Design and experimental evaluation of a data-oriented multivariable PID controller

On the design of multivariable PID controllers via LMI approach

An improvement on multivariable PID controller design via iterative LMI approach

Multivariable fractional order PID controller design via LMI approach

Design of a Data-Driven PID Controller using Operating Data

This paper proposes a new offline learning algorithm for a data-driven proportional-integral-derivative (DD-PID) controller based on an extended fictitious reference iterative tuning (E-FRIT). PID controllers have been used in many process systems. However, it is difficult to maintain a good control performance using PID controllers with fixed control parameters because of the nonlinearity of the systems. The DD-PID controller has been proposed as an effective control system for nonlinear systems. This controller can tune its PID parameters adaptively at each equilibrium point of the system output. In the conventional DD-PID controller, the PID parameters are learned so as to minimize a criterion of the FRIT method. However, the FRIT method is based on minimization of the error in system output, and therefore, the criterion is insufficient for systems, such as chemical process systems, for which the stability of a closed loop system is essential. In order to solve this problem, the E-FRIT method has been proposed; a penalty for input variation is incorporated in the criterion for this method. In the present study, an offline learning rule of PID parameters was derived based on the E-FRIT criterion. According to the rule, the PID parameters that are taken into stability can be calculated. The effectiveness of the proposed method was evaluated by simulations of a polystyrene reactor system. The simulation confirmed that the proposed DD-PID controller yields better control result than the conventional learning method.

This paper concerns design and implementation of PID and fractional-order PID (FOPID) controllers to control position of an electromagnetically suspended ferromagnetic ball in a magnetic levitation (Maglev) system in real time. The Maglev system, manufactured by Feedback Instruments (Model No 33-210) is used as a platform to test the performance of proposed controllers. Parameters of PID and FOPID controllers are tuned by firefly algorithm (FA). FA is a metaheuristic algorithm based on movement of fireflies toward more attractive and brighter ones. PID and FOPID controllers are implemented in MATLAB and SIMULINK environment inside PC using fractional-order modeling and control toolbox. Controller in the SIMULINK environment inside PC is connected to the Maglev system through Advantech card. Effectiveness of proposed controllers is tested by checking the ability of the suspended ball to track a reference signal. Step change, sine wave, and square wave are used as reference signals. Real-time results have revealed satisfactory transient and steady-state responses over the contemporary existing controllers. FOPID controller showed better results compared to PID.

Evolutionary tuning of PID parameters

This paper presents a dynamic model estimation using system identification (SI) technique and a multivariable controller design for an unmanned surface vehicle (USV) with two fixed thrusters. The catamaran shaped USV has been developed for marine research and surveying exploration in costal area. To validate the automatic control performance of USV, which is designed by classical PID controller, we carried out experiments to keep the USV's position at a fixed point and to track predefined positions. As a result, we have found that it needs time-consuming efforts to tuning the weight between heading and speed controller since the yawing and surge motions are tightly coupled to the two thrusters. In order to solve the problem, it is necessary to introduce the multivariable controller design method. And a numerical dynamic model is required for the model based design. This paper addresses the estimation of a dynamic model of the USV based on the experimental results and the design of Linear-Quadratic (LQ) controller based on a multivariable control method. To verify the efficiency of the designed controller using the estimated dynamic model, numerical simulations were carried out.

The design and implementation of a multi-stage PID (MS-PID) controller for non-inertial referenced UAVs are highly complex. Symmetrical multirotor UAVs are unstable systems, and it is thought that the kinematics of the symmetrical UAV rotor, such as the quadrotor and hexacopter resembles the kinematics of an inverted pendulum. Several researchers have investigated the structure and design of PID controllers for high-order systems during the last decade. The designs were always concerned with the enhanced response, robustness, model reduction and performance of PID controllers. An accurate tuning process of such a controller depends on the engineer’s experience level. This is due to the number of variables and hyperparameters tuned during the process. An adaptive genetic algorithm (AGA) is utilized to optimize the MS-PID controllers for controlling the quadrotor in this study. The proposed method optimizes the offline-planned approach, providing several possibilities for adapting the controllers with various paths and or varying weather conditions. The MS-PID parameters are optimized in parallel, as every PID controller affects the other controller’s behavior and performance. Furthermore, the proposed AGA generates new chromosomes for “new solutions” by randomly developing new solutions close to the previous best values, which will prevent any local minima solution. This study intends to investigate the design and development of a highly tuned robust multi-stage PID controller for a symmetrical multirotor UAV. The work presents a model for a non-referenced inertial frame multirotor UAV (quadcopter). Once the model is defined, a robust multi-stage PID controller for the non-inertial referenced frame symmetrical multirotor UAV is designed, tuned, and tested. A genetic algorithm (GA) will be used to tune the MS-PID controller. Finally, the performance comparison between the proposed and conventional methods is presented. The results show that the proposed method provides stability improvement, better transient response, and power consumption.

Single-input interval type-2 fuzzy PID (SI-IT2-FPID) control approach is a simple and effective way of adding nonlinear characteristics to linear PID controllers to increase the control performance and the capability of handling system nonlinearities. In the SI-IT2-FPID approach, the nonlinear characteristic of the PID controller is provided by a single-input–single-output interval type-2 fuzzy controller (IT2-FC) positioned before the PID controller. In the literature, a constant footprint of uncertainty (C-FOU) structure is used in SI-IT2-FPID controller design procedures in almost all studies. However, the C-FOU structure limits the performance of the SI-IT2-FPID controller. In this study, an online footprint of uncertainty (FOU) tuning mechanism is proposed for SI-IT2-FPID controllers in order to increase their control performances. Online tuning of FOUs of interval type-2 membership functions (IT2-MFs) enhances the capability of SI-IT2-FPID controllers to handle system nonlinearities since FOU levels of IT2-MFs have a dominant effect on the control and robustness performance of SI-IT2-FPID controllers. In the proposed method, FOUs of IT2-MFs of an IT2-FC are adjusted by an analytical function based on the system error and the change of the error. In this way, the simple structure of the SI-IT2-FPID controller is preserved. In order to illustrate the control and robustness performance of the proposed controller, simulation studies are carried out on three benchmark systems, namely a second-order nonlinear system, a ball and beam system, and a first-order plus dead time system. Additionally, the performance of the proposed controller is compared to a SI-IT2-FPID controller with C-FOU and a classical PID controller. The simulation results show that the proposed controller exhibits better control and robustness performance than the other controllers.

PID control schemes have been widely used in most process control systems for a long time. However, it is a very important problem how to choose suitable PID parameters. Because these parameters give a great influence on the control performance. Especially, it is difficult to tune these parameters for time-varying systems. In this paper, design scheme of a performance adaptive controller is proposed for such systems, which is based on the IMC tuning method. It is well known that the IMC tuning method includes a user-specified parameter. The control performance can be suitably improved by using the user-specified parameter.

The gain and phase margins design for SISO PID controllers is extended to the multivariable system Nyquist array. The design method allows the user to specify the robustness and performance of the system through gain and phase margin specifications. The automated design procedure given in this paper is well suited for implementing self-tuning PID control for multivariable processes. A laboratory implementation is given in the paper to demonstrate the design method.

PID control schemes have been widely employed for most process systems represented by chemical processes. However, it is a very important problem how to tune PID parameters, because these parameters have a great influence on the stability and the performance of the control system. On the other hand, lots of works for the robust control have been carried out to cope with system uncertainties. Then, some PID parameter tuning methods have been proposed based on the robust stability. However, if the range of uncertainties is very large, the control performance becomes quite conservative. By the way, the support vector machine (SVM) has been proposed as one of the pattern recognition methods and gets lots of attention in last decades. The main motivation in this paper is to present a design scheme of controllers with the switching structure, in which some robust PID controllers are suitably switched using the SVM. Finally, the proposed control scheme is numerically evaluated on a simulation example.

An optimal PID controller with incomplete derivation is proposed based on fuzzy inference and the genetic algorithm, which is called the fuzzy-GA PID controller with incomplete derivation. It consists of the off-line part and the on-line part. In the off-line part, by taking the overshoot, rise time, and settling time of system unit step response as the performance indexes and by using the genetic algorithm, a group of optimal PID parameters K*p, T*i, and T*i are obtained, which are used as the inital values for the on-line tuning of PID parameters. In a on-line part, based on K*p, T*i, and T*d and according to the current system error e and its time derivative, a dedicated program is written, which is used to optimize and adjust the PID parameters on line through a fuzzy inference mechanism to ensure that the system response has optimal dynamic and steady-state performance. The controller has been used to control the D. C. motor of the intelligent bionic artificial leg designed by the authors. The result of computer simulation shows that this kind of optimal PID controller has excellent control performance and robust performance.

For the stability problem of the active magnetic levitation ball, the application of the PID controller on the system is determined. Firstly, the linearized mathematical model of the active magnetic levitation ball system is established. Then the PID parameters are adjusted by the trial method. The influence of three PID parameters on the system is introduced, and a PID controller is designed for a set of actual systems. The performance is simulated and experimentally studied. The research results show that the active electromagnetic suspension ball system based on PID controller has high anti-interference performance and stability.