Parallel Distributed Compensation Controller Research Articles

Fuzzy Modeling Framework Using Sector Non-Linearity Techniques for Fixed-Wing Aircrafts

This paper presents a mathematical modeling approach utilizing a fuzzy modeling framework for fixed-wing aircraft systems with the goal of creating a highly desirable mathematical representation for model-based control design applications. The starting point is a mathematical model comprising fifteen non-linear ordinary differential equations representing the dynamic and kinematic behavior applicable to a wide range of fixed-wing aircraft systems. Here, the proposed mathematical modeling framework is applied to the AIRBUS A310 model developed by ONERA. The proposed fuzzy modeling framework takes advantage of sector non-linearity red techniques to recast all the non-linear terms from the original model to a set of combined fuzzy rules. The result of this fuzzification is a more suitable mathematical description from the control system design point of view. Therefore, the combination of this fuzzy model and the wide range of control techniques available in the literature for such kind of models, like parallel and non-parallel distributed compensation control laws using linear matrix inequality optimization, enables the development of control algorithms that guarantee stability conditions for a wide range of operations points, avoiding the classical gain scheduling schemes, where the stability issues can be extremely challenging.

On the boundedness of solutions of some fuzzy dynamical control systems

<abstract> <p>The asymptotic behavior of solutions of fuzzy control systems is a component of the study of fuzzy control theory. The study of stability for T-S (Takagi-Sugeno) fuzzy systems, which process qualitative data through linguistic expressions, is the subject of this paper. Asymptotic stability is conservative in many real-world applications due to measurement noise and other disruptions. The ultimate limit, which indicates that the mistakes stay in a specific area close to the origin after a long enough amount of time, is a crucial characteristic that is frequently defined for such systems. We are interested with the problem of the state feedback controller for T-S fuzzy models with uncertainties where the global exponential ultimate boundedness of solutions is studied for certain fuzzy control systems. We use common quadratic Lyapunov function and parallel distributed compensation controller techniques to study the asymptotic behavior of the solutions of fuzzy control system in presence of perturbations. An example demonstrating the validity of the main result is discussed.</p> </abstract>

Resilient control for T-S fuzzy systems with multiple transmission channels under asynchronous denial-of-Service attacks

This paper investigates the resilient control problem of the T-S fuzzy system with multiple transmission channels under asynchronous denial-of-service (DoS) attacks. A part of the transmission channels are chosen as ones corresponding to the premise variables of the T-S fuzzy system. The considered asynchronous DoS attacks occur on the sensor-to-controller transmission channels, which may DoS attacks cause the system state to be unstable. The stability of the T-S fuzzy system under random DoS attack mode is considered, including the influence of the premise variables attacked. A class of parallel distributed compensation controllers are proposed, which adopts the strategy of discarding the attacked channels information. By using a piecewise Lyapunov function method and a class of linear matrix inequalities, the system stability sufficient conditions related to the duration and frequency of DoS attacks on the transmission channels are presented. Compared with the existing method, the more general relationship between premise variables and transmission channels are considered in this paper. Finally, a numerical example is used to illustrate the effectiveness of the proposed scheme.

Convex control with H∞ performance of a hexarotor-UAV

This paper is dedicated to the modeling and control for a hexarotor-type unmanned aerial vehicle based in a convex rewrite that it is represents exactly the nonlinear model of the hexarotor. Then, the controller design is considered a parallel-distributed compensation control law to stabilitze of the vehicle and a H∞ performance criterion to aguratee robustness againts distrubances. The stability condition and robust performance are formulated using the function quadratic of Lyapunov where the sufficient conditions are given by a set of linear matrix inequalities. Finally, it is illustrated the numerical simulations of the proposed method through of the hexarotor.

Discrete-Time System Conditional Optimization Based on Takagi–Sugeno Fuzzy Model Using the Full Transfer Function

The study proposes a novel method for synthesis of a discrete-time parallel distributed compensation (PDC) controller for the nonlinear discrete-time Takagi–Sugeno (TS) fuzzy plant model. For each of the fuzzy plant model linear subsystems, a local linear first order proportional-sum (PS) controller is designed. The algebraic technique is used in two-dimensional parameter space, utilizing the characteristic polynomial of the row nondegenerate full transfer function matrix. Each system’s relative stability is accomplished in relation to the selected damping coefficient. The supplementary criterion is the minimal value of the performance index in the form of the sum of squared errors (SSE). However, unlike the traditional technique, output error is impacted by all simultaneous actions on the system: nonzero inputs and nonzero initial conditions. The full transfer function matrix of the system allows for the treatment of simultaneous actions of the input vector and unknown unpredictable initial conditions. In order to show the improvement caused by the application of a new optimization method that considers nonzero initial conditions, a comparison of PDC controllers designed under zero and nonzero initial conditions is given, where the system in both cases starts from the same nonzero initial conditions, which is often the case in practice. The simulation and experimental results on a DC servo motor are shown to demonstrate the suggested method efficiency.

Fuzzy Chaos Control of Fractional Order D-PMSG for Wind Turbine with Uncertain Parameters by State Feedback Design

To research the chaotic motion problem of the direct-drive permanent magnet synchronous generator (D-PMSG) for a wind turbine with uncertain parameters and fractional order characteristics, a control strategy established upon fuzzy state feedback is proposed. Firstly, according to the working mechanism of D-PMSG, the Lorenz nonlinear mathematical model is established by affine transformation and time transformation. Secondly, fractional order nonlinear systems (FONSs) are transformed into linear sub-model by Takagi–Sugeno (T-S) fuzzy model. Then, the fuzzy state feedback controller is designed through Parallel Distributed Compensation (PDC) control principle to suppress the chaotic motion. By applying the fractional Lyapunov stability theory (FLST), the sufficient conditions for Mittag–Leffler stability are formulated in the format of linear matrix inequalities (LMIs). Finally, the control performance and effectiveness of the proposed controller are demonstrated through numerical simulations, and the chaotic motions in D-PMSG can be eliminated quickly.

Modeling and Control of Delayed, Nonlinear, Uncertain, and Disturbed Air Heater Employing Fuzzy PDC-L 1 Adaptive Scheme

In this article, we proposed a scheme of modeling an air heater system with a long airflow duct, predominantly available in many industrial plants to maintain the desired temperature by simultaneously befitting the transport delay, nonlinearities, model uncertainties, and nonuniform disturbances. At first, the nonlinear delayed air heater system is formulated by combining linear fuzzy system models utilizing fuzzy parallel distributed compensation (PDC) logic. Then, a newly developed L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> adaptive control strategy is modified by replacing its conventional state feedback controller with fuzzy PDC control logic to maintain the desired temperature by nullifying nonlinearities, transport delays, uncertainties, and disturbances. The novelty of the proposed work lies in the fact that the proposed fuzzy PDC law augmented L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> adaptive scheme explicitly deals with the delays and nonlinearities by means of fuzzy PDC logic as well as eliminates time-varying uncertainties and disturbances utilizing L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> adaptive control strategy. The results obtained from real-life laboratory-scale experiments suitably demonstrate the usefulness of the proposed approach.

Design of a robust active fuzzy parallel distributed compensation anti-vibration controller for a hand-glove system.

Undesirable vibrations resulting from the use of vibrating hand-held tools decrease the tool performance and user productivity. In addition, prolonged exposure to the vibration can cause ergonomic injuries known as the hand-arm vibration syndrome (HVAS). Therefore, it is very important to design a vibration suppression mechanism that can isolate or suppress the vibration transmission to the users’ hands to protect them from HAVS. While viscoelastic materials in anti-vibration gloves are used as the passive control approach, an active vibration control has shown to be more effective but requires the use of sensors, actuators and controllers. In this paper, the design of a controller for an anti-vibration glove is presented. The aim is to keep the level of vibrations transferred from the tool to the hands within a healthy zone. The paper also describes the formulation of the hand-glove system’s mathematical model and the design of a fuzzy parallel distributed compensation (PDC) controller that can cater for different hand masses. The performances of the proposed controller are evaluated through simulations and the results are benchmarked with two other active vibration control techniques-proportional integral derivative (PID) controller and active force controller (AFC). The simulation results show a superior performance of the proposed controller over the benchmark controllers. The designed PDC controller is able to suppress the vibration transferred to the user’s hand 93% and 85% better than the PID controller and the AFC, respectively.

Parallel and Nonparallel Distributed Compensation Controller Design for T-S Fuzzy Discrete Singular Systems With Distinct Difference Item Matrices

The issues of admissibility and controller design for a class of extended T-S fuzzy discrete singular systems (FDSSs) with distinct difference item matrices are discussed in this article. A new augmented system which is the equivalent of the original system is introduced to convert these distinct difference item matrices into the easy treatment form. On this basis, using the fuzzy Lyapunov function (FLF), relaxed sufficient condition is given to ensure the admissibility of unforced systems. This condition is described via strict linear matrix inequalities (LMIs), which facilitates to analyze the admissibility. Meanwhile, the design methods of parallel and nonparallel distributed compensation (PDC and Non-PDC) controllers are also proposed. Finally, the advantages of the developed admissibility and controller design approach are illustrated by three examples.

Design of Fuzzy TS-PDC Controller for Electrical Power System via Rules Reduction Approach

In this paper, a new Takagi–Sugeno Fuzzy Logic controller (TS-FLC) is presented and applied for modeling and controlling the nonlinear power systems even in the presence of disturbances. Firstly, a nonlinear mathematical model for the electrical power system is presented with consideration of PSS and AVR controller. Then, a Takagi–Sugeno Fuzzy Logic controller is employed to control power system stability. Nevertheless, the study of the stability of Takagi–Sugeno fuzzy models will be difficult in the case where the number of nonlinearities is important. To cope with this problem, this study proposed a methodology to reduce the number of rules and to guarantee the global stability of the power system. The new model included only two rules. All the other nonlinearities were considered as uncertainties. In addition, a Parallel Distributed Compensation controller is designed using the Linear Matrix Inequalities constraints in order to guarantee system stability. Finally, this approach is applied on a Single Machine Infinite Bus affected by fault perturbation. To show the novelty of Takagi Sugeno’s method, we compared our approach to the Taylor linearization method. The numerical simulations prove the feasibility and performance of the proposed method.

Robust ℓ₁-Controller Design for Discrete-Time Positive T–S Fuzzy Systems Using Dual Approach

In this article, a new approach is proposed for stability analysis and controller design of nonlinear discrete-time positive systems by means of the Takagi&#x2013;Sugeno fuzzy model. The closed-loop stability and the positivity constraint are guaranteed by synthesizing a linear co-positive Lyapunov function and by applying the parallel distributed compensation controller. In contrast to the state-of-the-art approaches for ensuring the <inline-formula> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula>-stability of the positive system which are based on bilinear matrix inequalities, the proposed optimal robust control design under <inline-formula> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula>-induced performance is derived based on linear programming framework. It has been shown that the computational complexity of the proposed optimization problem can be effectively reduced. Finally, a numerical example and the Leslie population model are adopted to show the capabilities of the proposed method.

Novel robust observer‐controller synthesis method for Takagi‐Sugeno systems

AbstractFor the output feedback control problem of a T‐S fuzzy system, an observer‐controller synthesis method is proposed. First, with parallel distributed compensation fuzzy observer and controller, an augmented error system is obtained. Based on Lyapunov function approaches, system stability and robust conditions are achieved. Then, by dividing the non‐convex conditions into observer‐dominant and controller dominant parts, the conditions are converted into convex form to facilitate the numerical solving process. Also, input saturation and system measurement disturbance are considered in the synthesis procedure. Finally, a numerical and a vessel control example are adopted to make comparisons with existing methods, with the results clearly showing the conservatism reduction effects and good control performance of the proposed method.

Nonlinear modelling and optimal control via Takagi-Sugeno fuzzy techniques: A quadrotor stabilization

AbstractUsing the principles of Takagi-Sugeno fuzzy modelling allows the integration of flexible fuzzy approaches and rigorous mathematical tools of linear system theory into one common framework. The rule-based T-S fuzzy model splits a nonlinear system into several linear subsystems. Parallel Distributed Compensation (PDC) controller synthesis uses these T-S fuzzy model rules. The resulting fuzzy controller is nonlinear, based on fuzzy aggregation of state controllers of individual linear subsystems. The system is optimized by the linear quadratic control (LQC) method, its stability is analysed using the Lyapunov method. Stability conditions are guaranteed by a system of linear matrix inequalities (LMIs) formulated and solved for the closed loop system with the proposed PDC controller. The additional GA optimization procedure is introduced, and a new type of its fitness function is proposed to improve the closed-loop system performance.

A dual approach for positive T–S fuzzy controller design and its application to cancer treatment under immunotherapy and chemotherapy

This study proposes an effective positive control design strategy for cancer treatment by resorting to the combination of immunotherapy and chemotherapy. The treatment objective is to transfer the initial number of tumor cells and immune–competent cells from the malignant region into the region of benign growth where the immune system can inhibit tumor growth. In order to achieve this goal, a new modeling strategy is used that is based on Takagi–Sugeno. A Takagi-Sugeno fuzzy model is derived based on the Stepanova nonlinear model that enables a systematic design of the controller. Then, a positive Parallel Distributed Compensation controller is proposed based on a linear co-positive Lyapunov Function so that the tumor volume and administration of the chemotherapeutic and immunotherapeutic drugs is reduced, while the density of the immune-competent cells is reached to an acceptable level. Thanks to the proposed strategy, the entire control design is formulated as a Linear Programming problem. Finally, the simulation results show the effectiveness of the proposed control approach for the cancer treatment.

Takagi‐Sugeno tracking control of a fermentation process with respect to asymmetric constraints

SummaryThis article deals with the tracking problem for nonlinear biological process with asymmetric constraints on the controller. Using the fuzzy logic Takagi‐Sugeno (TS), the nonlinear process is modeled by a fuzzy model and a parallel distributed compensation (PDC) controller with respect asymmetric constraints is designed. The main contribution of this work is to extend the available results, in the context of a TS formulation, for symmetrical constraints to asymmetrical ones. Hence, sufficient conditions are obtained for the first time, in terms of linear matrix inequalities (LMIs), for the existence of an asymmetrical constrained PDC controller. Moreover, fuzzy observer based controller with unmeasured premise variables is designed. The performance and effectiveness of the method are illustrated in simulation by considering a fermentation process.

Parallel distributed compensation controller design for Markovian jump system with time-varying delays using Bessel-Legendre inequality method and improved positive definite rule

In this paper, based on time-varying delay Markovian jump system (MJS), Bessel-Legendre inequality method and improved positive definite condition of Lyapunov function are used, and parallel distributed compensation (PDC) state feedback controller is also introduced. The conservatism of the system is reduced by using this inequality method and positive definite conditions, and further decreases with the increase of the Legendre parameter N. The PDC controller considers two control parameters simultaneously, which can represent the actual system more truthfully. Finally, Example 1 proves the effectiveness of the improved method in this paper. Example 2 considers time-varying probability transition perturbations. Example 3 obtains the parameters of PDC controller with different parameters N. Example 4 illustrates the practical significance of methods in this paper by introducing a time-delay inverted pendulum system with Markovian parameters.

Tracking Control for Wheeled Mobile Robot Based on Delayed Sensor Measurements

This paper proposes a novel Takagi-Sugeno fuzzy predictor observer to tackle the problem of the constant and known delay in the measurements. The proposed observer is developed for a trajectory-tracking problem of a wheeled mobile robot where a parallel-distributed compensation control is used to control the robot. The L2-stability of the proposed observer is also proven in the paper. Both, the control and the observer gains are obtained by solving the proposed system of linear matrix inequalities. To illustrate the efficiency of the proposed approach, an experimental comparison with another predictor observer was done.

Linear Consequence-Based Fuzzy Parallel Distributed Compensation Type $L_{1}$ Adaptive Controller for Two Link Robot Manipulator

This paper presents a novel scheme of controller design for a cross-coupled multi-input multi-output (MIMO) two link robot manipulator (TLRM) system having time varying uncertainties, disturbances, and nonlinearity by employing fuzzy parallel distributed compensation (PDC) type ${L}_{1}$ adaptive controller. The combination of linear consequence-based fuzzy subsystems are utilized to represent the nonlinear TLRM system. The components of $ {L}_{1}$ adaptive control framework are also realized by combining linear consequence-based fuzzy systems to incorporate the zone-wise controlling of the TLRM system. A fuzzy PDC control has also been augmented to achieve robust stable transient and steady state performances. The stability of each fuzzy systems as well as the overall proposed control scheme is guaranteed by utilizing fuzzy Lyapunov theory-based analysis. The experimental results demonstrate the usefulness of the proposed control scheme.

Augmented TP model transformation‐based parallel distributed compensation control design

AbstractThe usual sampled hyper grid points of uniform sampling method are distributed equally in the TP model transformation, thus, the sampling results often omit the local extrema when the sampling step is not fine‐tuned. Then the resultant tensor which is used for controller design can not fully cover the state space, although the gain which is the feasible solution of the linear matrix inequalities. In this paper, we proposed a non‐uniform sampling method for tensor product model transformation, local extrema are considered in the sampling step, while the sampling step can vary dynamically for different function entries. In this paper, TP model transformation‐based parallel distributed compensation (PDC) controller is extended in three folds: (i) The existing TP model transformation‐based PDC controller with uniform sampling method is extended to TP model transformation‐based PDC tracking controller with the uniform sampling method and an extended signal. (ii) A new TP model transformation‐based PDC tracking controller is proposed based on a new sampling method, that is, the Hammersley sampling method. (iii) TP model transformation‐based PDC tracking controller is also proposed based on the non‐uniform sampling method. The proposed adaptive TP model transformation‐based PDC tracking controller is able to enhance the performance of the TP model transformation‐based PDC controller, and the adaptive TP model transformation‐based PDC controller obtains the best results due to the nearly exact sampling of the system.

Fuzzy model-based controller for blood glucose control in type 1 diabetes: An LMI approach

This paper deals with designing a robust controller with H∞ performance index criteria for regulating the glucose-insulin level in type 1 diabetes. The proposed approach employs a Takagi-Sugeno (TS) fuzzy modeling and fuzzy model-based parallel distributed compensation (PDC) and non-parallel distributed compensation (non-PDC) schemes to design a stabilizing control law for the injecting insulin in silico. Deploying a non-quadratic Lyapunov function (NQLF) candidate, the stabilization conditions are derived in terms of linear matrix inequalities (LMIs) and solved by convex optimization techniques. Furthermore, based on the convex property of the membership functions, a new null term is defined which increases the degree of freedom of the proposed LMI constraints and reduces the stabilization conditions conservativeness. The diabetes models that are considered are nonlinear minimal Bergman and Tolic models that describe the glucose-insulin process in diabetes type 1. Based on the so-called sector nonlinearity approach (SNA), the equivalent TS fuzzy models of the Bergman and Tolic models are obtained. Then, the stabilization LMI conditions are solved and the PDC and non-PDC controllers are designed. Simulation results are obtained with a single patient testing parameters uncertainties and verify the advantages of the proposed robust control technique in dealing with the effects of external meal disturbance and maintaining the blood glucose concentration in the desired region to avoid the hypoglycemia and hyperglycemia disorders.