General Type-2 Fuzzy Controller Research Articles

Structure Analysis of General Type-2 Fuzzy Controller and Its Application

In this paper, a general type-2 fuzzy controller is proposed. The proposed general type-2 fuzzy controller is based on α-plane representation, which converts the centroid of general type-2 fuzzy sets to centroids of several interval type-2 fuzzy sets. Also, the mathematical expression of general type-2 fuzzy controller is derived by fuzzy product operate and NT type reduction. By the mathematical expression, the relation between general type-2 fuzzy controller output with parameter of triangular secondary membership function is discussed. Finally, the control performances of proposed general type-2 fuzzy controller are compared with conventional PID controller, tradition type-1 fuzzy controller, and interval type-2 fuzzy controller. Furthermore, to show the effective and practical of the proposed controller, a nonlinear inverted pendulum system is tested. The simulation results show that general type-2 fuzzy controller achieves better control efforts than other compared controllers.

A class of general type-2 fuzzy controller based on adaptive alpha-plane for nonlinear systems

This study introduces a general type-2 Takagi–Sugeno–Kang fuzzy controller (GT2-TSKFC) for controlling uncertain systems. The proposed GT2-TSKFC uses equidistant type-2 triangular membership functions (MFs) for the antecedents, Larsen’s implication method, type-1 fuzzy sets for the consequent parameters, and a direct defuzzification method. The analytical structure of the proposed controller indicates that the alpha-plane and apex of the secondary MFs have a noticeable effect on calculating the control signal. Adaptation of the alpha-plane and apex of the secondary MFs is performed using the Lyapunov function to achieve the stability of the controlled system. The proposed controller is applied to an uncertain nonlinear inverted pendulum system. The results of the proposed control algorithm are compared with those of a general type-2 fuzzy controller with a specific number of alpha-planes, a quasi type-2 fuzzy controller, an interval type-2 fuzzy controller, and a type-1 fuzzy controller to demonstrate the robustness and effectiveness of the proposed scheme.

A Class of General Type-2 Fuzzy Controller Based on Adaptive Alpha-Plane for Nonlinear Systems

A Class of General Type-2 Fuzzy Controller Based on Adaptive Alpha-Plane for Nonlinear Systems

A new adaptive non-singleton general type-2 fuzzy control of induction motors subject to unknown time-varying dynamics and unknown load torque

A new adaptive non-singleton general type-2 fuzzy control of induction motors subject to unknown time-varying dynamics and unknown load torque

Mathematical analysis of a simplified general type-2 fuzzy PID controller

For the type reduction of general type-2 fuzzy PID controller is time consuming and the mathematical expression of general type-2 fuzzy PID controller is difficult to derived. So, a simplified general type-2 fuzzy PID (SGT2-FPID) controller is studied in this article. The SGT2-FPID controller adopts triangular function as the primary and secondary membership function. Then the primary membership degree of apex for the secondary membership degree will be applied to get the output of SGT2-FPID controller, which can reduce the computation complexity of general type-2 fuzzy controller type reduction. Furthermore, the mathematical expressions of SGT2-FPID controller, type-1 fuzzy PID controller and interval type-2 fuzzy PID controller are discussed. Finally, 4 plants are applied to demonstrate the effectiveness and robustness of SGT2-FPID controller. The simulation results show that when the plants have uncertainty in model structure, measurement and external disturbance, the SGT2-FPID controller can achieve better control performances in contrast to compared controllers.

General Type-2 Fuzzy Gain Scheduling PID Controller with Application to Power-Line Inspection Robots

In this paper, a general type-2 fuzzy gain scheduling PID (GT2FGS-PID) controller is presented to achieve self-balance adjustment of the power-line inspection (PLI) robot system. As the PLI robot system is an under-actuated nonlinear system, obtaining the full information of the four-state variables is necessary to balance the PLI robot. However, as the number of input variables increases, the number of control rules increases exponentially, making the design of the fuzzy controller extremely complex. Therefore, the proposed controller prevents the problem of rule explosion using information fusion and then simplifies the control design. Moreover, the particle swarm optimization algorithm is used to select improved controller parameters and make the controller achievable. In this paper, the control performance and anti-interference ability of the traditional PID control, type-1 fuzzy control, interval type-2 fuzzy control, and general type-2 fuzzy control methods are compared. By means of numerical simulation, we can conclude that the GT2FGS-PID controller exhibits superior stability and robustness over other controllers for the PLI robot system.

Non-singleton General Type-2 Fuzzy Control for a Two-Wheeled Self-Balancing Robot

This paper presents several non-singleton general type-2 fuzzy logic controllers (NGT2FLCs) for an under-actuated mobile two-wheeled self-balancing robot to improve the anti-interference capability of the system. Four kinds of fuzzifiers, including singleton fuzzifier, type-1 non-singleton fuzzifier, interval type-2 non-singleton fuzzifier and general type-2 non-singleton fuzzifier, are considered to construct different general type-2 fuzzy logic controllers (GT2FLCs). In order to show the superiority of the GT2FLCs, three kinds of interval type-2 fuzzy logic controllers (IT2FLCs), including singleton IT2FLCs, type-1 non-singleton IT2FLCs (N1IT2FLCs) and interval type-2 non-singleton IT2FLCs (N2IT2FLCs), are also presented. A comparative study between singleton fuzzy controllers and non-singleton fuzzy controllers, and IT2FLCs and GT2FLCs is also shown. All simulation results show that the performance of non-singleton fuzzy logic controllers is better than that of singleton fuzzy logic controllers. The NGT2FLCs get the best performance in the presence of uncertainties and external disturbances.

A novel general type-2 fuzzy controller for fractional-order multi-agent systems under unknown time-varying topology

In this paper, a robust adaptive control scheme is proposed for the leader following control of a class of fractional-order multi-agent systems (FMAS). The asymptotic stability is shown by a linear matrix inequality (LMI) approach. The nonlinear dynamics of the agents are assumed to be unknown. Moreover, the communication topology among the agents is assumed to be unknown and time-varying. A deep general type-2 fuzzy system (DGT2FS) using restricted Boltzmann machine (RMB) and contrastive divergence (CD) learning algorithm is proposed to estimate uncertainties. The simulation studies presented indicate that the proposed control method results in good performance under time-varying topology, unknown dynamics and external disturbances. The effectiveness of the proposed DGT2FS is verified also on modeling problems with high dimensional real-world data sets.

An improved general type-2 fuzzy sets type reduction and its application in general type-2 fuzzy controller design

The Karnik–Mendel (KM) or the enhanced Karnik–Mendel (EKM) algorithm is widely used for interval type-2 fuzzy sets type reduction in many applications. Compared with iterative procedures of KM/EKM, an iterative algorithm with a stop condition or an enhanced iterative algorithm with a stop condition based on the KM algorithm that converges monotonically is more efficient. In this article, a new iterative algorithm with stop condition type reduction for interval type-2 fuzzy sets is proposed, in which switch points are initialized and unidirectional search is performed based on monotone properties of the KM algorithm. Furthermore, the proposed algorithm is applied to general type-2 fuzzy sets type reduction based on α-plane representation. The experimental results of a triangular and gaussian secondary membership function show practicality and efficiency of this method. In accordance with the conventional PI, type-1 or interval type-2 fuzzy controller is difficult to achieve a desired control effect for steam temperature at collector outlet of trough solar thermal power generation system with large time delay, strong inertia and parameter time-variation, and a general type-2 fuzzy controller with more adjustable controller parameters is proposed in this article. In different working conditions, the proposed controller can reduce system overshoot and ensure system stability. Moreover, when the working condition changes, the controller can solve a model mismatch problem under same controller parameters and has faster response.

Indirect adaptive robust mixed H2/H∞ general type-2 fuzzy control of uncertain nonlinear systems

General type-2 fuzzy logic offers an added ability to manage uncertainties, but it also carries a high computational burden and added mathematical complexity. Further development of this paradigm is hence considerably challenged in terms of both time-constrained industrial implementations and mathematical guarantees of performance. In this paper, we propose a stable indirect adaptive robust mixed H2/H∞ control approach to an α-plane representation of a general type-2 fuzzy framework. The resulting structure is shown to be both computationally efficient and amenable to theoretical analysis. Specifically, this hybrid paradigm is mathematically derived to minimize energy consumption, keep all signals bounded during the transient states, guide the tracking error to zero, and keep the effect of uncertainties such as the external disturbances below a desired level. To validate these theoretical results, two sets of simulations on an inverted pendulum and a robotic manipulator with time-varying payloads and friction disturbances are performed. To illustrate real-time computational efficacy, the proposed algorithm is then experimentally implemented on a 3-PSP parallel robot in our laboratory. Comparative analysis indicates that the proposed method achieves smaller tracking error, less consumed control energy, and better robustness against uncertainties when compared with its type-1 fuzzy, interval type-2 fuzzy counterparts. This is while computational time for each control cycle increases only slightly when compared with its interval type-2 counterpart.