Control of T-S Fuzzy Systems Using Fuzzy Weighting-Dependent Lyapunov Function

This paper presents novel Takagi-Sugeno (T-S) fuzzy model-based robust finite time control methods for a class of uncertain nonlinear systems. First, the nonlinear system is approximated by a suitable T-S fuzzy model in which most of the parameters can be computed offline. Then, a T-S fuzzy model-based nonsingular terminal sliding mode control (TS-NTSMC) method is designed based on a proposed nonsingular terminal sliding mode (NTSM) surface. This method not only alleviates the online computational burden, but also preserves the advantages of fast and finite time convergence, high tracking precision, and robustness to uncertainties and disturbances. However, the discontinuous function [Formula: see text] causes the chattering phenomenon, which is unavoidable. In order to attenuate the chattering, maintain the key properties of the TS-NTSMC method and achieve higher control performance, a novel T-S fuzzy model-based super-twisting higher order nonsingular terminal sliding mode control (TS-STHONTSMC) method is proposed. The global finite time stability of the resulting closed-loop systems is analytically proven herein. Two numerical simulations are presented to illustrate the effectiveness and applicability of the proposed control methods and to validate the theoretical results.

Research on A Fuzzy Adaptive PID Control Method for Four Rotor UAV Control System With the continuous improvement of national living standards, people have higher and higher requirements for the reliability of power supply. The emergence of unmanned aerial vehicle inspection technology provides a new idea to solve the contradiction between the increasing equipment scale and the increasing inspection requirements. However, at present, the stability of the traditional proportion integration differentiation (PID) control system of the four rotor unmanned aerial vehicle (UAV) is not high enough. During the inspection, there are accidents of drones hitting power equipment from time to time. In view of the above problems, this paper studies the fuzzy adaptive PID control method to support the stable flight of four rotor UAV. The principle of fuzzy control is analyzed. The fuzzy control method and PID control method are deeply integrated. A fuzzy adaptive PID control system is designed. The universe and membership function of the relevant control parameters of the system are formulated. The tuning rules of fuzzy adaptive PID control system are formulated. Finally, the improved control system is simulated. The simulation results show that the fuzzy adaptive PID control algorithm can effectively improve the stability, reliability and emergency ability of UAV. This method can effectively improve the adaptability of UAV to perform complex missions in complex environments. The research results have guiding significance for expanding the application field of UAV.

This paper addresses the analysis and design of fuzzy control systems for a class of complex uncertain single input single output nonlinear systems. In the design procedure, we represent the nonlinear system using a Takagi-Sugeno fuzzy model and construct a global fuzzy logic controller by blending all local state feedback controllers with a sliding mode controller. Unlike the commonly used parallel distributed compensation technique, we can design a global stable fuzzy controller without finding a common Lyapunov function for all local control systems, and can obtain a good tracking performance. Furthermore, a stability analysis is carried out not for the fuzzy model but for a real nonlinear system with uncertainties. One simulation example is given to show the effectiveness and feasibility of the proposed fuzzy controller design method.

This paper presents new stability conditions and LMI (linear matrix inequality) based designs for both continuous and discrete fuzzy control systems. First, Takagi and Sugeno's fuzzy models and some stability results are recalled. To design fuzzy control systems, nonlinear systems are represented by Takagi-Sugeno fuzzy models. The concept of parallel distributed compensation is employed to design fuzzy controllers from the Takagi-Sugeno fuzzy models. New stability conditions are obtained by relaxing the stability conditions derived in previous papers. The stability analysis of the feedback system is reduced to a problem of finding a common Lyapunov function for a set of linear matrix inequalities. Convex optimization techniques involving LMIs are utilized to find a common Lyapunov function. A procedure to design the fuzzy controller is constructed using the parallel distributed compensation and the relaxed stability conditions. Some stability issues are remarked. A simple example demonstrates the effects of the derived stability conditions.

Aiming at increasing the performance of fuzzy control and keeping a fuzzy controller maintain an ideal given track to its objective value, and also aiming at finding an easy way to abstract fuzzy control rule set for the complex controlled process, this paper presents a new fuzzy control method, namely model based self-abstracting rule fuzzy control method (MBSAR). The MBSAR takes the one order inertia system as the reference model and abstracts the fuzzy control rules by self-organizing and self-tuning the consequences of each functioning fuzzy control rule both offline and online. A self-tuning rule set of the self-abstracting rules has been built by analyzing the dynamical response process of a controlled object. The simulations show that the MBSAR can decrease the overshoot significantly and has a wonderful control performance, which are better than that of the self-abstracting rule fuzzy control method without model and PI control method.

By employing the fuzzy control theory and Dynamic Matrix Control (DMC) method, the controllers for temperature control of a room cooled by a displacement ventilation system are developed. The fluid flow and heat transfer inside the room is calculated by solving the Reynolds Averaged Navier-Stokes (RANS) equations including the effects of buoyancy in conjunction with a two-equation realizable k-epsilon turbulence model. Thus the physical environment is represented by a nonlinear system of partial differential equations. The system also has a large time delay because of the slowness of the heat exchange. Additionally, the temperature of the exterior wall of the room first increases and then decreases with time during a twenty four hour period, which acts as a strong disturbance in changing the temperature of the room. The goal of this paper is to develop controllers that will maintain the temperature in room within the specified upper and lower bounds by deploying the displacement ventilation system. In order to solve this temperature control problem, we develop a special fuzzy control method. At the same time, we analyze the peak value of the error and employ the DMC method to replace the fuzzy control method with success. Results show that the fuzzy controller is effective in saving energy and the DMC method can contain the error within specified bounds in the worst situation (when the temperature of the exterior wall is highest). This kind of fuzzy control and DMC method can also be employed for other HVAC systems such as Overhead VAV (Variable Air Volume) system and radiant cooling hydronic system.

Control of a polymerization reactor by fuzzy control method with genetic algorithm

PMSM servo system has nonlinear, parameter time-varying, load disturbance and other issues. In the face of these problems, traditional PI control strategies often fail to achieve ideal parameter tracking and load immunity, showing a large degree of limitations. Aiming at this kind of problem, this paper designs a fuzzy PI control method combining PI control and fuzzy control, and uses the vector rotation control method of current speed double closed loop to drive the permanent magnet synchronous motor for control. Finally, the traditional PI control system and fuzzy PI control system simulation model are built in Matlab/Simulink environment. The simulations were carried out in three cases of high speed, medium speed and low speed, and the speed and current waveforms of the two control methods were observed. The simulation results show that the fuzzy PI control system can increase the response rate, reduce the overshoot of the speed and reduce the current fluctuation in the full speed range. The robustness of the system is improved, the adaptability of the system to load changes is enhanced, and the correctness of the theoretical analysis is verified.

The present work is concerned to solve the problem of nonlinear robotic control systems on the basis of Takagi- Sugeno (T-S) fuzzy models. In addition, controllability and observability studies for T-S fuzzy model systems are considered for Single-Input Single-Output (SISO) and Multiple-Input Multiple-Output (MIMO) systems. In particular, the robust pole assignment approach is extended to the fuzzy field. This approach is used to design fuzzy stabilizers and fuzzy observers directly on the overall T-S fuzzy system. The latter one is the representation of the nonlinear robotic system, which is linearized around certain operation regions. The suggested method is considered for either SISO or MIMO systems. Furthermore, the method allows inducing an arbitrary behavior into the fuzzy plant in a relatively easy way. Two examples are used to verify the effectiveness of the proposed approach. The results are compared with the well-known Parallel Distributed Compensation (PDC) method, which is designed on the basis of Linear Matrix Inequalities (LMIs).

In the paper, the fuzzy control method is proposed to control the synchronization of chaotic systems. Based on fuzzy dynamic model approximating the non-linear system, the fuzzy model is decomposed into local linear model. The structure of fuzzy controller designed by control theories is simple and needs few rules. The synchronization of chaotic system is studied by means of the proposed controller. It is shown the validity of the fuzzy control method based on the simulating result of the synchronization of two different chaotic systems

This paper presents new stability conditions satisfying decay rate for both continuous and discrete fuzzy control systems. Linear matrix inequality (LMI) based designs for decay rate are also considered using the concept of parallel distributed compensation (PDC). To design fuzzy control systems, nonlinear systems are represented by Takagi-Sugeno fuzzy models. The PDC is employed to design fuzzy controllers from the Takagi-Sugeno fuzzy models. The stability analysis discussed here is reduced to a problem of finding a common Lyapunov function for a set of LMIs. Convex optimization techniques involving LMIs are utilized to find a common Lyapunov function and stable feedback gains satisfying decay rate. A simple example demonstrates the utility of the LMI-based designs proposed in this paper.

Based on the properties analysis of Takagi-Sugeno (T-S) fuzzy systems with two-overlapped fuzzy partition (TFP) inputs, an analytical design approach of T-S fuzzy control systems is proposed in this paper. This approach includes two parts: (1) a new method to check the stability of a T-S fuzzy control system which only requires to find a common positive-definite matrix in each maximal overlapped-rules group (MORG). This method can reduce the conservatism and difficulty of the former stability analysis methods. (2) The systematic design of T-S fuzzy controllers by means of the parallel distributed compensation (PDC) and linear matrix inequalities (LMI). The simulation results of a nonlinear mass-spring-damper system show that this approach is effective.

This chapter investigates the problem of stabilization of nonlinear discrete-time networked control systems (NCS) with event-triggering communication scheme in the presence of signal transmission delay. A Takagi–Sugeno (T–S) fuzzy model and parallel-distributed compensation (PDC) scheme are first employed to design a nonlinear fuzzy event-triggered controller for the stabilization of nonlinear discrete-time NCS. The idea of the event-triggering communication scheme (a soft computation algorithm) under consideration is that the current sensor data is transmitted only when the current sensor data and the previously transmitted one satisfy a certain state-dependent trigger condition. By taking the signal transmission delay into consideration and using delay system approach, a T–S fuzzy delay system model is established to describe the nonlinear discrete-time NCSs with event-triggering communication scheme. Attention is focused on the design of fuzzy event-triggered controller which ensures asymptotic stability of the closed-loop fuzzy systems. Linear matrix inequality- (LMI-) based conditions are formulated for the existence of admissible fuzzy event-triggered controller. If these conditions are feasible, a desired fuzzy event-triggered controller can be readily constructed. A nonlinear mass-spring-damper mechanical system is presented to demonstrate the effectiveness of the proposed method.

At high speed, electric vehicles (EVs) have limited torque when powered by an induction machine (IM). In IM, the high-speed region is called field weakening, and the region is known for torque limitation. This article proposes a control method that increases the torque without applying discontinuous-modulation techniques, which is commonly used. A bespoke model-based voltage control method has been developed, which enables reaching the hexagonal voltage reference trajectory for the field weakening region. So far, all model-based control methods are constrained by the inscribed voltage circle, which lies within the hexagonal voltage boundary. This restriction limits the available inverter output voltage across the motor windings, which, in turn, restricts the output torque of the drive. To achieve the hexagonal voltage trajectory, this article introduces a new calculation of the d-axis current for the entire speed range in the field weakening region. This calculation is based on the hexagonal voltage boundary equations and the stator voltage vector position. This generates a new reference d-axis current that minimizes the difference between the hexagonal voltage boundary and its inscribed voltage circle. As a result, the proposed d-axis current maximizes the output torque and output power in the field weakening region. The proposed method is presented analytically. Simulation and experimentally validated results are presented to confirm its feasibility and effectiveness.

A variable universe fuzzy control method for the HCOTSG feedwater system of small pressurized water reactor