Fuzzy Proportional Derivative Controller Research Articles

Bat algorithm optimized fuzzy PD based speed controller for brushless direct current motor

In this paper, design of fuzzy proportional derivative controller and fuzzy proportional derivative integral controller for speed control of brushless direct current drive has been presented. Optimization of the above controllers design is carried out using nature inspired optimization algorithms such as particle swarm, cuckoo search, and bat algorithms. Time domain specifications such as overshoot, undershoot, settling time, recovery time, and steady state error and performance indices such as root mean squared error, integral of absolute error, integral of time multiplied absolute error and integral of squared error are measured and compared for the above controllers under different operating conditions such as varying set speed and load disturbance conditions. The precise investigation through simulation is performed using simulink toolbox. From the simulation test results, it is evident that bat optimized fuzzy proportional derivative controller has superior performance than the other controllers considered. Experimental test results have also been taken and analyzed for the optimal controller identified through simulation.

Monitoring and control of the processes involved in the capture and filtering of biogas using FPGA embedded fuzzy logic

This article focuses on the development of an intelligent control platform capable of improving the capture and filtration of biogas with the aim of raising the calorific value of the fuel. The biogas was produced in an upflow anaerobic sludge blanket (UASB) reactor at the sewage treatment plant (STP) located near to the town of Los Angeles, Campo Grande, Mato Grosso do Sul, Brazil. For the purposes of system identification, the concentrations, flow rates and pressures of the gases were continuously monitored before and after the filtering processes. The fuzzy proportional derivative controller described herein was required to sustain maximum biogas flow whilst ensuring that the concentration of oxygen did not exceed a predetermined point (the SetPoint) regardless of the variation in load received by the digester. The controller input was oxygen concentration, and the processed output signal was sent to an inverter responsible for raising or lowering the speed of the compressor used in the capture of the biogas. The controller design was developed using MATLAB software and implemented in a field-programmable gate array (FPGA)-embedded Nios II processor. The embedded control algorithm was validated with the aid of ModelSim software. Electronic circuits were developed to allow the FPGA board and the sensors and actuators to communicate via protocols widely used in the industrial setting. This design factor, taken together with the incorporation of reconfigurable hardware and the facility of changing the rules of the fuzzy controller, afforded maximum flexibility of the control platform for use in other applications.

Genetic Algorithm and Particle Swarm Optimization Based Cascade Interval Type 2 Fuzzy PD Controller for Rotary Inverted Pendulum System

This paper presents the design of an optimized Interval Type 2 Fuzzy Proportional Derivative Controller (IT2F-PDC) in cascade form for Rotary Inverted Pendulum (RIP) system. The parameters of the IT2F-PDC are optimised by using Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). The goal is to balance the pendulum in upright unstable equilibrium position. The IT2F-PDC which is the extended version of conventional type 1 fuzzy logic controller, improves the control strategy by using the advantage of its footprint of uncertainty for the fuzzy membership function. The performance characteristics considered for the controller are steady state error, settling time, rise time, maximum overshoot, and control energy. Experimental and simulation results indicated that the effectiveness and robustness of the proposed GA- and PSO-based controllers on the RIP with respect to load disturbances, parameter variation, and noise effects have been improved over state-of-the-art method. However, the comparative results for simulation and experiment based on cascade IT2F-PDC indicate that GA-based IT2F-PDC has lower steady state error while PSO-based IT2F-PDC has lower overshoot, settling time, and control energy, but both have almost the same rise time. The proposed control strategy can be regarded as a promising strategy for controlling different unstable and nonlinear systems.

Coordinated control method of space-tethered robot system for tracking optimal trajectory

Space-tethered robot system is a new kind of space robot, which consists of a robot platform, space tether, and operation robot. This paper presents the coordinated control method in order to save thruster fuel of operation robot in the process of tracking the optimal approach trajectory. First, the optimal approach trajectory of an operation robot is designed using the Gauss pseudospectral method, which resulted in continuous optimal control force using the Lagrange interpolation scheme. The optimal control force is optimized and distributed to space tether and thrusters through simulated annealing algorithm in discrete points, which minimized fuel consumption of thrusters. The distributive continuous force is obtained via cubic polynomial fitting of optimal distributive force in 0.1s discrete time point. To tracking the optimal trajectory, Fuzzy Proportional-Derivative controller is designed with the help of optimal distribution force which come from optimization model. Simultaneously, the relative attitude of the operation robot is stabilized using attitude time-delay algorithm through the reaction wheels. Numerical results are presented, demonstrating the validity of saving thruster fuel and well performance in tracking the optimal trajectory.

An electro-hydraulic servo control system research for CFETR blanket RH

Based on the technical design requirements of China Fusion Engineering Test Reactor (CFETR) blanket remote handling (RH) maintenance, this paper focus on the control method of achieving high synchronization accuracy of electro-hydraulic servo system. Based on fuzzy control theory and practical experience, a fuzzy adaptive proportional-derivative (PD) controller was designed. Then a more precise co-simulation model was established with AMESim/Simulink. Through the analysis of simulation results, a fuzzy adaptive PD control algorithm was designed as the core strategy of electro-hydraulic servo control system.

Image-Based Visual Servoing of a 7-DOF Robot Manipulator Using an Adaptive Distributed Fuzzy PD Controller

This paper is concerned with the design and implementation of a distributed proportional-derivative (PD) controller of a 7-degrees of freedom (DOF) robot manipulator using the Takagi-Sugeno (T-S) fuzzy framework. Existing machine learning approaches to visual servoing involve system identification of image and kinematic Jacobians. In contrast, the proposed approach actuates a control signal primarily as a function of the error and derivative of the error in the desired visual feature space. This approach leads to a significant reduction in the computational burden as compared to model-based approaches, as well as existing learning approaches to model inverse kinematics. The simplicity of the controller structure will make it attractive in industrial implementations where PD/PID type schemes are in common use. While the initial values of PD gain are learned with the help of model-based controller, an online adaptation scheme has been proposed that is capable of compensating for local uncertainties associated with the system and its environment. Rigorous experiments have been performed to show that visual servoing tasks such as reaching a static target and tracking of a moving target can be achieved using the proposed distributed PD controller. It is shown that the proposed adaptive scheme can dynamically tune the controller parameters during visual servoing, so as to improve its initial performance based on parameters obtained while mimicking the model-based controller. The proposed control scheme is applied and assessed in real-time experiments using an uncalibrated eye-in-hand robotic system with a 7-DOF PowerCube robot manipulator.

Design Parallel Linear PD Compensation by Fuzzy Sliding Compensator for Continuum Robot

In this paper, a linear proportional derivative (PD) controller is designed for highly nonlinear and uncertain system by using robust factorization approach. To evaluate a linear PD methodology two type methodologies are introduced; sliding mode controller and fuzzy logic methodology. This research aims to design a new methodology to fix the position in continuum robot manipulator. PD method is a linear methodology which can be used for highly nonlinear system's (e.g., continuum robot manipulator). To estimate this method, new parallel fuzzy sliding mode controller (PD.FSMC) is used. This estimator can estimate most of nonlinearity terms of dynamic parameters to achieve the best performance. The asymptotic stability of fuzzy PD control with first- order sliding mode compensation in the parallel structure is proven. For the parallel structure, the finite time convergence with a super-twisting second-order sliding-mode is guaranteed.

Stable Fuzzy PD Control with Parallel Sliding Mode Compensation with Application to Rigid Manipulator

Both fuzzy logic and sliding mode can compensate the steady-state error of proportional- derivative (PD) control. This paper presents parallel sliding mode compensations for fuzzy PD controllers. The asymptotic stability of fuzzy PD control with first- order sliding mode compensation in the parallel structure is proven. For the parallel structure, the finite time convergence with a super-twisting second-order sliding-mode is guaranteed.

FPGA Based Modified Fuzzy PID Controller for Pitch Angle of Bench-top Helicopter

Fuzzy PID controller design is still a complex task due to the involvement of a large number of parameters in defining the fuzzy rule base. To reduce the huge number of fuzzy rules required in the normal design for fuzzy PID controller, the fuzzy PID controller is represented as Proportional-Derivative Fuzzy (PDF) controller and Proportional-Integral Fuzzy (PIF) controller connected in parallel through a summer. The PIF controller design has been simplified by replacing the PIF controller by PDF controller with accumulating output. In this paper, the modified Fuzzy PID controller design for bench-top helicopter has been presented. The proposed Fuzzy PID controller has been described using Very High Speed Integrated Circuit Hardware Description Language (VHDL) and implemented using the Field Programmable Gate Array (FPGA) board. The bench-top helicopter has been used to test the proposed controller. The results have been compared with the conventional PID controller and Internal Model Control Tuned PID (IMC-PID) Controller. Simulation results show that the modified Fuzzy PID controller produces superior control performance than the other two controllers in handling the nonlinearity of the helicopter system. The output signal from the FPGA board is compared with the output of the modified Fuzzy PID controller to show that the FPGA board works like the Fuzzy PID controller. The result shows that the plant responses with the FPGA board are much similar to the plant responses when using simulation software based controller.

Analytical Structure and Characteristics of Symmetric Karnik–Mendel Type-Reduced Interval Type-2 Fuzzy PI and PD Controllers

This paper presents the analytical structure of a class of interval type-2 (IT2) fuzzy proportional derivative (PD) and proportional integral (PI) controllers that have symmetrical rule base and symmetrical consequent sets. Two assumptions are made: 1) The Zadeh AND operator is employed as the t-norm operator; 2) type-reduction is performed by the Karnik-Mendel (KM) type-reduction method. The main contributions are the methodology that identifies the input conditions, where the KM algorithm uses a new switch point to compute the bounds of the type-reduced set, the closed-form expressions that relate the inputs and output of an IT2 fuzzy controller, and insights into the potential performance improvement because of the inclusion of the footprint of uncertainty (FOU). Compared with its T1 counterpart, two additional FOU parameters generate 31 extra local regions, each providing a unique relationship between the inputs and output signals. The generation of a relatively large number of local regions at the cost of two extra design parameters indicates that an IT2 fuzzy controller may be able to provide better performance. Furthermore, by comparing the analytical structure with the corresponding T1 counterpart, the potential advantages to use the IT2 over the T1 fuzzy controller are studied. Four interesting characteristics are identified, and they provide insights into why the IT2 fuzzy controller may better balance the conflicting aims of fast rise time and small overshoot.

Design and implementation of a hybrid fuzzy logic controller for a quadrotor VTOL vehicle

Helicopters have generated considerable interest in both the control community due to their complex dynamics, and in military community because of their advantages over regular aerial vehicles. In this paper, we present the modeling and control of a four rotor vertical take-off and landing (VTOL) unmanned air vehicle known as quadrotor aircraft. This model has been generated using Newton-Euler equations. In order to control the helicopter, classical PD (proportional derivative) and Hybrid Fuzzy PD controllers have been designed. Although fuzzy control of various dynamical systems has been presented in literature, application of this technology to quadrotor helicopter control is quite new. A quadrotor helicopter has nonlinear characteristics where classical control methods are not adequate especially when there are time delays, disturbances and nonlinear vehicle dynamics. On the other hand, Fuzzy control is nonlinear and it is thus suitable for nonlinear system control. Matlab Simulink has been used to test, analyze and compare the performance of the controllers in simulations. For the evaluation of the autonomous flight controllers, some experiments were also performed. For this purpose, an experimental test stand has been designed and manufactured. This study showed that although, both of the classical PD and the Fuzzy PD controllers can control the system properly, the Fuzzy PD controllers performed slightly better than the classical PD controllers, and have benefits such as better disturbance rejection, ease of building the controllers.

Comparison of PID and Fuzzy Controller for Automobile Suspension System

The main aim of suspension system is to isolate a vehicle body from road irregularities in order to maximize passenger ride comfort and retain continuous road wheel contact in order to provide road holding. The aim of the work described in the paper was to illustrate the application of fuzzy logic technique to the control of a continuously damping automotive suspension system. The ride comfort is improved by means of the reduction of the body acceleration caused by the car body when road disturbances from smooth road and real road roughness. The paper describes also the model and controller used in the study and discusses the vehicle response results obtained from a range of road input simulations. In the conclusion, a comparison of active suspension fuzzy control and Proportional Integration derivative (PID) control is shown using MATLAB simulations.

Stability Analysis of a Type of Takagi-Sugeno PI Fuzzy Control Systems Using Circle Criterion

A type of Takagi-Sugeno (T-S) Proportional-Integral (PI) fuzzy controllers is studied. The T-S PI fuzzy controller is formed by a T-S Proportional-Derivative (PD) fuzzy controller connected with an integrator. In this particular structure, the T-S PD fuzzy controller is a weighted sum of some linear PD sub-controllers. The mathematical properties of our T-S PI fuzzy controller are also investigated. Based on these properties, the global asymptotic stability of the fuzzy control systems, in which the T-S PI fuzzy controllers are employed, are analyzed by using the well-known circle criterion. A sufficient condition with an elegant graphical interpretation in the frequency domain is further derived to guarantee the global asymptotic stability of the above fuzzy control systems. Finally, two numerical examples are provided to demonstrate how to deploy this method in analyzing the T-S PI fuzzy control systems in the frequency domain with the aid of some simple graphs.

Architecture, performance and stability analysis of a formula-based fuzzy I − fuzzy P − fuzzy D controller

In this paper, a formula-based fuzzy integral minus fuzzy proportional minus fuzzy derivative (FI − FP − FD) controller is proposed based on the modified conventional parallel PID controller, i.e. parallel integral minus proportional minus derivative (I − P − D) controller, in order to avoid some practical industrial process problems. It freezes the linear structure of conventional parallel I − P − D controller, with analytical formulas. The final shape of the controller is a discrete-time fuzzy version of conventional parallel I − P − D controller. Computer simulation is performed to evaluate the performance of FI − FP − FD controller for setpoint tracking and load-disturbance rejection for some complex processes, such as, first- and second-order process with delay, inverse response process with and without delay and higher order processes. The simulation is done using National Instrument™ software (LabVIEW™). The response of FI − FP − FD controller is compared with the conventional parallel I − P − D controller, tuned with the Ziegler–Nichols tuning technique. It is observed that the FI − FP − FD controller performed much better than conventional I − P/I − P − D controller. Simulation results demonstrate the effectiveness and usefulness of proposed formula-based FI − FP − FD controller. Also, the bounded-input bounded-output (BIBO) stability of the overall fuzzy control system is established with sufficient conditions, using the famous “Small Gain Theorem”.

Rapid prototyping of fuzzy controller pneumatic servo-system

The results of simulation and experimental tests conducted for pneumatic servo-drive with FLC (fuzzy logic controller) are presented. For positioning control and teaching/play-back control of pneumatic servo-drive, a fuzzy PD (proportional-derivative) controller was designed and constructed by means of xPC Target software of Matlab-Simulink package for rapid prototyping and hardware-in-the-loop simulation. The non-linear simulation model of pneumatic servo-drive was constructed and used to tune fuzzy PD controller by means of Fuzzy Logic Toolbox of Matlab-Simulink package. The fuzzy logic PD controller enables precise positioning of pneumatic servo-drive with the precision specified for industrial manipulators. A lot of simulation and experimental tests were carried on pneumatic servo-drive with fuzzy controller which was used for its transpose and follow-up control. The designed fuzzy system is efficient, stable, and resistant to disturbances and can be applied in any configurations of pneumatic servo-drive without the necessity to tune the regulator, apply signal filtration, or additional operations in track control or restrict the signals generated. Pneumatic servo-drives with teaching/playback control system have considerable practical significance, especially in the control of manipulating machines, manipulators, and industrial robots as well as rehabilitation and physiotherapy manipulators.

Developing a fuzzy proportional–derivative controller optimization engine for engineering design optimization problems

In real world engineering design problems, decisions for design modifications are often based on engineering heuristics and knowledge. However, when solving an engineering design optimization problem using a numerical optimization algorithm, the engineering problem is basically viewed as purely mathematical. Design modifications in the iterative optimization process rely on numerical information. Engineering heuristics and knowledge are not utilized at all. In this article, the optimization process is analogous to a closed-loop control system, and a fuzzy proportional–derivative (PD) controller optimization engine is developed for engineering design optimization problems with monotonicity and implicit constraints. Monotonicity between design variables and the objective and constraint functions prevails in engineering design optimization problems. In this research, monotonicity of the design variables and activities of the constraints determined by the theory of monotonicity analysis are modelled in the fuzzy PD controller optimization engine using generic fuzzy rules. The designer only needs to define the initial values and move limits of the design variables to determine the parameters in the fuzzy PD controller optimization engine. In the optimization process using the fuzzy PD controller optimization engine, the function value of each constraint is evaluated once in each iteration. No sensitivity information is required. The fuzzy PD controller optimization engine appears to be robust in the various design examples tested.

Evolutionary algorithm-based fuzzy PD control of spillway gates of dams

In this paper, an evolutionary algorithm (EA)-based fuzzy proportional-derivative (PD)-type controller is employed to reservoir control of dams with the purpose of operating spillway gates during any flood of any magnitude, which is not predictable beforehand. EA is used to evolve the main parameters of the fuzzy PD controller. The use of the EA, in conjunction with a systematic neighborhood structure for the determining of fuzzy rule-base parameters, leads to a significant improvement in the performance of the controller. The major objective of the controller is to achieve better system performance over the conventional control methods. In order to demonstrate the high performance of the presented method, we simulate the control system using different probable inflow hydrographs of various magnitudes. The simulation results indicate that the EA-based fuzzy PD controller not only performs an accurate and efficient solution, but also exhibits more desirable and reliable results than the conventional approaches.

A two-stage design of adaptive fuzzy controllers for time-delay systems with unknown models

In this article, a systematic two-stage design method for adaptive fuzzy controllers is presented. The proposed control scheme has low computational complexity. Moreover, the exact mathematical model of the plant to be controlled is not required. The fuzzy controller under consideration is based on the proportional-derivative fuzzy control scheme and triangular membership functions. In the design procedure, the domain intervals of the input and output variables are selected with a heuristic approach to minimize a cost function under the constraint of tolerable overshoots in the response curve. A learning scheme is then proposed to automatically adjust the parameters in the fuzzy controller to reduce the error of the system. It can also be used adaptively to improve the system performance of a time-varying system. Simulations and comparisons are included to demonstrate the effectiveness of the proposed method.

A Genetic Fuzzy Controller for Vehicle Automatic Steering Control

This paper presents the design and experimental implementation of a genetic fuzzy controller for automatic steering of a small-scaled vehicle. We first derive a dynamic model of the vehicle via system identification and show that the model exhibits similar characteristics to full-sized vehicles. Subsequently, a stable fuzzy proportional-derivative controller is designed and optimized by genetic algorithms. The control system is transformed into a Lureacute system, and Lyapunov's direct method is used to guarantee the stability of the control system. Experimental studies suggest that the control system is insensitive to parametric uncertainty, load, and disturbances. The performance of the proposed controller is also compared against a conventional proportional derivative (PD) controller. Experimental results confirm that it outperforms the conventional PD controller, particularly in terms of robustness

A fuzzy proportional-derivative controller for engineering optimization problems using an optimality criteria approach

This paper proposes a fuzzy proportional-derivative (PD) controller optimization engine for engineering optimization problems using an optimality criteria approach. Traditional numerical optimization algorithms treat optimization problems as pure mathematical problems. Engineering knowledge about the problem is not utilized in the optimization process. The idea of using the fuzzy PD controller in engineering optimization is that, instead of using purely numerical information to obtain the new design point in the next iteration, engineering knowledge and human supervision process can be modeled in the optimization algorithm using fuzzy rules. The fuzzy PD controller optimization engine developed in this work appears to have stable performance in both structural optimization and blow molding parameter optimization examples.