A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Non-linear predictive control for manufacturing and robotic applications

The paper discusses predictive control algorithms in the context of applications to robotics and manufacturing systems. Special features of such systems, as compared to traditional process control applications, require that the algorithms are capable of dealing with faster dynamics, more significant unstabilities and more significant contribution of non-linearities to the system performance. The paper presents the general framework for state-space design of predictive algorithms. Linear algorithms are introduced first, then, the attention moves to non-linear systems. Methods of predictive control are presented which are based on the state-dependent state space system description. Those are illustrated on examples of rather difficult mechanical systems

New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems

This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use

Performance Improvement of Low-Cost Iterative Learning-Based Fuzzy Control Systems for Tower Crane Systems

This paper is dedicated to the memory of Prof. Ioan Dzitac, one of the fathers of this journal and its founding Editor-in-Chief till 2021. The paper addresses the performance improvement of three Single Input-Single Output (SISO) fuzzy control systems that control separately the positions of interest of tower crane systems, namely the cart position, the arm angular position and the payload position. Three separate low-cost SISO fuzzy controllers are employed in terms of first order discrete-time intelligent Proportional-Integral (PI) controllers with Takagi-Sugeno-Kang Proportional-Derivative (PD) fuzzy terms. Iterative Learning Control (ILC) system structures with PD learning functions are involved in the current iteration SISO ILC structures. Optimization problems are defined in order to tune the parameters of the learning functions. The objective functions are defined as the sums of squared control errors, and they are solved in the iteration domain using the recent metaheuristic Slime Mould Algorithm (SMA). The experimental results prove the performance improvement of the SISO control systems after ten iterations of SMA

Robust H∞ control for uncertain discrete-time-delay fuzzy systems via output feedback controllers

This paper investigates the problem of robust output feedback H∞ control for a class of uncertain discrete-time fuzzy systems with time delays. The state-space Takagi - Sugeno fuzzy model with time delays and norm-bounded parameter uncertainties is adopted. The purpose is the design of a full-order fuzzy dynamic output feedback controller which ensures the robust asymptotic stability of the closed-loop system and guarantees an H∞ norm bound constraint on disturbance attenuation for all admissible uncertainties. In terms of linear matrix inequalities (LMIs), a sufficient condition for the solvability of this problem is presented. Explicit expressions of a desired output feedback controller are proposed when the given LMIs are feasible. The effectiveness and the applicability of the proposed design approach are demonstrated by applying this to the problem of robust H∞ control for a class of uncertain nonlinear discrete delay systems. © 2005 IEEE.published_or_final_versio

Model predictive fuzzy control of a steam boiler

This thesis is devoted to apply a Model Predictive Fuzzy Controller (MPC and Takagi-Sugeno) to a specific Steam Boiler Plant. This is a very common problem in control. The considered plant is based on the descriptions obtained from the data of a referenced boiler in the combined cycle plant as Abbot in Champaign, Illinois. The idea is to take all the useful data from the boiler according to its performance and capability in different operation points in order to model the most accurate plant for control. The considered case study is based in a modification of a model proposed by Pellegrinetti and Bentsman in 1996, considering to be tested under the demands of the Control Engineering Association (CEA). The system is Multi-Input and Multi-Output (MIMO), where each controlled output has a specific weight in order to measure the performance. The objective is to minimize cost index but also make it operative and robust for a wide range of variables, discovering the limits of the plant and its behaviour. The model is supposed to manage real data and was constructed under real physical descriptions. However, this model is not a white box, so the analysis and development of the model to be used with the MPC strategy have to be identified to continue with the evaluation of the controlled plant. There are some physical variables that have to be taken into account (Drum Pressure, Excess of Oxygen, Water Level, Water Flow, Fuel Flow, Air Flow and Steam Demand) to know if these variables and other parameters are evolving in the correct way and satisfy the logic of the mass and energy balances in the system. After measuring and analysing the data, the model is validated testing it for different values of steam demands. The controller is tuned for every one of the considered demands. Once tuned, the controller computes the manipulated variables receiving information from the controlled ones, including their references. Finally, the resulting controller is a combination of a set of local controllers using the Takagi-Sugeno approach using the steam demand setpoint as scheduling variable. To apply this approach, a set of local models approximating the non-linear boiler behaviour around a set of steam demand set-points are obtained and then their a fused using the Takagi-Sugeno approach to approximate any unknown steam demand located in the valid range of values

Hierarchical Optimization-Based Model Predictive Control for a Class of Discrete Fuzzy Large-Scale Systems Considering Time-Varying Delays and Disturbances

Altres ajuts: Acord transformatiu CRUE-CSICIn this manuscript, model predictive control for class of discrete fuzzy large-scale systems subjected to bounded time-varying delay and disturbances is studied. The considered method is Razumikhin for time-varying delay large-scale systems, in which it includes a Lyapunov function associated with the original non-augmented state space of system dynamics in comparison with the Krasovskii method. As a rule, the Razumikhin method has a perfect potential to avoid the inherent complexity of the Krasovskii method especially in the presence of large delays and disturbances. The considered large-scale system in this manuscript is decomposed into several subsystems, each of which is represented by a fuzzy Takagi-Sugeno (TS) model and the interconnection between any two subsystems is considered. Because the main section of the model predictive control is optimization, the hierarchical scheme is performed for the optimization problem. Furthermore, persistent disturbances are considered that robust positive invariance and input-to-state stability under such circumstances are studied. The linear matrix inequalities (LMIs) method is performed for our computations. So the closed-loop large-scale system is asymptotically stable. Ultimately, by two examples, the effectiveness of the proposed method is illustrated, and a comparison with other papers is made by remarks

Multivariable nonlinear advanced control of copolymerization processes

A reliable multivariable model of a process is a fundamental prerequisite for the design of an efficient control strategy. Though, such a model is often very hard to obtain via a first-principles approach. The development of two fuzzy model-based multivariable nonlinear predictive control schemes and their implementation on a copolymerization process are described in this paper. Multi-input/single-output models are developed using fuzzy logic and combined to form a parallel system model for simulation and online prediction. The behavior of the outlined controllers were compared to the dynamic matrix control (DMC) and to a typical nonlinear model-based predictive control (NMPC) for regulatory problem and the obtained results showed the effectiveness of the proposed structures