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

Using 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.Web of Science71110

A LOW-COST APPROACH TO DATA-DRIVEN FUZZY CONTROL OF SERVO SYSTEMS

Servo systems become more and more important in control systems applications in various fields as both separate control systems and actuators. Ensuring very good control system performance using few information on the servo system model (viewed as a controlled process) is a challenging task. Starting with authors’ results on data-driven model-free control, fuzzy control and the indirect model-free tuning of fuzzy controllers, this paper suggests a low-cost approach to the data-driven fuzzy control of servo systems. The data-driven fuzzy control approach consists of six steps: (i) open-loop data-driven system identification to produce the process model from input-output data expressed as the system step response, (ii) Proportional-Integral (PI) controller tuning using the Extended Symmetrical Optimum (ESO) method, (iii) PI controller parameters mapping onto parameters of Takagi-Sugeno PI-fuzzy controller in terms of the modal equivalence principle, (iv) closed-loop data-driven system identification, (v) PI controller tuning using the ESO method, (vi) PI controller parameters mapping onto parameters of Takagi-Sugeno PI-fuzzy controller. The steps (iv), (v) and (vi) are optional. The approach is applied to the position control of a nonlinear servo system. The experimental results obtained on laboratory equipment validate the approach

Analysis, filtering, and control for Takagi-Sugeno fuzzy models in networked systems

Copyright © 2015 Sunjie Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.The fuzzy logic theory has been proven to be effective in dealing with various nonlinear systems and has a great success in industry applications. Among different kinds of models for fuzzy systems, the so-called Takagi-Sugeno (T-S) fuzzy model has been quite popular due to its convenient and simple dynamic structure as well as its capability of approximating any smooth nonlinear function to any specified accuracy within any compact set. In terms of such a model, the performance analysis and the design of controllers and filters play important roles in the research of fuzzy systems. In this paper, we aim to survey some recent advances on the T-S fuzzy control and filtering problems with various network-induced phenomena. The network-induced phenomena under consideration mainly include communication delays, packet dropouts, signal quantization, and randomly occurring uncertainties (ROUs). With such network-induced phenomena, the developments on T-S fuzzy control and filtering issues are reviewed in detail. In addition, some latest results on this topic are highlighted. In the end, conclusions are drawn and some possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grants 61134009, 61329301, 11301118 and 61174136, the Natural Science Foundation of Jiangsu Province of China under Grant BK20130017, the Fundamental Research Funds for the Central Universities of China under Grant CUSF-DH-D-2013061, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Intelligent control of a class of nonlinear systems

The objective of this study is to improve and propose new fuzzy control algorithms for a class of nonlinear systems. In order to achieve the objectives, novel stability theorems as well as modeling techniques are also investigated. Fuzzy controllers in this work are designed based on the fuzzy basis function neural networks and the type-2 Takagi-Sugeno fuzzy models. For a class of single-input single-output nonlinear systems, a new stability condition is derived to facilitate the design process of proportional-integral Mamdani fuzzy controllers. The stability conditions require a new technique to calculate the dynamic gains of nonlinear systems represented by fuzzy basis function network models. The dynamic gain of a fuzzy basis function network can be approximated by finding the maximum of norm values of the locally linearized systems or by solving a non-smooth optimal control problem. Based on the new stability theorem, a multilevel fuzzy controller with self-tuning algorithm is proposed and simulated in a tower crane control system. For a class of multi-input multi-output nonlinear systems with measurable state variables, a new method for modeling unstructured uncertainties and robust control of unknown nonlinear dynamic systems is proposed by using a novel robust Takagi-Sugeno fuzzy controller. First, a new training algorithm for an interval type-2 fuzzy basis function network is presented. Next, a novel technique is derived to convert the interval type-2 fuzzy basis function network to an interval type-2 Takagi-Sugeno fuzzy model. Based on the interval type-2 Takagi-Sugeno and type-2 fuzzy basis function network models, a robust controller is presented with an adjustable convergence rate. Simulation results on an electrohydraulic actuator show that the robust Takagi-Sugeno fuzzy controller can reduce steady-state error under different conditions while maintaining better responses than the other robust sliding mode controllers can. Next, the study presents an implementation of type-2 fuzzy basis function networks and robust Takagi-Sugeno fuzzy controllers to data-driven modeling and robust control of a laser keyhole welding process. In this work, the variation of the keyhole diameter during the welding process is approximated by a type-2 fuzzy-basis-function network, while the keyhole penetration depth is modelled by a type-1 fuzzy basis function network. During the laser welding process, a CMOS camera integrated with the welding system was used to provide a feedback signal of the keyhole diameter. An observer was implemented to estimate the penetration depth in real time based on the adaptive divided difference filter and the feedback signal from the camera. A robust Takagi-Sugeno fuzzy controller was designed based on the fuzzy basis function networks representing the welding process with uncertainties to adjust the laser power to ensure that the penetration depth of the keyhole is maintained at a desired value. Experimental results demonstrated that the fuzzy models provided an accurate estimation of both the welding geometry and its variations due to uncertainties, and the robust Takagi-Sugeno fuzzy controller successfully reduced the penetration depth variation and improved the quality of the welding process

Optimal Control of Unknown Nonlinear System From Inputoutput Data

Optimal control designers usually require a plant model to design a controller. The problem is the controller\u27s performance heavily depends on the accuracy of the plant model. However, in many situations, it is very time-consuming to implement the system identification procedure and an accurate structure of a plant model is very difficult to obtain. On the other hand, neuro-fuzzy models with product inference engine, singleton fuzzifier, center average defuzzifier, and Gaussian membership functions can be easily trained by many well-established learning algorithms based on given input-output data pairs. Therefore, this kind of model is used in the current optimal controller design. Two approaches of designing optimal controllers of unknown nonlinear systems based on neuro-fuzzy models are presented in the thesis. The first approach first utilizes neuro-fuzzy models to approximate the unknown nonlinear systems, and then the feasible-direction algorithm is used to achieve the numerical solution of the Euler-Lagrange equations of the formulated optimal control problem. This algorithm uses the steepest descent to find the search direction and then apply a one-dimensional search routine to find the best step length. Finally several nonlinear optimal control problems are simulated and the results show that the performance of the proposed approach is quite similar to that of optimal control to the system represented by an explicit mathematical model. However, due to the limitation of the feasible-direction algorithm, this method cannot be applied to highly nonlinear and dimensional plants. Therefore, another approach that can overcome these drawbacks is proposed. This method utilizes Takagi-Sugeno (TS) fuzzy models to design the optimal controller. TS fuzzy models are first derived from the direct linearization of the neuro-fuzzy models, which is close to the local linearization of the nonlinear dynamic systems. The operating points are chosen so that the TS fuzzy model is a good approximation of the neuro-fuzzy model. Based on the TS fuzzy model, the optimal control is implemented for a nonlinear two-link flexible robot and a rigid asymmetric spacecraft, thus providing the possibility of implementing the well-established optimal control method on unknown nonlinear dynamic systems

BIBO stabilisation of continuous time takagi sugeno systems under persistent perturbations and input saturation

[EN] This paper presents a novel approach to the design of fuzzy state feedback controllers for continuous-time non-linear systems with input saturation under persistent perturbations. It is assumed that all the states of the Takagi¿Sugeno (TS) fuzzy model representing a non-linear system are measurable. Such controllers achieve bounded input bounded output (BIBO) stabilisation in closed loop based on the computation of inescapable ellipsoids. These ellipsoids are computed with linear matrix inequalities (LMIs) that guarantee stabilisation with input saturation and persistent perturbations. In particular, two kinds of inescapable ellipsoids are computed when solving a multiobjective optimization problem: the maximum volume inescapable ellipsoids contained inside the validity domain of the TS fuzzy model and the smallest inescapable ellipsoids which guarantee a minimum *-norm (upper bound of the 1-norm) of the perturbed system. For every initial point contained in the maximum volume ellipsoid, the closed loop will enter the minimum *-norm ellipsoid after a finite time, and it will remain inside afterwards. Consequently, the designed controllers have a large domain of validity and ensure a small value for the 1-norm of closed loop.The authors wish to thank the Editor-in-Chief and the anonymous reviewers for their valuable comments and suggestions. This work has been funded by Ministerio de Economia y Competitividad (Spain) through the research project DPI2015-71443-R and by Generalitat Valenciana (Valencia, Spain) through the research project GV/2017/029.Salcedo-Romero-De-Ávila, J.; Martínez Iranzo, MA.; Garcia-Nieto, S.; Hilario Caballero, A. (2018). BIBO stabilisation of continuous time takagi sugeno systems under persistent perturbations and input saturation. International Journal of Applied Mathematics and Computer Science (Online). 28(3):457-472. https://doi.org/10.2478/amcs-2018-0035S45747228

Parallel distribution compensation PID based on Takagi-Sugeno fuzzy model applied on egyptian load frequency control

This paper presents a new technique for a Takagi-Sugeno (TS) fuzzy parallels distribution compensation-PID'S (TSF-PDC-PID'S) to improve the performance of Egyptian load frequency control (ELFC). In this technique, the inputs to a TS Fuzzy model are the parameters of the change of operating points. The TS Fuzzy model can definite the suitable PID control for a certain operating point. The parameters of PID'S controllers are obtained by ant colony optimization (ACO) technique in each operating point based on an effective cost function. The system controlled by the proposed TSF-PDC-PID’S is investigated under different types of disturbances, uncertainty and parameters variations. The simulation results ensure that the TSF-PDC-PID'S can update the suitable PID controller at several operating points so, it has a good dynamic response under many types of disturbances compared to fixed Optimal PID controller

Parallel Distributed Compensation for Voltage Controlled Active Magnetic Bearing System using Integral Fuzzy Model

Parallel Distributed Compensation (PDC) for current-controlled Active Magnetic Bearing System (AMBS) has been quite effective in recent years. However, this method does not take into account the dynamics associated with the electromagnet. This limits the method to smaller scale applications where the electromagnet dynamics can be neglected. Voltage-controlled AMBS is used to overcome this limitation but this comes with serious challenges such as complex mathematical modelling and higher order system control. In this work, a PDC with integral part is proposed for position and input tracking control of voltage-controlled AMBS. PDC method is based on nonlinear Takagi-Sugeno (T-S) fuzzy model. It is shown that the proposed method outperforms the conventional fuzzy PDC. It stabilizes the bearing shaft at any chosen operating point and tracks any chosen smooth trajectory within the air gap with a high external disturbance rejection capability

Soft Computing Techniques and Their Applications in Intel-ligent Industrial Control Systems: A Survey

Soft computing involves a series of methods that are compatible with imprecise information and complex human cognition. In the face of industrial control problems, soft computing techniques show strong intelligence, robustness and cost-effectiveness. This study dedicates to providing a survey on soft computing techniques and their applications in industrial control systems. The methodologies of soft computing are mainly classified in terms of fuzzy logic, neural computing, and genetic algorithms. The challenges surrounding modern industrial control systems are summarized based on the difficulties in information acquisition, the difficulties in modeling control rules, the difficulties in control system optimization, and the requirements for robustness. Then, this study reviews soft-computing-related achievements that have been developed to tackle these challenges. Afterwards, we present a retrospect of practical industrial control applications in the fields including transportation, intelligent machines, process industry as well as energy engineering. Finally, future research directions are discussed from different perspectives. This study demonstrates that soft computing methods can endow industry control processes with many merits, thus having great application potential. It is hoped that this survey can serve as a reference and provide convenience for scholars and practitioners in the fields of industrial control and computer science