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

PID control has been applied in many real systems. The control performance strongly depends on PID parameters. Although, some schemes for tuning PID parameters have been proposed, these schemes require system parameters which are estimated by system identification in order to calculate PID parameters. Moreover, most process systems are multivaliable systems which have interference of each respective inputs. On the other hand, data-oriented controller design schemes represented by VRFT or FRIT have received much attention in the last few years. These methods can calculate control parameters using closed loop data, and are expected to reduce computational costs. However, these methods have not been extended for MIMO systems. In this paper, a type of data-oriented multivariable PID controller using closed loop data is proposed. According to the proposed method, full matrices PID parameters which suppress mutual interference are calculated based on the implicit GMVC. Moreover, the control performance can be suitably adjusted by user-specified parameters. The effectiveness of the proposed method is numerically and experimentally evaluated.

The paper considers the problem of PID controller design for stabilizing fractional systems with time delay. An analytic approach developed for rational systems with time delay is extended for fractional systems with time delay. It consists in determining the stability regions in the PID controller parameters planes and choosing the optimal controller by analyzing the stability of the closed-loop corrected system using a graphical criterion, like the dual-locus diagram. The performances of the proposed approach are illustrated using two numerical examples.

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.

Weighted sensitivity design of multivariable PID controllers via a new iterative LMI approach

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.

The photovoltaic (PV) system’s nonlinear nature, uncertainty in temperature, and light intensity in the environment are responsible for the fluctuation of the maximum power point (MPP). Many maximum power point tracking (MPPT) algorithms are proven effective in the literature, including use of artificial intelligence. Proportional integral derivative controller and fuzzy controllers found effective to track MPP. Using the combination of Fuzzy-PID controller, swiftly adapt to changes in the atmosphere to confirm the solar array is continually operating at its highest efficiency with MPP. Easy and effective oscillation elimination is possible with PID control. To regulate the maximum power of the PV system combination of Fuzzy-PID self-tuning controllers is found effective.The goal is to enhance a PV system’s dynamic response to in presence of irradiation and temperature fluctuations. For tuning Fuzzy logic controller (FLC), gain scheduler values of the proportional, integral, and derivative constants are fundamental. The design processes for non-linear conventional PID controllers, FLC, and series combination of Fuzzy-PID controller are discussed. It compares the traditional PID controller, FLC, and Fuzzy-PID controller. The comparison of outputs produced for PID, FLC, and series Fuzzy-PID controller confirms the effectiveness of the algorithm. Use of Fuzzy controller helps in self-tuning of PID controller constant value. MATLAB/Simulink based environment used to perform the simulations.

The main advantage of one-cycle control method is its ability to reject input disturbance in one-cycle. But despite of this great ability, it can not provide good responses in following commands and rejection of load disturbance. In this work, it is shown that it is possible to overcome these problems by the use of another controller. Although the idea of using output feedback has been used in previous works, the design of controller has become simpler in this work, by consideration of a simple model for one-cycle controller. In proposed method, difficult mathematical modeling is avoided. Based on decoupling of effects of feedback and input voltage disturbance, a simple model for one-cycle controller has been given. Therefore, by employing a conventional averaging method and the model of one-cycle controller, design of PID controller has become straightforward.

The main purpose of this article is to present the design, optimal setting and experimental study of a multivariable PID controller supposed for electrohydraulic power steering system with load-sensing function. The set of the controller is performed through an optimization procedure based on a genetic algorithm. The PID controller is embedded into a microcontroller for mobile machinery used in laboratory test rig for investigation of an electrohydraulic servo steering system. Results obtained in conditions of physical experiment and numerical simulation with the optimally tuned PID controller are presented. An analysis of the control performance, as well as some features of the used method for setting the PID controller.

Adaptive Design of PID Controllers Based on an Alternative Method to Root Locus ⋆

The mathematic model considering magnetic flux loss of Maglev train and the design of PID controller are studied. During the process of analysis and design of PID controller, some new performance indexes, which were firstly put forward by Wang Guangxiong and are used to judge sufficient stable degree for controlling unstable system, are studied. Bode plot is used to validate the modified phase margin. Compared to Wang's conclusion, the more widely accepted phase margin is brought forward. Furthermore, the PID controller and performance indexes are validated by nonlinear simulation model.

It is the function of the design of a fuzzy-logic controller to determine the universes of discourse of the antecedents and the consequents, number of membership labels, distribution and shape of membership functions, rule formulation, etc. Much of the information is usually extracted from expert knowledge, operator experience, or heuristic thinking. It is hence difficult to mechanize the first-stage design of fuzzy-logic controllers using linguistic labels whose performance is no worse than that of conventional multivariable linear controllers such as state-feedback controllers, PID controllers, etc. In this paper, an original systematic seven-step linear-to-fuzzy (LIN2FUZ) algorithm is proposed for generating the labels, universes of discourse of the antecedents and the consequents, and fuzzy rules of ;basically linear' fuzzy-logic controllers, given the reference design of available conventional multivariable linear controllers. The functionally equivalent fuzzy-logic controllers can thus provide the sound basis for the further development to achieve performance beyond the capability or the conventional controllers. The validity and effectiveness of the proposed LIN2FUZ algorithm are demonstrated by a four-input one-output inverted pendulum system.

Researching optimization problems of controller is need of industrial process control ,in which PID controller is widely used,which its parameters can be equivalent to optimization problems. In the industrial control the PID controller is widely used in excitation control system to improve its control performance.In order to find the optimal PID controller parameters effectively ,a kind of Adaptive Particle Swarm Optimization method (CAPSO) based on Cloud Theory is applied to fuzzy PID controller. Through the establishment of particle swarm algorithm of fuzzy PID controller parameters optimization model, which it can be used to optimize the membership function of fuzzy PID controller. Particle code adopts real coding. Particle dimension is related with the number of the input variables divided by fuzzy set and the number of control rules of whole fuzzy control system, thus the parameters of PID control are optimized on real time. The result from the simulation shows that compared with PID control and fuzzy control this system has several advantages which are small overshoots ,fast response ,and good stable performance to improve the control performance of excitation control system.

PID controller design with a new method based on proportional gain for cruise control system