Fuzzy Control Law Research Articles

Fuzzy tracking control of fuzzy linear dynamical systems

This paper deals with the fuzzy tracking control problem of a class of uncertain linear dynamical systems. In the uncertain linear dynamical system the uncertainty is considered as fuzzy numbers. This kind of uncertain linear dynamic systems is called fuzzy linear dynamic systems which are expressed in the form of a fuzzy differential equations system. The Mazandarani’s approach and the powerful concept of granular differentiability are utilized to deal with the fuzzy differential equations system. Fuzzy tracking control of fuzzy linear dynamic systems looks for a law for the fuzzy control signal by which the output of the system tracks the reference input. In this regard, two fuzzy control laws are proposed under two theorems. First, it is proved that the fuzzy control law is in the form of a fuzzy state feedback with fuzzy gains and an additional term which is a pre-compensator as a fuzzy number. Since in the presence of disturbances this fuzzy control law fails to tackle the problem then other fuzzy control law is proposed under the second theory. Thus, in the second theory, it is proved that the proposed fuzzy controller desirably leads to the output of the fuzzy linear dynamic system tracks the input and the fuzzy disturbance is rejected. In addition, two lemmas regarding the theories are also proved. Moreover, fuzzy tracking control of output of a two tanks in series system and landing jet aircraft are given showing the effectiveness of the proposed approaches.

Fuzzy dipole magnetic control law

This paper presents a new fuzzy logic system that decouples the measured Earth's magnetic field problem from the control analysis. The fuzzy logic takes care of the coupling between the magnetic field lines so that a classical controller is used to determine the necessary magnetic dipole moment to hold the satellite attitude motion. Although the fuzzy logic can have rules based on the vehicle states, the present method takes advantage of the magnetic field knowledge so that the controller can be simplified. In order to verify this method, an orbiting satellite was used to test this control system. Even though this method was used for a small satellite class, this control technique could be applied to nano and pico satellites using magnetic torquers.

Disturbance-observer-based fuzzy model predictive control for nonlinear processes with disturbances and input constraints

This paper proposes a disturbance-observer-based fuzzy model predictive control (DOBFMPC) scheme for the nonlinear process subject to disturbances and input constraints. The proposed control scheme is composed of the baseline fuzzy model predictive control (FMPC) law designed on the Takagi–Sugeno fuzzy model and the disturbance compensation law. To build a fuzzy model of appropriate complexity and accuracy for the nonlinear process model, a systematic approach is developed via the gap metric to determine the linearization points. With FMPC, the asymptotic stability is theoretically proved, and the input constraints are satisfied by both the free control variables and the future control inputs in the form of the state feedback law. The disturbance compensation gain is designed such that the influence of the disturbance is removed from the output channels by the composite DOBFMPC law at the steady state. The application to a subcritical boiler–turbine system demonstrate the effectiveness of the proposed control scheme.

Generalized Discrete-time nonlinear disturbance observer based fuzzy model predictive control for boiler–turbine systems

The boiler–turbine system (BTS) is usually subject to the tight input constraint, the strong nonlinearity and the complex disturbance, which makes the control a challenging task To this end, a disturbance observer based fuzzy model predictive control (DOBFMPC) scheme is proposed for the BTS in this paper. The generalized discrete-time nonlinear disturbance observer (GDNDO) is first developed to estimate the higher-order disturbance by systematically extending the conventional nonlinear disturbance observer. The GDNDO exhibits a series structure of the internal states, and can precisely estimate the disturbance if its order is equal to or greater than that of the disturbance In addition, a baseline fuzzy model predictive control (FMPC) law is synthesized on the fuzzy model. With FMPC, the asymptotic stability is guaranteed, and meanwhile the input constraints are satisfied by both the free control variables and the future control inputs in the form of the state feedback law. At last, the disturbance estimate and the FMPC are applied to constitute the DOBFMPC law. With the proper design of the disturbance compensation gain, the disturbance influence is removed from the output channels by the composite DOBFMPC law at the steady state. Simulations for a 300 MW subcritical BTS well demonstrate the effectiveness of the proposed control scheme.

Analytical Fuzzy Predictive Control Applied to Wastewater Treatment Biological Processes

A novel control fuzzy predictive control law is proposed and successfully applied to a wastewater treatment process in this paper. The proposed control law allows us to evaluate the control signal in an analytical way, each sampling time being a nonlinear and fuzzy alternative to other classic predictive controllers. The control law is based on the formalization of the internal fuzzy predictive model of the process as linear time‐varying state space equations that are updated every discrete time instant to take into account the nonlinearity effects due to disturbance action and changes in the operating point with time. The model is then used to evaluate the predictions, and, taking them as a starting point and considering them as a paradigm of the predictive functional control strategy, a control law, it is derived in an analytical and explicit way by imposing on the outputs of the follow‐up of certain reference trajectories previously established. The work presented here addresses the application of this particular strategy of intelligent predictive control to the case of an activated sludge wastewater treatment process successfully in a simulation environment of a real plant taking into account real data for the disturbance records. Such a process is multivariable, nonlinear, time varying, and difficult to control due to its biological nature. The proposed control law can be straightforwardly used within a dual-mode MPC scheme to handle constraints, as a nonlinear and fuzzy alternative to the classic state feedback control law.

Output-Feedback Control for Cooperative Diving of Saucer-Type Underwater Gliders Based on a Fuzzy Observer and Event-Triggered Communication

This paper presents an output-feedback control method for cooperative diving of multiple homogenous under-actuated saucer-type autonomous underwater gliders (AUGs) subjected to unmeasured velocities, model uncertainties, as well as unknown environmental disturbances. A robust cooperative diving controller is constructed by using a modular back-stepping design method. First, a fuzzy observer combined with a low-frequency learning scheme is presented to identify the unknown AUG dynamics as well as to estimate the unmeasured velocities. Second, a commanded guidance law is designed based on the observed velocities and a vertical line-of-sight guidance scheme at the kinematic level, and fuzzy dynamic control law is developed at the kinetic level. Finally, a non-periodic path update law based on an event-triggered mechanism is designed to reduce the communication frequency. By using the cascade theory, the stability of the closed-loop system is analyzed. The simulation results are provided to show the effectiveness of the proposed output-feedback control approach for saucer-type AUGs.

Notice of Violation of IEEE Publication Principles: A Novel Robust Fuzzy Integral Sliding Mode Control for Nonlinear Semi-Markovian Jump T–S Fuzzy Systems

This paper addresses the issue of robust fuzzy sliding mode control for continuous-time nonlinear Takagi–Sugeno fuzzy systems with semi-Markovian switching. The focus is on designing a novel fuzzy integral sliding surface without assuming that the input matrices are the same with full column rank and then developing a fuzzy sliding-mode controller for stochastic stability purpose. Based on Lyapunov theory, a set of newly developed linear matrix inequality conditions are established for stochastic stability of the sliding-mode dynamics with generally uncertain transition rates, and then extended to where the input matrix is plant-rule-independent, as discussed in most existing literatures. Furthermore, finite-time reachability of the sliding surface is also guaranteed by the proposed fuzzy sliding-mode control laws. A practical example is provided to demonstrate the effectiveness of the established method numerically.

Fuzzy logic based speed optimization and path following control for sail-assisted ships

This note aims to solve the speed optimization and path following control for sail-assisted ships. The ideology of retrofitting a common bulk carrier with wing sails is investigated. Based on an established mathematical model with four degrees of freedom, we proceed with the subsequent analysis. First, a novel speed optimization scheme combining the extremum seeking (ES) algorithm with the self-tuning fuzzy logic system is proposed. After adequate online training, the fuzzy logic system is capable to maximize the ship's speed with less chattering. Next, an adaptive fuzzy control law for such a ship is developed under the skeleton of line of sight (LOS) guidance. The uncertainties are offset by fuzzy approximation and the least parameters updating is acquired. The derived control outputs are characterized by rudder angles, which conforms to the nautical practice. Finally, the proposed scheme is testified in the simulated sea environment.

A fuzzy adaptive backstepping control based on mass observer for trajectory tracking of a quadrotor UAV

SUMMARYIn this paper, a fuzzy adaptive backstepping control law that combines mass observer and fuzzy control strategy with backstepping control is developed for the trajectory tracking control of a quadrotor unmanned aerial vehicle. In the control law, the mass change disturbance to the flight control could be restrained by the mass observer to estimate the real‐time mass and correct the mass parameter of the quadrotor, and the time‐varying external disturbance to the flight control could be restrained by fuzzy compensation of the fuzzy control law. Lyapunov stability theorem is used to analyze the stability of the closed‐loop control system. Two cases of trajectory tracking numerical simulations are presented in MATLAB/SIMULINK simulation environment. In addition, the quadrotor hovering experiment was completed on the actual flight experimental system with the time‐varying disturbance from wind outdoors. The simulation and actual flight results illustrate that the proposed control strategy is effective and stable under the simulating environment and the actual environment.

Adaptive fuzzy control method for a linear switched reluctance motor

A new direct adaptive fuzzy speed control method for a linear switched reluctance motor with unknown control gain sign is presented. The proposed control system consists of two parts: a fuzzy system and an adaptive law. Fuzzy system approximates an unknown ideal control law with unknown adjustable parameters. After determination of the control law, an appropriate adaptation law is designed to update the adjustable parameters to achieve control objectives. The adaptation law is designed using the error between the unknown ideal control law and fuzzy control law. Unlike previous works, in this study, the unknown control gain sign is taken as an unknown constant parameter and is determined online by an appropriate adaptation law. Proposed control method along with a fuzzy sliding mode speed control and a proportional integral speed control strategies are experimentally studied and the performance index is used to evaluate each strategy. The robustness of the proposed method to the parameters and external load force change has been verified via simulation and experiments. The results indicate that the proposed control method has an acceptable performance.

Delay Dependent Local Stabilization Conditions for Time-delay Nonlinear Discrete-time Systems Using Takagi-Sugeno Models

We propose convex conditions for stabilization of nonlinear discrete-time systems with time-varying delay in states through a fuzzy Takagi-Sugeno (T-S) modeling. These conditions are developed from a fuzzy Lyapunov-Krasovskii function and they are formulated in terms of linear matrix inequalities (LMIs). The results can be applied to a class of nonlinear systems that can be exactly represented by T-S fuzzy models inside a specific region called the region of validity. As a consequence, we need to provide an estimate of the set of safe initial conditions called the region of attraction such that the closed-loop trajectories starting in this set are assured to remain in the region of validity and to converge asymptotically to the origin. The estimate of the region of attraction is done with the aid of two sets: one dealing with the current state, and the other concerning the delayed states. Then, we can obtain the feedback fuzzy control law depending on the current state, x k , and the maximum delayed state vector, xk−d. It is shown that such a control law can locally stabilize the nonlinear discrete-time system at the origin. We also develop convex optimization procedures for the computation of the fuzzy control gains that maximize the estimates of the region of attraction. We present two examples to demonstrate the efficiency of the developed approach and to compare it with other approaches in the literature.

Disturbance observer based reliable H∞ fuzzy attitude tracking control for Mars entry vehicles with actuator failures

This paper introduces a disturbance observer (DO) based reliable H∞ fuzzy attitude tracking control design for Mars entry vehicles with actuator failures. Initially, to reduce the complexity of Takagi–Sugeno (T–S) fuzzy modeling, the two time-scale decomposition technique is used to divide the original nonlinear attitude tracking error model of Mars entry vehicles into a slow subsystem describing the attitude kinematics and a fast subsystem describing the attitude dynamics. The dynamic inversion control (DIC) method is subsequently applied to the slow subsystem to generate the angular velocity command. Then, the T–S fuzzy modeling method is employed to exactly represent the fast subsystem and a disturbance observer (DO) is constructed to estimate the modeled disturbance based on the derived tracking error fuzzy system of angular velocity. By the technique of linear matrix inequalities (LMIs), a DO based reliable H∞ fuzzy controller of attitude tracking is developed to stabilize exponentially the angular velocity tracking error and the modeled-disturbance state estimation error with an H∞ tracking performance both in nominal and actuator failure cases. Furthermore, it is shown that the original nonlinear tracking error system is also exponentially stable and satisfies an H∞ tracking performance both in nominal and actuator failure cases under the proposed fuzzy control law together with the DIC law, provided that the timescale separation between the fast and slow subsystems is valid. Finally, simulation results illustrate the effectiveness of the proposed design method.

Exponential Pointwise Stabilization of Semilinear Parabolic Distributed Parameter Systems via the Takagi–Sugeno Fuzzy PDE Model

This paper deals with the problem of exponential stabilization for nonlinear parabolic distributed parameter systems using the Takagi–Sugeno (T–S) fuzzy partial differential equation (PDE) model, where a finite number of actuators are active only at some specified points of the spatial domain (these actuators are referred to as pointwise actuators). Three cases of state feedback are respectively considered in this study as follows: full state feedback, piecewise state feedback, and collocated pointwise state feedback. It is initially assumed that a T–S fuzzy PDE model obtained via the sector nonlinearity approach is employed to accurately represent the semilinear parabolic PDE system. Based on the obtained T–S fuzzy PDE model, Lyapunov-based design methodologies of fuzzy feedback control laws are subsequently derived for the above three state feedback cases by using the vector-valued Wirtinger's inequality to guarantee locally exponential pointwise stabilization of the semilinear PDE system, and presented in terms of standard linear matrix inequalities (LMIs). Moreover, the favorable property offered by sharing all the same premises in the T–S fuzzy PDE models and fuzzy controllers is not applicable for the case of collocated pointwise state feedback. A parameterized LMI is introduced for this case to enhance the stabilization ability of the fuzzy controller. Finally, the merit and effectiveness of the proposed design methods are demonstrated by numerical simulation results of two examples.

Adaptive fuzzy PID control for a quadrotor stabilisation

This paper deals with the design of an adaptive fuzzy PID control law for attitude and altitude stabilization of a quadrotor despite the system model uncertainties and disturbances. To this end, a PID control with adaptive gains is used in order to approximate a virtual ideal control previously designed to achieve the predefined objective. Specifically, the control gains are estimated and adjusted by mean of a fuzzy system whose parameters are adjusted online via a gradient descent-based adaptation law. The analysis of the closed-loop system is given by the Lyapunov approach. The simulation results are presented to illustrate the efficiency of the proposed approach.

Laser-range-finder localization based fuzzy control for mobile robots

PurposeBased on laser-range-finder (LRF) sensing, the control design of location and orientation stabilization for the mobile robot is investigated. However, the practical limitation of the LRF sensing is usually ignored in the control design, which leads to incorrect localization and unexpected control results. The purpose of this study is to design the fuzzy controller subject to the practical limitation on the LRF-based localization for a differentially driven wheeled mobile robot.Design/methodology/approachFirst, the Takagi–Sugeno (T-S) fuzzy model is derived from the polar kinematic model of a differentially driven mobile robot. Then, the fuzzy controller is designed to the derived T-S fuzzy kinematic model in accordance with the Lyapunov stabilization theorem. The derived Lyapunov stabilization conditions for the fuzzy control design are expressed as the linear matrix inequality (LMI) form and effectively solved by LMI tools. The practical limitation on the LRF-based localization is also expressed as the LMI form and simultaneously solved with the control design.FindingThe location and posture stabilization experiments are carried out on a mobile robot with LRF-based localization to prove the effectiveness of the proposed T-S fuzzy model-based control design. Furthermore, the ground truth experiment evaluates the accuracy of LRF-based localization.Originality/valueThe contribution of this study is to develop the fuzzy control law for a differentially driven wheeled mobile robot under the practical limitation on LRF-based localization. The proposed control design can be applied to other robots with practical limitations on the sensors.

Affine TS Fuzzy Model-Based Estimation and Control of Hindmarsh–Rose Neuronal Model

In this paper, an affine Takagi–Sugeno (TS) fuzzy modeling-based observer and controller are proposed for the estimation and control of a chaotic Hindmarsh–Rose (HR) neuronal model. The main contributions are given as follows. 1) First, an affine TS fuzzy model of the HR chaotic neuronal model is constructed using sector nonlinearity-based approach. 2) Based on the constructed TS fuzzy model, a TS fuzzy observer is designed for simultaneous state and parameter estimation of HR neuronal model for unmeasurable state and parameters. 3) In the same way, a novel affine TS fuzzy model-based output feedback control law is designed with observed state and parameters where the exponential stability of the designs are guaranteed by Lyapunov approach. 4) Finally, numerical simulations are conducted to illustrate the observation and stimulation with regular and fast spiking trains and annihilation of the membrane potential.

Nonlinear dynamic modeling and fuzzy sliding-mode controlling of electromagnetic levitation system of low-speed maglev train

The electromagnet levitation system (ELS) of low-speed maglev train is taken as the research object. The nonlinear dynamics and control law of ELS are discussed. Specifically, by employing the Euler-Lagrange’s method, a nonlinear dynamic model is constructed for the single-ELS. Then, the linear control law is studied, which has a disadvantage of weak robustness. To improve the performance of the controller, a fuzzy sliding-mode control law is proposed. According to the dynamic nonlinear model, a novel sliding surface which can make the system reach the stable point within the finite time is presented. Moreover, the fuzzy inference method is utilized to slow down the speed of the states crossing the sliding surface. The simulation results demonstrate that the global robustness of external disturbance and parameter perturbation can be achieved through the proposed control law. And the chattering phenomenon can be reduced significantly. Finally, the experiments are also implemented to examine its practical dynamic performance of the proposed control law.

Adaptive Self-Learning Fuzzy Autopilot Design for Uncertain Bank-to-Turn Missiles

This paper proposes an adaptive self-learning fuzzy autopilot design for uncertain bank-to-turn (BTT) missiles due to external disturbances and system errors from the variations of the aerodynamic coefficients and control surface loss. The self-learning fuzzy systems called extended sequential adaptive fuzzy inference systems (ESAFISs) are utilized to compensate for these uncertainties in an adaptive backstepping architecture. ESAFIS is a real‐time self-learning fuzzy system with simultaneous structure identification and parameter learning. The fuzzy rules of the ESAFIS can be added or deleted based on the input data. Based on the Lyapunov stability theory, adaptation laws are derived to update the consequent parameters of fuzzy rules, which guarantees both tracking performance and stability. The robust control terms with the adaptive bound-estimation schemes are also designed to compensate for modeling errors of the ESAFISs by augmenting the self-learning fuzzy autopilot control laws. The proposed autopilot is validated under the control surface loss, aerodynamic parameter perturbations, and external disturbances. Simulation study is also compared with a conventional backstepping autopilot and a neural autopilot in terms of the tracking ability. The results illustrate that the designed fuzzy autopilot can obtain better steady‐state and transient performance with the dynamically self-learning ability.

Distributed Adaptive Fuzzy Control for Output Consensus of Heterogeneous Stochastic Nonlinear Multi-Agent Systems

This paper investigates the output consensus problem of heterogeneous stochastic nonlinear multiagent systems with directed communication topologies, with a view of making the outputs of a group of follower agents track the output of a leader. Fuzzy logic systems are applied to approximate the unknown nonlinear functions of agents. A special case that all followers can get access to the leader is first considered, and a novel decentralized adaptive fuzzy control law based on the output regulation framework is presented. Next, the proposed control scheme is further applied to design the distributed adaptive fuzzy control law for a more general case that only part of agents can get access to the leader. By applying Lyapunov stability analysis, it is shown that the outputs of followers will achieve consensus to a sufficient small bound of the output of the leader under the proposed control law. Finally, simulation results demonstrate that the proposed control law is effective and efficient. The developed distributed control scheme can be widely applied to solve the cooperative control problem of practical autonomous systems with uncertain dynamics such as synchronization of mechanical systems with vibration, formation control of autonomous underwater vehicles, etc.

Voltage Regulation System of Doubly Salient Electromagnetic Generator Based on Indirect Adaptive Fuzzy Control

In this paper, a voltage regulation system based on indirect adaptive fuzzy (IAF) control for doubly salient electromagnetic generator (DSEG) is proposed to improve the robustness of the system and reduce output voltage ripple. The operating principle of IAF controller is described in detail subsequently and the stability condition of the system is deduced by Lyapunov function based on the mathematical model and working principle of the generator. Moreover, the selection method of parameters and control strategy are determined with the adaptive fuzzy control law. Finally, a field-circuit coupling simulation model of voltage regulation system for DSEG using IAF controller is constructed by finite element analysis technique and transient solver of control circuit. The simulation results show that DSEG using IAF controller has good static characteristics, high robustness, and low output voltage ripple.