A unified approach to stability and robustness in dynamic nonlinear general type-2 TSK fuzzy control systems

In an intelligent manufacturing context, the smooth operations of mechanical equipment in the production process of enterprises and timely fault diagnosis during operations have become increasingly important. However, the effect of traditional fault diagnosis depends on the feature extraction quality and experts’ empirical knowledge, which is inefficient and costly, and cannot match the needs of mechanical equipment fault diagnosis in intelligent manufacturing. The TSK fuzzy system has a strong approximation capability and the ability to interpret expert knowledge. The broad learning system (BLS) has strong feature extraction and fast computation capabilities. In this paper, we present a new model—the TSK fuzzy broad learning system (TSK-BLS). The model integrates the advantages of the BLS and the fuzzy system at the same time, which can be calculated quickly and accurately by pseudo-inverse and symmetry methods. On the other hand, the model is an embedded model-building mechanism, which extends the application scope of BLS theory. The model was tested on a bearing fault data set, provided by Case Western Reserve University, and the model’s fault diagnosis accuracy was as high as 0.9967. The results were compared with those of the convolutional neural network (CNN) and the BLS models, whose fault diagnosis accuracies are 0.6833 and 0.9133, respectively. Comparison showed that the proposed fault diagnosis model—TSK-BLS, achieved significant improvements.

Fuzzy controllers and fuzzy sliding-mode controllers have found extensive use in a variety of applications. Generally, type-1 fuzzy sets are used for the membership functions of these controllers. However, in real-time applications, uncertainty associated with the available information always occurs. A type-2 fuzzy controller and a type-2 fuzzy sliding-mode controller are proposed that are able to solve the problem that the words used in the inference rules can mean different things to different people. Since the membership functions use type-2 fuzzy sets then, the proposed control schemes can handle the rule uncertainties when the operation is extremely uncertain and/or the membership grades cannot be exactly determined. The proposed control systems are applied to control a buck DC–DC converter. A comparison between a PI controller, a type-2 fuzzy controller and a type-2 fuzzy sliding-mode controller is made. The experimental results show that the type-2 fuzzy sliding-mode controller achieves the best control performance.

Fuzzy logic control based on the Takagi–Sugeno inference method has been applied for the yeast alcoholic fermentation running in a continuous-time biochemical reactor in this paper. A type-1 fuzzy PID controller was designed to temperature control in a biochemical reactor. The fuzzy PID controller was also designed using type-2 fuzzy sets. The advantage of the fuzzy control is that it can be used very successfully for control of strongly non-linear processes and processes that are difficult to model because of complicated reaction kinetics. Obtained simulation results confirm this fact. The disadvantage of the fuzzy control design lies in the time-consuming tuning of controllers. The subtractive clustering method was used to identify the rule base. This approach was chosen to minimize the number of rules of the designed fuzzy logic controllers and to simplify the fuzzy controller design. Simulation results confirm that fuzzy PID controllers can assure better performance than conventional PID controllers. Yeast alcoholic fermentation is an exothermic process and the cooling is necessary to maintain the optimal temperature in the reactor. Fuzzy PID control reduces coolant consumption in comparison with conventional PID control and so it assures energy-efficient control of continuous-time alcoholic fermentation. Using type-2 fuzzy sets in the fuzzy PID controller design is very promising as the type-2 fuzzy controller offers even better results than the type-1 fuzzy controller.

Cascade fuzzy control of a tubular chemical reactor

Fuzzy systems (FSs) have been extensively applied to automatic control, pattern recognition, and decision analysis. However, a common bottleneck is encountered in the derivation of fuzzy rules, which is often difficult, time consuming, and relies on expert knowledge. To automate the design of FSs, many metaheuristic learning algorithms have been proposed. One major optimization category uses Swarm Intelligence (SI) model (Kennedy et al., 2001). The SI technique studies collective behavior in decentralized systems. Its development was based on mimicking the social behavior of animals or insects in an effort to find the optima in the problem space. SI models are initialized with a population of random solutions. One well-known SI model is particle swarm optimization (PSO) (Kennedy & Eberhart, 1995). Many modified PSO models have been proposed and successfully applied to different optimization problems (Clerc & Kennedy, 2002; Bergh & Engelbrecht, 2004; Ratnaweera et al., 2004; Juang, 2004; Kennedy & Mendes, 2006; Parrott & Li, 2006; Chen & Li, 2007). FS design using PSO has also been proposed in several studies (Juang, 2004; Chatterjee et al., 2005; Juang et al., 2007; Araujo & Coelho, 2008; Sharma et al., 2009). Another well-known SI is ant colony optimization (ACO) (Dorigo & Stutzle, 2004). The ACO technique is inspired by real ant colony observations. It is a multi-agent approach that was originally proposed to solve difficult discrete combinatorial optimization problems, such as the traveling salesman problem (TSP) (Dorigo et al., 1996; Dorigo & Gambardella, 1997). In the original ACO meta-heuristic, artificial ant colonies cooperate to find good solutions for difficult discrete optimization problems. Different ACO models have been applied to FS design problems (Cassillas et al., 2000; Cassillas et al., 2005; Mucientes & Casillas; 2007; Juang & Lo, 2007; Juang et al., 2008; Juang & Lu; 2009). In (Cassillas et al.,2000; Mucientes & Casillas; 2007; Juang et al., 2008; Juang & Lu; 2009), the FS input space was partitioned in grid type with antecedent part parameters of an FS manually assigned in advance. In (Juang & Lo, 2007), the FS input space was flexibly partitioned using a fuzzy clustering-like algorithm in order to reduce the total number of rules. For all of these studies, the consequent part parameters were optimized in discrete space using ACO. Since only the consequent part parameters are optimized, and the optimization space is restricted to be discrete, the designed FSs are unsuitable for problems where high accuracy is a major concern. Source: Fuzzy Systems, Book edited by: Ahmad Taher Azar, ISBN 978-953-7619-92-3, pp. 216, February 2010, INTECH, Croatia, downloaded from SCIYO.COM

Studies on interval type-2 TSK fuzzy logic system is a hot topic in the current academic area. Parameter identification is very important for system design. Commonly used parameter identification methods are the least-square algorithm, BP algorithm, etc., few scholars use QPSO algorithm for parameter identification. In this paper, we propose a design of interval type-2 TSK fuzzy logic system based on quantum behaved particle swarm optimization (QPSO) intelligent algorithm. Firstly, by combining the A1–C1, A2–C0, A2–C1 interval type-2 TSK fuzzy logic system with neural network, the fuzzy neural network system is designed. Then, the QPSO intelligent algorithm was used to tune the fuzzy neural network system parameters, and the designed system model is applied to predict the Nasdaq Composite Index and International Gold Prices. Both QPSO algorithm and BP algorithm have been used to train the system model. By comparing QPSO algorithm and BP algorithm, the performance index and simulation results illustrated the proposed model is effective and feasible, which can achieve a better performance. Finally, compare the performance of the four fuzzy logic systems, it can be seen the effect of A2–C1 fuzzy logic system is better than that of the other three fuzzy logic systems.

Artificial intelligence methods such as fuzzy logic and particle swarm optimization (PSO) have been applied to maximum power point tracking (MPPT) for solar panels. The P-V curve of a solar panel exhibits multiple peaks under partial shading condition (PSC) when all modules of a solar panel do not receive the same solar irradiation. Although conventional PSO has been shown to perform well under uniform insolation, it is often unable to find the global maximum power point under PSC. Fuzzy adaptive PSO controllers have been proposed for MPPT. However, the controller became computation-intensive in order to adjust the PSO parameters for each particle. In this paper, fuzzy adaptive PSO-based and conventional PSO-based MPPT are compared and evaluated in the aspect of design and performance. A simple fuzzy adaptive PSO controller for MPPT was designed to reach the global optimal point under PSC and uniform irradiation. The controller combines the advantages of both PSO and fuzzy control. The fuzzy controller dynamically adjusts the PSO parameter to improve the convergence speed and global search capability. Since tuning of the PSO parameter is designed to be common for all particles, it reduced the computation complexity. The fuzzy controller’s rule base is designed to obtain a fast transient response and stable steady state response. Design of the fuzzy adaptive PSO-based MPPT is verified with simulation results using a boost converter. The results are evaluated in comparison to the results using a conventional PSO controller under PSC. Simulation shows the fuzzy adaptive PSO-based MPPT is able to improve the global search process and increase the convergency speed. The comparison indicates the settling time using the fuzzy adaptive PSO-based MPPT is 14% faster under PSC on average and 30% faster under uniform irradiation than the settling time using the conventional PSO. Both the fuzzy adaptive and conventional PSO controllers have similar output power tracking accuracy.

In this paper the identification and control of dynamic plants using type-2 TSK fuzzy neural system (FNS) is considered. The systems constructed on the base of type-1 fuzzy systems cannot directly handle the uncertainties associated with information or data in the knowledge base of the process. One possible way to alleviate the problem is to resort to the use of type-2 fuzzy systems. In this paper, a type-2 TSK fuzzy neural system (FNS), is proposed and its gradient learning algorithm is derived. Its performance for identification and control of time-varying plants is evaluated and compared with other approaches seen in the literature; the time-varying nature of the plants being handled as uncertainties in the plant coefficients which can be described by type-2 fuzzy sets.

In this paper, an algorithm was presented to control the satellite attitude in orbit in order to reduce the fuel consumption and increase longevity of satellite. Because of proper operation and simplicity, fuzzy controller was used to save fuel and analyze the uncertainty and nonlinearities of satellite control system. The presented control algorithm has a high level of reliability facing unwanted disturbances considering the satellite limitations. The controller was designed based on Takagi-Sugeno satellite dynamic model, a powerful tool for modeling nonlinear systems. Inherent chattering related to on-off controller produces limit cycles with low frequency amplitude. This increases the system error and maximizes the satellite fuel consumption. Particle Swarm Optimization (PSO) algorithm was used to minimize the system error. The satellite simulation results show the high performance of fuzzy on-off controller with the presented algorithm. DOI: http://dx.doi.org/10.11591/ijece.v4i3.5831

This paper presents a practical implementation of an interval type-2 fuzzy logic controller for two stages photovoltaic system consisting of DC- DC boost converter and three-phase inverter. The power converter circuits are nonlinear and have uncertainties. These uncertainties cause noise and delay in the response of power systems. A photovoltaic system has also uncertainties caused by itself. The change in temperature and irradiation cause the change in parameters of photovoltaic systems. Conventional controllers and type-1 fuzzy controllers can’t overcome uncertainties. The main objective of this study is to show the superiority of interval type-2 fuzzy logic controller to overcome the uncertainties. Interval type-2 fuzzy logic controller algorithm was developed for DC- DC boost converter and three-phase space vector modulated inverter. To make comparison, the system was controlled by a type-1 and an interval type-2 fuzzy controller respectively. Simulation studies and real time application were performed. Settling time, overshoot and ripple voltage were investigated for the boost converter. Current and voltage harmonic analysis, frequency and phase angle data were analyzed for three-phase inverter. According to the simulation results and the practical results, interval type-2 fuzzy logic controller offered better solution for the whole system.

This paper presents a systematic design method of a controller using the discrete fuzzy PI control and the particle swarm optimization (PSO). Unlike a conventional PI controller, the discrete fuzzy PI controller has variable gains according to its input variables. Generally, it is complicated to tune the parameters of a fuzzy controller because there are too many parameters which are strongly coupled. In the discrete-time domain, the discrete fuzzy PI controller is a superset of the conventional PI controller. And the initial parameters of the fuzzy PI controller are selected by using the inclusion relationship. And, for the sake of simplicity, only four rules are used to construct a nonlinear fuzzy control surface. The tuning parameters of the discrete fuzzy PI controller are optimized by using the PSO. To verify the effectiveness of the controller designed by using the discrete fuzzy PI control and the PSO, we applied it to a wind turbine pitch controller. As a result, the proposed controller has variable gains, unlike the PI controller, and make the pitch controller operate in boarder operating regions.

Nowadays, general type-2 fuzzy systems are an attractive alternative for non-linear control problems because they provide good robustness in real-world environments, where there exist many noise sources. This kind of fuzzy systems can have better performance in comparison to type-1 fuzzy systems as they offer uncertainty handling capabilities. However, one of the main problems in implementing general type-2 fuzzy systems is their elevated computational cost. The computational cost of a general type-2 fuzzy system depends on the representation that is used, for example, the α-planes representation consists on a discretization of general type-2 fuzzy systems into several horizontal slices called α-planes, then solving every α-plane as an interval type-2 fuzzy system and after that the integration of the results to approximate a general type-2 fuzzy system. The main contribution of this work is the proposed computational cost reduction of the α-planes representation by optimizing the α-planes integration process based on the composite Newton–Cotes rules. In this way, the number of α-planes required for a good approximation is reduced, and the computational cost is also reduced by introducing new equations for the α-planes aggregation. Finally, a systematic comparative analysis of the improvement offered by the proposed method with respect to the conventional approach is presented.

Type-1 fuzzy PID controllers are widely used in industrial control systems due to their well-established theoretical foundation, simplicity of structure, and ease of operation. However, as control systems become increasingly complex and demands for higher control performance intensify, the limitations of Type-1 fuzzy controllers become more apparent. Additionally, the difficulty in tuning PID parameters and the inability to adjust these parameters online as the controlled system changes further constrain the effectiveness of traditional PID controllers. To address these challenges, this paper introduces a generalized Type-2 fuzzy logic control approach. The generalized Type-2 fuzzy controller extends the capabilities of interval Type-2 fuzzy controllers, offering enhanced ability to handle higher-order uncertainties. Moreover, the integration of memristor devices enables online adaptive tuning of controller parameters. By combining the generalized Type-2 fuzzy logic with memristor-based PID control, a novel memristor-based controller was designed, which allows for real-time adaptive adjustment of the controller parameters. Theoretical analysis is followed by simulations and experimental validation. The results demonstrate that the proposed memristor-based controller with generalized Type-2 fuzzy logic exhibits superior robustness. Specifically, when evaluated using the Integral of Time-weighted Absolute Error (ITAE) performance index, the controller achieves improvements of 65.9% and 40.2% compared to traditional PID and Type-1 fuzzy PID controllers, respectively. These findings confirm the excellent tracking performance and robustness of the proposed control system.

In this study, we will present the novel application of Type-2 (T2) fuzzy control into the popular video game called flappy bird. To the best of our knowledge, our work is the first deployment of the T2 fuzzy control into the computer games research area. We will propose a novel T2 fuzzified flappy bird control system that transforms the obstacle avoidance problem of the game logic into the reference tracking control problem. The presented T2 fuzzy control structure is composed of two important blocks which are the reference generator and Single Input Interval T2 Fuzzy Logic Controller (SIT2-FLC). The reference generator is the mechanism which uses the bird's position and the pipes' positions to generate an appropriate reference signal to be tracked. Thus, a conventional fuzzy feedback control system can be defined. The generated reference signal is tracked via the presented SIT2-FLC that can be easily tuned while also provides a certain degree of robustness to system. We will investigate the performance of the proposed T2 fuzzified flappy bird control system by providing comparative simulation results and also experimental results performed in the game environment. It will be shown that the proposed T2 fuzzified flappy bird control system results with a satisfactory performance both in the framework of fuzzy control and computer games. We believe that this first attempt of the employment of T2-FLCs in games will be an important step for a wider deployment of T2-FLCs in the research area of computer games.

This paper presents a rigorous mathematical development for the design of robust intelligent type-2 fuzzy control systems with regards to the disturbance rejection problem. The majority of the papers in the literature uses only type-1 fuzzy systems for the modeling of both plant ant controller. In the control structure presented in this paper, we use type-2 fuzzy systems, which are more generalized than their type-1 counterparts and particularly known for handling uncertainties. This work extends and generalizes the previous results for the design of robust intelligent control systems. The final robust criteria are given based on linear matrix inequalities (LMIs), and two examples are provided to demonstrate the developed methodologies. The simulation results also show the potential of type-2 fuzzy controllers in improving robustness compared to type-1. The mathematically-sound general framework proposed in this paper provides a systematic tool for the design of robust intelligent controllers, and hence it is expected to widen their applications.