Fuzzy integral tracking control of an activated sludge process

This paper proposes an integral fuzzy control strategy to solve output regulation problem for the micro unmanned helicopter. In order to eliminate the system's bias and guarantee the zero-offset output regulation performance, we firstly take coordinate translation at equilibrium point and introduce an added integral state of output regulation error, and then the resulting augmented system is represented into a Takagi-Sugeno fuzzy model. Next, utilizing parallel distributed compensation (PDC) technique and direct Lyapunov method, an integral state feedback control law for output regulation is established by solving a set of linear matrix inequalities (LMIs). Moreover, the proposed controller design has following merits: i) capability to dealing with nonlinear affine system; ii) giving the exponential stability in the presence of model uncertainty; iii) possessing a piecewise constant output regulation performance. Finally, a micro unmanned helicopter dynamic model is presented to demonstrate the validity of the proposed integral fuzzy controller.

This study proposes an LMI-based integral fuzzy model predictive control (MPC) for output regulation via piece-wise Lyapunov function. In order to eliminate the system's bias and guarantee the zero-offset output regulation performance, firstly we take coordinate translation on equilibrium point and introduce an added integral state of output regulation error for the nonlinear plant, and then convert the resulting augmented system into a Takagi-Sugeno fuzzy model. Under the input constraint, an integrator based state feedback control law is computed by solving a convex optimization problem based on the infinite horizon predictive control scheme. Moreover, the proposed control design has following merits: i) reducing the conservatism by using piecewise Lyapunov function; ii) improving the transient performance by adding a decay rate condition; and iii) ensuring asymptotic stability for output regulation in the presence of time varying parameter. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed integral fuzzy predictive controller.

As the classical PID can not adapt to the dynamic characteristics of the brushless DC motor, integral separation fuzzy control combined with classical PI is put forward to build up brushless DC motor speed current double closed-loop control system. Among them, the speed outer loop uses integral separation fuzzy PI control; the current inner loop uses integral separation PI control. With the core of LPC1769 microprocessor, the hardware system is designed, in which the integral separation double closed-loop fuzzy control software is achieved. Simulation and practical test show that integral separation fuzzy control strategy has fast response, small overshoot, and strong ability of anti-disturbance, which is more suitable for dynamic control of brushless DC motor.

The primary aim of a vehicle's suspension system is to isolate the vehicle's main body from road irregularities, thus improving passenger comfort and ensuring optimal handling stability. This research discusses a stabilizing fuzzy control design for active vehicle suspension systems. The nonlinear model of the active suspension is then represented using a Takagi-Sugeno (TS) fuzzy model. The control approach uses a TS fuzzy controller utilizing an observer to estimate the state while reducing road disturbances. The closed-loop stability requirements of the vehicle utilizing the fuzzy controller and observer are expressed as a Linear Matrix Inequalities (LMI) problem, which can be effectively resolved through convex optimization methods. In this paper, we study the stability of the nonlinear automotive active suspension system with two degrees of freedom represented by a TS fuzzy model, where we will present the stabilization conditions by state feedback via the PDC (Parallel Distributed Compensation) control law and in the last section we introduced the TS fuzzy observer for the case of non-measurable premise variables.

Boost converter is a type of DC/DC converter that can produce a higher output voltage (step-up) than the input voltage. In designing this converter, a control method is needed so that the converter can produce a stable output, especially when there is uncertainty in the input voltage. This study aims to design a DC/DC boost converter using a fuzzy integral controller (FIC) to regulate output voltage under input uncertainty. The controller is designed with two schemes, namely fuzzy logic control (FLC) and integral control. FLC is designed with input error and error change values, while the output is a duty cycle. The integral control acts to eliminate error steady state when the uncertainty of input voltage occurs. This controller is then implemented in a boost converter model based on the state-space average model. The simulation results show that the FIC controller can produce a more robust response when compared to the PI and FLC controllers in several scenarios testing.

Takagi-Sugeno (T-S) fuzzy model is a system described by a set of fuzzy if-then rules which give local linear representations of the underlying nonlinear system. Usually, a fuzzy control law is constructed by a set of controllers for each local linear representation to carry out the control of a T-S fuzzy system. While, simultaneous control addresses the stability and performance of multiple plants under a single feedback controller. In this paper, simultaneous linear control for nonlinear uncertain systems described by general T-S fuzzy model is considered. A procedure for simultaneous control of T-S fuzzy systems with parametric uncertainties is presented, by which robust reliability method is adopted to deal with uncertainties. Simultaneously linear controller design for an uncertain T-S fuzzy system is carried out by solving a problem of robust reliability based optimization, in which, both the robustness with respect to uncertainties and the control cost can be taken into account simultaneously. It is demonstrated by numerical simulation of the chaotic Lorenz system control that the presented method is effective and feasible.

Based on Takagi-Sugeno fuzzy model, employing parallel distributed compensation, the multivariable integral control and state observer in the linear system theory are applied to nonlinear systems for the problem of output tracking and rejecting disturbance with reference and/or disturbance signals in the form of step, and the fuzzy integral controller and fuzzy state observer are synthesized. The stability condition of continuous closed-loop fuzzy control system and a similar separation principle to the counterpart on observer design in the linear system theory are obtained.

In this paper, the Takagi-Sugeno (TS) fuzzy modelling and the fuzzy regulation theory are considered in order to design a fuzzy controller capable of taking the output of a fuzzy plant to the reference signal generated by an external system. It is well-known that TS fuzzy modelling allows the stabilizer to be obtained by means of numerical techniques. As a result, stability region defined by the fuzzy stabilizer is larger than the one obtained when a simple linear stabilizer is considered. On the other hand, a fuzzy regulator constructed from linear controllers does not solve the exact regulation problem in general [6], [12], [13], [15]. Therefore, a fully nonlinear regulator, defined on the overall TS fuzzy model, is considered in this work. The results are applied on a simple fuzzy model in order to illustrate the improvement achieved with the proposed approach.

The present work is concerned to solve the problem of nonlinear robotic control systems on the basis of Takagi- Sugeno (T-S) fuzzy models. In addition, controllability and observability studies for T-S fuzzy model systems are considered for Single-Input Single-Output (SISO) and Multiple-Input Multiple-Output (MIMO) systems. In particular, the robust pole assignment approach is extended to the fuzzy field. This approach is used to design fuzzy stabilizers and fuzzy observers directly on the overall T-S fuzzy system. The latter one is the representation of the nonlinear robotic system, which is linearized around certain operation regions. The suggested method is considered for either SISO or MIMO systems. Furthermore, the method allows inducing an arbitrary behavior into the fuzzy plant in a relatively easy way. Two examples are used to verify the effectiveness of the proposed approach. The results are compared with the well-known Parallel Distributed Compensation (PDC) method, which is designed on the basis of Linear Matrix Inequalities (LMIs).

This paper presents new stability conditions and LMI (linear matrix inequality) based designs for both continuous and discrete fuzzy control systems. First, Takagi and Sugeno's fuzzy models and some stability results are recalled. To design fuzzy control systems, nonlinear systems are represented by Takagi-Sugeno fuzzy models. The concept of parallel distributed compensation is employed to design fuzzy controllers from the Takagi-Sugeno fuzzy models. New stability conditions are obtained by relaxing the stability conditions derived in previous papers. The stability analysis of the feedback system is reduced to a problem of finding a common Lyapunov function for a set of linear matrix inequalities. Convex optimization techniques involving LMIs are utilized to find a common Lyapunov function. A procedure to design the fuzzy controller is constructed using the parallel distributed compensation and the relaxed stability conditions. Some stability issues are remarked. A simple example demonstrates the effects of the derived stability conditions.

This paper proposes new algorithms based on the fuzzy c-regressing model algorithm for Takagi-Sugeno (T-S) fuzzy modeling of the complex nonlinear systems. A fuzzy c-regression state model (FCRSM) algorithm is a T-S fuzzy model in which the functional antecedent and the state-space-model-type consequent are considered with the available input-output data. The antecedent and consequent forms of the proposed FCRSM consists mainly of two advantages: one is that the FCRSM has low computation load due to only one input variable is considered in the antecedent part; another is that the unknown system can be modeled to not only the polynomial form but also the state-space form. Moreover, the FCRSM can be extended to FCRSM-ND and FCRSM-Free algorithms. An algorithm FCRSM-ND is presented to find the T-S fuzzy state-space model of the nonlinear system when the input-output data cannot be precollected and an assumed effective controller is available. In the practical applications, the mathematical model of controller may be hard to be obtained. In this case, an online tuning algorithm, FCRSM-FREE, is designed such that the parameters of a T-S fuzzy controller and the T-S fuzzy state model of an unknown system can be online tuned simultaneously. Four numerical simulations are given to demonstrate the effectiveness of the proposed approach.

This paper proposes the robust fuzzy fault tolerant control (FTC) problem for the fuzzy Takagi-Sugeno (TS) systems with sensor faults and actuator faults in the presence of parameter uncertainties. The TS fuzzy model is first employed to approximate a nonlinear uncertain system, and then the fuzzy sensor fault, fuzzy actuator fault model and the fuzzy state observer are developed. Sufficient stabilization conditions of the fuzzy FTC systems are given, which are formulated in terms of linear matrix inequalities (LMIs). The LMIs can be efficiently solved using the convex optimization techniques. Finally, fuzzy observer based on fuzzy fault tolerant controller is developed. It is proved that the fuzzy control system is reliable in the sense of that the closed-loop system is asymptotic stability and the all sensor and actuator components can operate well in the presence of some component failures. The control scheme is tested for real profiles of wind speed pattern and provides satisfactory results

Takagi-Sugeno (TS) fuzzy models have been the popular choice for multi-model based nonlinear system identification for controller design. However, the interpretation of the model from a dynamical systems point of view is still unclear. In this paper, we investigate the interpretation of the TS fuzzy models in terms of local dynamics of nonlinear systems in state space. The investigation is based on the comparison between the constant-affine recursive i/o equation and constant-affine state space representations. We show that the true local dynamics is not identifiable by TS fuzzy models by analysis and example. For the identification of constant-affine state space models, a subspace identification algorithm is proposed to identify the true local dynamics with zero initial conditions.

Conducting polymer actuators are used in a diverse range of applications including biomimetic robots and biomedical devices. In comparison to robotic joints, they do not have friction or backlash, but on the other hand, they have complicated electro-chemo-mechanical dynamics which makes modelling and control of the actuator really difficult. In addition they also have the disadvantages of creep, hysteresis, and highly uncertain and time-varying dynamics. In this paper a Takagi-Sugeno (T-S) fuzzy model is used to represent the uncertain dynamics of the actuator, and the resulted fuzzy model is validated using experimental data. A system that consists of fuzzy state feedback to a PI controller is designed on the basis of the obtained T-S fuzzy model using the parallel distributed compensation scheme. The sufficient conditions for the existence of such a controller are derived in terms of linear matrix inequalities. The obtained results show that the designed controller can achieve a good control performance despite the existence of uncertain actuator dynamics.

The dynamic model of a Human Operator (HO) inherits not only nonlinear dynamics but also a large amount of uncertainty due to the reaction time and expertize level of humans. In this study, the Interval valued Takagi-Sugeno (TS) fuzzy modelling approach is employed to efficiently capture the dynamics of HOs. For this purpose, we have conducted experimental studies in which a simple target tracking computer game is used as a platform. We have collected input-output data from individual players that have different talent levels. Then, by using symbolic data analysis, we have obtained interval valued TS fuzzy models of the HOs and evaluated their performances. It is concluded that, via the interval-valued TS fuzzy modelling approach, HOs can be modelled successfully as the predicted upper and lower bounds can successfully envelope the uncertainties and nonlinearities of HOs.