A Self-Tuning zSlices-Based General Type-2 Fuzzy PI Controller

The interval type-2 fuzzy Proportional-Integral (PI) controller (IT2-FPI) might be able to handle high levels of uncertainties to produce a satisfactory control performance, which could be potentially due to the robust performance as a result of the smoother control surface around the steady state. However, the transient state and disturbance rejection performance of the IT2-FPI may degrade in comparison with the type-1 fuzzy PI (T1-FPI) counterpart. This drawback can be resolved via general type-2 fuzzy PI controllers which can provide a tradeoff between the robust control performance of the IT2-FPI and the acceptable transient and disturbance rejection performance of the type-1 PI controllers. In this paper, we will present a zSlices-based general type-2 fuzzy PI controller (zT2-FPI), where the secondary membership functions (SMFs) of the antecedent general type-2 fuzzy sets are adjusted in an online manner. We will examine the effect of the SMF on the closed-system control performance to investigate their induced performance improvements. This paper will focus on the case followed in conventional or self-tuning fuzzy controller design strategies, where the aim is to decrease the integral action sufficiently around the steady state to have robust system performance against noises and parameter variations. The zSlices approach will give the opportunity to construct the zT2-FPI controller as a collection of IT2-FPI and T1-FPI controllers. We will present a new way to design a zT2-FPI controller based on a single tuning parameter where the features of T1-FPI (speed) and IT2-FPI (robustness) are combined without increasing the computational complexity much when compared with the IT2-FPI structure. This will allow the proposed zT2-FPI controller to achieve the desired transient state response and provide an efficient disturbance rejection and robust control performance. We will present several simulation studies on benchmark systems, in addition to real-world experiments that were performed using the PIONEER 3-DX mobile robot that will act as a platform to evaluate the proposed systems. The results will show that the control performance of the self-tuning zT2-FPI control structure enhances both the transient state and disturbance rejection performances when compared with the type-1 and IT2-FPI counterparts. In addition, the self-tuning zT2-FPI is more robust to disturbances, noise, and uncertainties when compared with the type-1 and interval type-2 fuzzy counterparts

Analysis and Applications of the Km Algorithm in Type-2 Fuzzy Logic Control and Decision Making

Ph.DDOCTOR OF PHILOSOPH

Systematic Design of Type-2 Fuzzy Logic Systems for Modeling and Control with Applications to Modular and Reconfigurable Robots

Fuzzy logic systems (FLSs) are well known in the literature for their ability to model linguistics and system uncertainties. Due to this ability, FLSs have been successfully used in modeling and control applications such as medicine, finance, communications, and operations research. Moreover, the ability of higher order fuzzy systems to handle system uncertainty has become an interesting topic of research in the field. In particular, type-2 FLSs (T2 FLSs), systems consisting of fuzzy sets with fuzzy grades of membership, a feature that type-1 (T1) does not offer, are most well-known for this capability. The structure of T2 FLSs allows for the incorporation of uncertainty in the input membership grades, a common situation in reasoning with physical systems. General T2 FLSs have a complex structure, thus making them difficult to adopt on a large scale. As a result, interval T2 FLSs (IT2 FLSs), a special class of T2 FLSs, have recently shown great potential in various applications with input-output (I/O) system uncertainties. Due to the sophisticated mathematical structure of IT2 FLSs, little to no systematic analysis has been reported in the literature to use such systems in control design. Moreover, to date, designers have distanced themselves from adopting such systems on a wide scale because of their design complexity. Furthermore, the very few existing control methods utilizing IT2 fuzzy logic control systems (IT2 FLCSs) do not guarantee the stability of their system. Therefore, this thesis presents a systematic method for designing stable IT2 Takagi-Sugeno-Kang (IT2 TSK) fuzzy systems when antecedents are T2 fuzzy sets and consequents are crisp numbers (A2-C0). Five new inference mechanisms are proposed that have closed-form I/O mappings, making them more feasible for FLCS stability analysis. The thesis focuses on control applications for when (a) both plant and controller use A2-C0 TSK models, and (b) the plant uses T1 Takagi-Sugeno (T1 TS) and the controller uses IT2 TS models. In both cases, sufficient stability conditions for the stability of the closed-loop system are derived. Furthermore, novel linear matrix inequality-based algorithms are developed for satisfying the stability conditions. Numerical analyses are included to validate the effectiveness of the new inference methods. Case studies reveal that a well-tuned IT2 TS FLCS using the proposed inference engine can potentially outperform its T1 TSK counterpart, a result of IT2 having greater structural flexibility than T1. Moreover, due to the simple nature of the proposed inference engine, it is easy to implement in real-time control systems. In addition, a novel design methodology is proposed for IT2 TSK FLC for modular and reconfigurable robot (MRR) manipulators with uncertain dynamic parameters. A mathematical framework for the design of IT2 TSK FLCs is developed for tracking purposes that can be effectively used in real-time applications. To verify the effectiveness of the proposed controller, experiments are performed on an MRR with two degrees of freedom which exhibits dynamic coupling behavior. Results show that the developed controller can outperform some well-known linear and nonlinear controllers for different configurations. Therefore, the proposed structure can be adopted for the position control of MRRs with unknown dynamic parameters in trajectory-tracking applications. Finally, a rigorous mathematical analysis of the robustness of FLSs (both T1 and IT2) is presented in the thesis and entails a formulation of the robustness of FLSs as a constraint multi-objective optimization problem. Consequently, a procedure is proposed for the design of robust IT2 FLSs. Several examples are presented to demonstrate the effectiveness of the proposed methodologies. It was concluded that both T1 and IT2 FLSs can be designed to achieve robust behavior in various applications. IT2 FLSs, having a more flexible structure than T1 FLSs, exhibited relatively small approximation errors in the several examples investigated. The rigorous methodologies presented in this thesis lay the mathematical foundations for analyzing the stability and facilitating the design of stabilizing IT2 FLCSs. In addition, the proposed control technique for tracking purposes of MRRs will provide control engineers with tools to control dynamic systems with uncertainty and changing parameters. Finally, the systematic approach developed for the analysis and design of robust T1 and IT2 FLSs is of great practical value in various modeling and control applications

Switching control systems and their design automation via genetic algorithms

The objective of this work is to provide a simple and effective nonlinear controller. Our strategy involves switching the underlying strategies in order to maintain a robust control. If a disturbance moves the system outside the region of stability or the domain of attraction, it will be guided back onto the desired course by the application of a different control strategy. In the context of switching control, the common types of controller present in the literature are based either on fuzzy logic or sliding mode. Both of them are easy to implement and provide efficient control for non-linear systems, their actions being based on the observed input/output behaviour of the system. In the field of fuzzy logic control (FLC) using error feedback variables there are two main problems. The first is the poor transient response (jerking) encountered by the conventional 2-dimensional rule-base fuzzy PI controller. Secondly, conventional 3-D rule-base fuzzy PID control design is both computationally intensive and suffers from prolonged design times caused by a large dimensional rule-base. The size of the rule base will increase exponentially with the increase of the number of fuzzy sets used for each input decision variable. Hence, a reduced rule-base is needed for the 3-term fuzzy controller. In this thesis a direct implementation method is developed that allows the size of the rule-base to be reduced exponentially without losing the features of the PID structure. This direct implementation method, when applied to the reduced rule-base fuzzy PI controller, gives a good transient response with no jerking

Fuzzy Controllers

Trying to meet the requirements in the field, present book treats different fuzzy control architectures both in terms of the theoretical design and in terms of comparative validation studies in various applications, numerically simulated or experimentally developed. Through the subject matter and through the inter and multidisciplinary content, this book is addressed mainly to the researchers, doctoral students and students interested in developing new applications of intelligent control, but also to the people who want to become familiar with the control concepts based on fuzzy techniques. Bibliographic resources used to perform the work includes books and articles of present interest in the field, published in prestigious journals and publishing houses, and websites dedicated to various applications of fuzzy control. Its structure and the presented studies include the book in the category of those who make a direct connection between theoretical developments and practical applications, thereby constituting a real support for the specialists in artificial intelligence, modelling and control fields

Experimental and theoretical control of a smart projectile fin using piezoelectric bimorph actuator

The goal of this work is to develop efficient control algorithms for the control of a smart projectile fin. Smart fins are deployed as soon as the projectile reaches the apogee and are used to steer the projectile towards its target by controlling the rotation angle of the fin. The fin is actuated using the piezoelectric macro-fiber composite (MFC) bimorph actuator which is completely enclosed within the aero-shell. The actuator is composed of two Macro Fiber Composites (MFC\u27s), manufactured by Smart Material Co. The presented smart fin design minimizes the volume and weight of the unit; Two different models of the smart fin are developed. One is mathematical model that uses finite element approach to describe dynamics of the smart fin system. This model includes the aerodynamic moment which is a function of the angle of attack of the projectile. Second model is based on system identification approach. A linear model of the actuator and fin is identified experimentally by exciting the system using a chirp signal. Comparison is done between these two models based on open-loop step response of the smart fin system; In this dissertation, five kinds of control systems based on fuzzy logic, inverse dynamics and adaptive structure theory are developed. The aerodynamic disturbances and parameter uncertainties are considered in these controllers. The simulation results illustrate that asymptotic trajectory tracking of the fin angle is achieved, in spite of uncertainties in the system parameters and presence of aerodynamic disturbance. A prototype model of the projectile fin is developed in the laboratory for real-time control. The designed controllers are validated using the subsonic wind tunnel at University of Nevada, Las Vegas (UNLV) for various wind speeds. Experimental results show that the designed controllers accomplish fin angle control

Type-2 fuzzy sets applied to multivariable self-organizing fuzzy logic controllers for regulating anesthesia

In this paper, novel interval and general type-2 self-organizing fuzzy logic controllers (SOFLCs) are proposed for the automatic control of anesthesia during surgical procedures. The type-2 SOFLC is a hierarchical adaptive fuzzy controller able to generate and modify its rule-base in response to the controller's performance. The type-2 SOFLC uses type-2 fuzzy sets derived from real surgical data capturing patient variability in monitored physiological parameters during anesthetic sedation, which are used to define the footprint of uncertainty (FOU) of the type-2 fuzzy sets. Experimental simulations were carried out to evaluate the performance of the type-2 SOFLCs in their ability to control anesthetic delivery rates for maintaining desired physiological set points for anesthesia (muscle relaxation and blood pressure) under signal and patient noise. Results show that the type-2 SOFLCs can perform well and outperform previous type-1 SOFLC and comparative approaches for anesthesia control producing lower performance errors while using better defined rules in regulating anesthesia set points while handling the control uncertainties. The results are further supported by statistical analysis which also show that zSlices general type-2 SOFLCs are able to outperform interval type-2 SOFLC in terms of their steady state performance

Global Research Performance on the Design and Applications of Type-2 Fuzzy Logic Systems: A Bibliometric Analysis

There has been a significant contribution to scientific literature in the design and applications of Type-2 fuzzy logic systems (T2FLS). The T2FLSs found applications in many aspects of our daily lives, such as engineering, pure science, medicine and social sciences. The online web of science was searched to identify the 100 most frequently cited papers published on the design and application of T2FLS from 1980 to 2016. The articles were analyzed based on authorship, source title, country of origin, institution, document type, web of science category, and year of publication. The correlation between the average citation per year (ACY) and the total citation (TC) was analyzed. It was found that there is a strong relationship between the ACY and TC (r = 0.91643, P<0.01), based on the papers consider in this research.  The “Type -2 fuzzy sets made simple” authored by Mendel and John (2002), published in IEEE Transactions on Fuzzy Systems received the highest TC as well as the ACY. The future trend in this research domain was also analyzed. The present analysis may serve as a guide for selecting qualitative literature especially to the beginners in the field of T2FLS

Microprocessor based signal processing techniques for system identification and adaptive control of DC-DC converters

PhD ThesisMany industrial and consumer devices rely on switch mode power converters (SMPCs) to provide a reliable, well regulated, DC power supply. A poorly performing power supply can potentially compromise the characteristic behaviour, efficiency, and operating range of the device. To ensure accurate regulation of the SMPC, optimal control of the power converter output is required. However, SMPC uncertainties such as component variations and load changes will affect the performance of the controller. To compensate for these time varying problems, there is increasing interest in employing real-time adaptive control techniques in SMPC applications. It is important to note that many adaptive controllers constantly tune and adjust their parameters based upon on-line system identification. In the area of system identification and adaptive control, Recursive Least Square (RLS) method provide promising results in terms of fast convergence rate, small prediction error, accurate parametric estimation, and simple adaptive structure. Despite being popular, RLS methods often have limited application in low cost systems, such as SMPCs, due to the computationally heavy calculations demanding significant hardware resources which, in turn, may require a high specification microprocessor to successfully implement. For this reason, this thesis presents research into lower complexity adaptive signal processing and filtering techniques for on-line system identification and control of SMPCs systems. The thesis presents the novel application of a Dichotomous Coordinate Descent (DCD) algorithm for the system identification of a dc-dc buck converter. Two unique applications of the DCD algorithm are proposed; system identification and self-compensation of a dc-dc SMPC. Firstly, specific attention is given to the parameter estimation of dc-dc buck SMPC. It is computationally efficient, and uses an infinite impulse response (IIR) adaptive filter as a plant model. Importantly, the proposed method is able to identify the parameters quickly and accurately; thus offering an efficient hardware solution which is well suited to real-time applications. Secondly, new alternative adaptive schemes that do not depend entirely on estimating the plant parameters is embedded with DCD algorithm. The proposed technique is based on a simple adaptive filter method and uses a one-tap finite impulse response (FIR) prediction error filter (PEF). Experimental and simulation results clearly show the DCD technique can be optimised to achieve comparable performance to classic RLS algorithms. However, it is computationally superior; thus making it an ideal candidate technique for low cost microprocessor based applications.Iraq Ministry of Higher Educatio