results are also provided, for the design of a multivariable fractional-order IMC controller in a Smith predictor structure for a quadruple-tank system.

Fractional order control of a DC motor with load changes

This paper investigates the robustness of a fractional-order controller against the load changes of a DC motor. The gains and time constants of the DC motor are modified by means of a change in the brake. Two different setups of a DC motor, one with 25% brake and the other with 50% brake are considered in the experimental evaluation. The closed-loop performances of the fractional-order controller are compared with integer-order controller using the same performance criteria and the same tuning algorithm. Both controllers were designed based on time domain specifications. The experimental results show that the fractional-order controller outperforms the classical controller under nominal conditions as well as under gain variations situation.

Microcontroller Implementation of a Multivariable Fractional Order PI Controller

Fractional order calculus has been used intensively to control various types of processes. The main approaches towards fractional order controllers focus on the single-input-single-output systems. The general design procedure consists in a frequency domain specification of various performance criteria followed by optimization routines. The implementation issues regarding fractional order controllers are based on Oustaloup approximations and are centered on SISO processes. The present paper addresses the problem of implementing on a microcontroller a fractional order multivariable controller for time delay processes. The paper presents a tuning algorithm for determining the parameters of the multivariable fractional order controller and the implementation issues. The multivariable time delay process is implemented in Matlab Simulink environment. The experimental results show that the fractional order multivariable controller implemented on a simple microcontroller provides similar results to that obtained by simulation, even under uncertainty conditions.

Design and analysis of a multivariable fractional order controller for a non-minimum phase system

Two control strategies for multivariable processes are proposed that are based on a decentralised and a steady state decoupling approach. The designed controllers are fractional order PIs. The efficiency and robustness of the proposed strategies is tested and validated using a non-minimum phase process. Previous research for the same non-minimum phase process has proven that simple decentralised or decoupling techniques do not yield satisfactorily results and a multivariable IMC controller has been proposed as an alternative solution. The simulation results presented in this paper, as well as the experimental results, show that the proposed fractional order multivariable control strategies ensure an improved closed loop performance and disturbance rejection, as well as increased robustness to modelling uncertainties, as compared to traditional multivariable IMC controllers.

Fractional Calculus: From Simple Control Solutions to Complex Implementation Issues

Fractional calculus is currently gaining more and more popularity in the control engineering world. Several tuning algorithms for fractional order controllers have been proposed so far. This chapter describes a simple tuning rule for fractional order PI controllers for single-input–single-output processes and an extension of this method to the multivariable case. The implementation of a fractional order PI on an FPGA target for controlling the DC motor speed, as well as the implementation of a multivariable fractional order PI controller for a time delay system is presented. Experimental results are given to show the efficiency and robustness of the tuning algorithm.

A Portable Implementation on Industrial Devices of a Predictive Controller Using Graphical Programming

This paper presents an approach for developing an extended prediction self-adaptive controller employing graphical programming of industrial standard devices for controlling fast processes. For comparison purposes, the algorithm has been implemented on three different field-programmable gate arrays (FPGAs) chips. This paper presents research aspects regarding graphical-programming controller design, showing that a single advanced control application can run on different targets without requiring significant program modifications. Based on the time needed for processing the control signal and on the application, one can efficiently and easily select the most appropriate device. To exemplify the procedure, a conclusive case study is presented.

Vibration suppression in smart structures using fractional order PD controllers

Several important domains, such as the aerospace industry, are confronted with problems related to vibration. The solutions for reducing these vibrations are numerous, but are limited to a large number of passive methods, while the active solutions involve classical and intelligent control techniques. The present paper proposes a fractional order PD controller, for which the control parameters are computed in order to directly limit the vibrations at the resonance frequencies. The case study consists in a beam containing smart sensors and actuators using piezoelectric materials. The simulation results, considering both free and forced vibrations responses of the smart beam, show that the proposed method is simple and leads to an improvement of the closed loop behavior.