Interval Type-2 Controller Research Articles

Derivation and characteristic investigation of a two-input, two-output interval type-2 fuzzy controller using product and operations

Interval type-2 (IT2) fuzzy logic, with the footprint of uncertainty (FOU) in membership functions, is very effective in dealing with disturbances and uncertainties of nonlinear systems. With this advantage, a two-input, two-output IT2 fuzzy controller with IT2 input and singleton type-1 fuzzy output sets is proposed for coupling systems. Firstly, the controller's input-output relationship is determined. Derivation results indicate that the controller is equivalent to the sum of a relay module and a local proportional-integral (PI) controller with variable gains. Next, analytical structure properties and gain variations are explored. It is demonstrated that the relay module is independent of the FOU, playing a dominant role in determining the control behavior of the IT2 controller. On the other hand, the control action of the PI controller diminishes when increasing the FOU and the number of fuzzy input sets. These properties contribute to the fast responsiveness of the controller and advantages in handling system uncertainty. Furthermore, the stability condition of this controller is established using the small gain theorem. Finally, both simulation and experiments are carried out to illustrate the applicability of the IT2 controller. The experimental results show that the controller's performance is embodied as the tracking errors of the two-linkage axes equal to ±4 μm, while the repeated positioning accuracy values are within ±3 μm.

Design of an Improved Interval Type-2 Controller Using FCM and Supervised Clustering Algorithms

Design of an Improved Interval Type-2 Controller Using FCM and Supervised Clustering Algorithms

Behavioral Analysis of an Interval Type-2 Fuzzy Controller Designed with Harmony Search Enhanced with Shadowed Type-2 Fuzzy Parameter Adaptation

The challenges we face in today’s world are increasingly complex, and effectively managing uncertainty when modeling control problems can yield significant benefits. However, the complexity of these models often leads to higher computational costs. Therefore, the main contribution of this article is the use of the theory of shadowed type-2 fuzzy sets to address these challenges and to control the search space exploration in the harmony search algorithm by employing two alpha planes, and with this, it was possible to reduce the computational cost and obtain effective results. Furthermore, the application of this approach aims to find optimal parameters for the membership functions of a type-2 fuzzy controller and analyze its behavior. By adopting the proposed methodology, it becomes possible to minimize computational costs while still achieving feasible solutions for interval type-2 control problems. A key aspect is that symmetry is considered in the design of the controller to also obtain good results. To validate the effectiveness of the approach, extensive simulations were conducted with varying levels of noise introduced to the type-2 controller. This comprehensive analysis allowed for a thorough examination of the results obtained. The findings of the simulations are presented, showcasing the advantages of the proposed methodology. By incorporating noise into the system, it was observed that the objective function, in this case, the root mean square error (RMSE), was reduced. Moreover, the signal obtained with the presence of noise demonstrated a superior performance compared to the noise-free reference. In conclusion, the proposed approach of utilizing shadowed type-2 fuzzy systems, combined with the harmony search algorithm, offers a promising solution for managing complex control problems. By carefully analyzing the behavior of the system through simulations, it is evident that the inclusion of noise helps improve the system’s performance.

Interval Type-2 Fuzzy Sliding-Mode Control of Three-Axis Stabilization Gimbal

Aiming at the attitude control problem of three-axis stabilization gimbal, an algorithm combining interval type-2 fuzzy control and sliding-mode control was designed. Firstly, the mathematical model of the three-axis stabilization gimbal actuator was established after analyzing the mechanical structure of the three-axis stabilization gimbal. Then, a sliding-mode controller was designed based on the position ring of the actuator of three-axis stabilization gimbal. An interval type-2 control was used to reduce chattering in sliding-mode control. The switching function and its derivative are taken as the input of fuzzy control, and the rate of change of the approach law is taken as the output of fuzzy control. Fuzzy control can adjust the gain of sliding-mode surface dynamically, enhance the adaptability on external random disturbance, improve the speed of convergence and weaken chattering. The simulation results show that the output of the controller designed in this paper is more stable, and the tracking of the three-axis stabilization gimbal is more rapid and accurate.

Effects of Increasing the Footprints of Uncertainty on Analytical Structure of the Classes of Interval Type-2 Mamdani and TS Fuzzy Controllers

The fundamental difference between an interval type-2 (IT2) fuzzy controller and a type-1 fuzzy controller is the footprint of uncertainty (FOU) of an IT2 fuzzy set. In this paper, we study how FOUs affect the analytical structure (i.e., the input–output mathematical relationship) of a broad class of IT2 Mamdani and takagi-sugeno (TS) controllers. The controllers employ arbitrary fuzzy rules, the Karnik–Mendel (KM) or Enhanced KM type-reducer, the minimum AND operator, and the centroid defuzzifier. The controllers utilize commonly used IT2 fuzzy sets for their input variables and any kind of type-2 fuzzy sets for their output variable. We prove that, with increase of FOUs of the input fuzzy sets, the Mamdani controllers approach constant controllers, and the TS controllers approach piecewise linear controllers. The resemblance to the constant or pricewise linear controllers increases as the FOUs increase. When all the FOUs are at their maximum (to reflect the highest level of uncertainties), the Mamdani and TS controllers become the constant controllers and piecewise linear controllers, respectively. We investigate how change in the resemblance takes place progressively as FOUs increase. We also show that an increase in the resemblance narrows control gain variations for part of the IT2 controllers, which can worsen control performance. These findings implicit controller design—too large FOUs are generally undesirable for the input fuzzy sets because they can make an IT2 controller behave like a constant or piecewise linear controller. Real-time control experiment results are provided to illustrate the theoretical analysis.

Type-2 fuzzy logic controller for position control of shape memory alloy wire actuator

The main aim of this article is to present the usage of type-2 fuzzy logic controller to control a shape memory actuator. One of the main advantages of the fuzzy systems is that they do not require creating any mathematical model of the controlled plant which simplifies the control task. However, a dynamic system model was created to adjust the proportional–integral–derivative controller parameters. Different types of controllers were tested experimentally by controlling the position of the commercially available shape memory alloy actuator NM70 made by Miga Motor company. Despite its small size, it distinguishes itself by its strength. To enhance real-time performance, simplified interval fuzzy sets were used. The algorithm was implemented in the ATmega32 microcontroller. The dedicated PC application was also built. The obtained results confirmed that type-2 fuzzy controller performed efficiently with a nonlinear plant which is difficult to control. The research also proved that interval type-2 controllers, which are a simplified version of the general type-2 controllers, are very efficient. They can handle uncertainties without increasing drastically the computational complexity. Experimental data comparison of the proportional–integral–derivative reference with the fuzzy logic controller type-2 and type-1 clearly indicates the superiority of the former, especially in reducing overshooting.

Deriving and Analyzing Analytical Structures of a Class of Typical Interval Type-2 TS Fuzzy Controllers.

A conventional controller's explicit input-output mathematical relationship, also known as its analytical structure, is always available for analysis and design of a control system. In contrast, virtually all type-2 (T2) fuzzy controllers are treated as black-box controllers in the literature in that their analytical structures are unknown, which inhibits precise and comprehensive understanding and analysis. In this regard, a long-standing fundamental issue remains unresolved: how a T2 fuzzy set's footprint of uncertainty, a key element differentiating a T2 controller from a type-1 (T1) controller, affects a controller's analytical structure. In this paper, we describe an innovative technique for deriving analytical structures of a class of typical interval T2 (IT2) TS fuzzy controllers. This technique makes it possible to analyze the analytical structures of the controllers to reveal the role of footprints of uncertainty in shaping the structures. Specifically, we have mathematically proven that under certain conditions, the larger the footprints, the more the IT2 controllers resemble linear or piecewise linear controllers. When the footprints are at their maximum, the IT2 controllers actually become linear or piecewise linear controllers. That is to say the smaller the footprints, the more nonlinear the controllers. The most nonlinear IT2 controllers are attained at zero footprints, at which point they become T1 controllers. This finding implies that sometimes if strong nonlinearity is most important and desired, one should consider using a smaller footprint or even just a T1 fuzzy controller. This paper exemplifies the importance and value of the analytical structure approach for comprehensive analysis of T2 fuzzy controllers.

ON THE CONTROL OF TUMOR GROWTH VIA TYPE-1 AND INTERVAL TYPE-2 FUZZY LOGIC

This paper deals with growth control of cancer cells population using type-1 and interval type-2 fuzzy logic. A type-1 fuzzy controller is designed in order to reduce the population of cancer cells, adjust the drug dosage in a manner that allows normal cells re-grow in treatment period and maintain the maximum drug delivery rate and plasma concentration of drug in an appropriate range. Two different approaches are studied. One deals with reducing the number of cancer cells without any concern about the rate of decreasing, and the other takes the rate of malignant cells damage into consideration. Due to the fact that uncertainty is an inherent part of real systems and affects controller efficacy, employing new methods of design such as interval type-2 fuzzy logic systems for handling uncertainties may be efficacious. Influence of noise on the system is investigated and the effect of altering free parameters of design is studied. Using an interval type-2 controller can diminish the effects of incomplete and uncertain information about the system, environmental noises, instrumentation errors, etc. Simulation results confirm the effectiveness of the proposed methods on tumor growth control.

Interval type-2 fuzzy control for nonlinear discrete-time systems with time-varying delays

This paper is concerned with the problem of fault-tolerant control for discrete-time interval type-2 (IT2) fuzzy time delay system with actuator faults under imperfect premise matching. The time-varying delay and actuator fault are first taken into account for the IT2 fuzzy discrete-time systems. The novel IT2 state-feedback controller and the IT2 fuzzy model share different lower and upper membership functions. The fault-tolerant controller is designed to compensate for the effect of faults by stabilizing the closed-loop system under the actuator failures. Furthermore, the standard IT2 state-feedback controller is designed such that the closed-loop system is asymptotically stable and has an H∞ performance. The obtained conditions of the fault-tolerant controller and the standard IT2 controller can be expressed by the convex optimization problems. A numerical example is presented to show the effectiveness of the proposed results.

Output tracking control for a class of continuous-time T–S fuzzy systems

This paper investigates the problem of output tracking for nonlinear systems with actuator fault using interval type-2 (IT2) fuzzy model approach. An IT2 state-feedback fuzzy controller is designed to perform the tracking control problem, where the membership functions can be freely chosen since the number of fuzzy rules is different from that of the IT2 T–S fuzzy model. Based on Lyapunov stability theory, an existence condition of IT2 fuzzy H∞ output tracking controller is obtained to guarantee that the output of the closed-loop IT2 control system can track the output of a given reference model well in the H∞ sense. Finally, two illustrative examples are given to demonstrate the effectiveness and merits of the proposed design techniques.