Fuzzy Logic Control Systems

This paper investigates the performance of adaptive particle swarm optimization (APSO) algorithm to find the best optimal gain parameters (Kp, Ki, Kd) in linear PID (L-PID) and nonlinear PID (NL-PID) controllers for the trajectory control of a nonlinear dynamical system (NLDS). Mathematical modeling, stability and performance analysis of a NLDS are being carried out with L-PID and NL-PID controllers. It is found that the APSO based tuning of NL-PID controller provides better tracking of NLDS than L-PID controller in respect of its search domain, premature convergence, and computational efficiency. Simulation analysis of various variables of controllers and system response such as error, cost function, and response of NLDS and their comparison to that of APSO tuned L-PID controller is described.

. Recently, digital technologies and software packages as MATLAB and MATCAD are widely used for modeling and research of control systems. When analyzing and synthesizing the control system, ”manual” operations do not allow one to cover fully the systematic approach both from the constructive and computational points of view. The most widely used in practice and at the same time simplest control device is the linear PID controller. However, computer modeling and digital studies of this controller are not at the required level. This paper reveals some features of the functioning of a linear digital PID controller with three settings on a 2nd order object. Considering these assumptions, in the paper, the object modeled in the terms of output and state variables and the known theoretical parameters occurring in the ACS with a PID controller are more adequately confirmed. For the experiments, the Matlab/Simulink system with the ”Simulink Response Optimization/Signal Constraint” package was used. In order to facilitate access to the package, some important features of the algorithm for solving the control problem are revealed using a specific example.

Both linear PID controllers and fuzzy controllers are designed and implemented for a boost converter. Comparison between the two controllers is made in the aspect of design, implementation and experimental results. Design of fuzzy controllers is based on heuristic knowledge of the converter and tuned using trial and error, while the design of linear PID and PI controllers is based on the frequency response of the boost converter. Implementation of linear controllers is quite straightforward, while implementation of fuzzy controllers has its unique issues. A comparison of experimental results indicates that the performance of the fuzzy controller is superior to that of the linear PID and PI controllers. The fuzzy controller is able to achieve faster transient response, has more stable steady-state response, and is more robust under different operating points.

A software model of NASA's Shuttle Training Aircraft is used to model-follow a Boeing 747. A classical linear control system is used to perform the model-following. In addition a fuzzy optimizer is created which modifies the gains of a classical control system to enhance performance. The fuzzy optimizer uses the past performance of the control system as input and outputs chances to the gains. >

The designs of two linear control systems approach to stabilize the balance of an unmanned bicycle system are presented. Both approaches are based on the use of a reaction wheel or flywheel to balance the bicycle. The two linear control approaches, based on the linearization of a nonlinear model obtained using Lagrange formalism, are the classic linear controllers, PID and State Feedback control. The performance of both controllers is verified by digital simulation and real-time experimental results.

Thestability of a control system is essential for its effective operation. Stability implies that small changes in input, initial conditions, or parameters do not lead to significant fluctuations in output. Various stability properties, such as inner stability, asymptotic stability, and BIBO (Bounded Input, Bounded Output) stability, are well understood for classical linear control systems in Euclidean spaces. This paper aims to thoroughly address the stability problem for a class of linear control systems defined on matrix Lie groups. This approach generalizes classical models corresponding to the latter when the group is Abelian and non-compact. It is important to note that this generalization leads to a very difficult control system, due to the complexity of the state space and the special dynamics resulting from the drift and control vectors. Several mathematical concepts help us understand and characterize stability in the classical case. We first show how to extend these algebraic, topological, and dynamical concepts from Euclidean space to a connected Lie group of matrices. Building on classical results, we identify a pathway that enables us to formulate conjectures about stability in this broader context. This problem is closely linked to the controllability and observability properties of the system. Fortunately, these properties are well established for both classes of linear systems, whether in Euclidean spaces or on Lie groups. We are confident that these conjectures can be proved in future work, initially for the class of nilpotent and solvable groups, and later for semi-simple groups. This will provide valuable insights that will facilitate, through Jouan’s Equivalence Theorem, the analysis of an important class of nonlinear control systems on manifolds beyond Lie groups. We provide an example involving a three-dimensional solvable Lie group of rigid motions in a plane to illustrate these conjectures.

In practice, the intelligent PID control algorithm which is an improved algorithm based on the classical PID control was put forward by many researchers to resolve some control problems, such as time-delay, lag and nonlinear. In this paper, an intelligent PID control algorithm is considered and applied to an internal combustion control system. Then, the semi-physical simulation platform based on PLC (Programmable Logic Controller) is set up, where the internal combustion engine is simulated by using simulation model and the intelligent PID controller is realized by using PLC. The results show that the designed control system is stable, and high accuracy and short response time are obtained. Also, the results show the advantage of the presented intelligent PID control algorithm comparing with the classical PID control algorithm.

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.

The purpose of the study is to develop an adaptive electropneumatic automatic system based on the classical PID controller using modern technology for controlling like fuzzy controlling. The need of an adaptive setting occurred because of the fact that the classic controller has high sensitivity towards interferences with the main signal and the need for the parameters to be regulated often and be done by hand. Another reason is the inability to provide optimal parameters for the controller for nonlinear processes and changes of the parameters in time. In this article the work of electropneumatic system with linear actuator, is examined. A mathematical model describing the dynamics of the processes, is developed. An adaptive fuzzy PID controller with variable coefficients is synthesized. The system is studied in the environment of Matlab Simulink. The transient processes in the system are compared to processes where the classical PID controller. The results are presented in graphical form.

There are a lot of methods for the stabilization of quadcopters and the newest are based on AI. A neural network is a simplified model that imitates the human brain's processes. In the research paper, we present a neural network control model for quadcopter stabilization. A single hidden layer network model was estimated to investigate the dynamics of the UAV. A control system with a classical PID controller was used to train the neural network model. This method is used for examining how the neural network imitates the stabilization of the quadcopter in real flight mode. The novelty of the work was to design of small size 3 layers NN model that runs in real-time in a quadcopter. The PID and machine learning controllers' operation results were compared to each other andshown in the experiment.

In allusion to unmanned vehicle steering control of the brushless DC motor control system, traditional PID controller parameter adjustment complex, weak ability to adapt to the environment and other issues, on the basis of the analysis of internal model control and classical PID control internal corresponding relationship, comprehensive its advantages, The design uses a brushless DC motor in the steering control system for unmanned vehicles based on the internal model PID controller ( IMC-PID) for speed. Based on the build object theoretical model, online simulation controller show that, for the design objects, based on the internal model PID controller whether the system step response or disturbance tracking control effect can reach the classic PID control requirements, also reduces the complexity and randomness of the design parameters.

High efficiency due to reduced losses, low maintenance and low rotor inertia of the brushless dc (BLDC) motor have increased the demand of BLDC motors in high power servo and robotic applications. Since fuzzy logic with human like but systematic property can convert the linguistic control rules based on expert knowledge into automatic control strategy, it can be well applied to control the systems with uncertain or unmodelled dynamics. In view of fuzzy logic merits, this paper proposes three types of fuzzy logic controllers for BLDC motor drive using advanced simulation model and presents a comparative study of performance specifications of classical PI and PID controllers and three fuzzy logic controllers. The three fuzzy logic controllers considered are PI-like fuzzy logic controller (PI-Like FLC), Hybrid fuzzy logic controller (HFLC) and integrated fuzzy logic controller (IFLC). The steady state and dynamic characteristics of speed and torque are effectively monitored and analyzed using the proposed model. The aim of fuzzy logic controllers is to obtain improved performance in terms of disturbance rejection or parameter variation than obtained using classical controllers. In the HFLC, the proportional term of the traditional PID controller is replaced with an incremental fuzzy logic controller. For the PI-Like FLC, the output of the controller is modified by a rule base with the error and change of error of the controlled variable as the inputs. The IFLC is constructed by using Fuzzy logic controller and PID controller. A performance comparison of classical and fuzzy logic controllers has been carried out by several simulations at different speeds and different load conditions.

This paper investigates the application of a multi-loop PID controller in an automated treadmill exercise machine. The approach is to design a computer-controlled treadmill control system for the regulation of heart rate (HR) during treadmill exercise. A single-input and multiple-output (SIMO) controller was implemented to fast track a given heart rate profile in treadmill exercise. Two separate single-input and single-output (SISO) PID control systems are initially implemented to modify either the treadmill speed or its angle of inclination in order to achieve a desired HR. The purpose of this paper is to apply a SIMO control system by implementing a control algorithm which includes the two PID controllers working simultaneously to track the desired HR profile. The performance of the SIMO and SISO control systems are compared through the closed loop responses recorded during experimentation. This would also help future development of safe treadmill exercise system.

Here, the robustness of the nuclear reactor control system is discussed by its computer simulation results which are obtained respectively from the analysis without the external control system and the analysis with the external control system. After this, the simulation tests both with the classical PID control and with the advanced PID control are also given. And then, the comparative analysis on the robustness of the reactor control system is shown. Finally, the useful approach improving the robustness of the nuclear reactor control system is provided, too.

Delays are a common physic effect that is present in a huge quantity of industrial systems with feedback control. Sometimes the impact of the delay presence in a system is neglected without any difference in the performance of the controller. But in some cases, the Delay quantity reaches levels that increase the overshoot significantly or destabilizes the system. For this system the CTCR method can be used to design a “delayed scheduled” controller able to reject the delays effect. To be able to apply this method it is necessary for both the system and the controller to be Linear or linearized. In this article the study case is an articulated inverted pendulum or also called “Pendubot”. This configuration of pendulum was selected because, in spite of being a simple pendulum, it has four equilibrium points, where two equilibrium points were selected to be controlled, the most unstable which has the maximum potential energy for each link and the most stable with the lowest potential energy. The purpose of work with those equilibrium points is compare the difference between the delay rejection in each point with similar setting times and overshoots from controllers. In order to get an accurate model, the state of the current is added along with the viscous friction terms for each joint in the pendulum. To tune the linear and non-linear model an experimental validation was carry on the physical prototype from the Universidad Industrial de Santander (VIE-5373 UIS). The control laws applied were a classical PID and LQR control. Due the controller sample frequency is extremely high in comparison to the states response, all the controllers and linear models were implemented in continuous space. In the first tuning process it was observed that the PID control gets a significantly lowest performance than the LQR control in the unstable equilibrium point, for that reason the comparison between points only was carried on with the LQR equation of feedback system, this can be done in different ways, but for the PID control the Mason theorems was applied and for LQR control only with matrix operation the equation can be obtained. After applying the “Delay scheduling” it was observed that the tuned LQR get a highest delay rejection that PID. An observer fact was that although the controllers for each point have a similar performance the delay pockets have completely different values due the final poles locations for each point. Also was observed that the system only gets one stability pocket, this could because only one delay in the actuator was induced.