Hybrid Fuzzy Modelling for Model Predictive Control

Model predictive control (MPC) has become an important area of research and is also an approach that has been successfully used in many industrial applications. In order to implement a MPC algorithm, a model of the process we are dealing with is needed. Due to the complex hybrid and nonlinear nature of many industrial processes, obtaining a suitable model is often a difficult task. In this paper a hybrid fuzzy modelling approach with a compact formulation is introduced. The hybrid system hierarchy is explained and the Takagi–Sugeno fuzzy formulation for the hybrid fuzzy modelling purposes is presented. An efficient method for identifying the hybrid fuzzy model is also proposed. A MPC algorithm suitable for systems with discrete inputs is treated. The benefits of the MPC algorithm employing the hybrid fuzzy model are verified on a batch-reactor simulation example: a comparison between the proposed modern intelligent (fuzzy) approach and a classic (linear) approach was made. It was established that the MPC algorithm employing the proposed hybrid fuzzy model clearly outperforms the approach where a hybrid linear model is used, which justifies the usability of the hybrid fuzzy model. The hybrid fuzzy formulation introduces a powerful model that can faithfully represent hybrid and nonlinear dynamics of systems met in industrial practice, therefore, this approach demonstrates a significant advantage for MPC resulting in a better control performance.     

Robust adaptive feedforward control and achievable tracking for systems with time delays

A feedback/feedforward controller architecture is developed that characterises the achievable reference tracking of real time inputs for both minimum phase and non-minimum phase systems with time delays, when there are no modelling errors or external disturbances. This characterisation is obtained by factoring the plant into its minimum phase, non-minimum phase, and time delay components, which are used to design two feedforward controllers that inject signals into two points of the feedback loop. Design constraints are provided that determine both the types of signals that may be achieved, and the feedforward controllers that will generate that output. Of course, in practice, both modelling errors and external disturbances will be present. In this case, we develop robust analysis tools that both guide the feedback controller design process, and provide rigorous robust tracking performance that guarantees for the overall resulting closed-loop system. Robust methods for designing the feedforward controllers are presented, and numerical examples are provided. The performance of this architecture depends strongly on the choice of design parameters, and the accuracy of the plant model used. Hence, the use of adaptation methods is also considered, and it is shown that they can readily be employed to improve the performance of this control methodology.     

Computation of stabilizing Lag/Lead controller parameters

One of the central problems in control theory relates to the design of controllers for stabilization of systems. The paper deals with the problem of computing all stabilizing values of the parameters of Lag/Lead controllers for linear time-invariant plant stabilization. It is well known that linear controllers of Lag/Lead type are still widely used in many industrial applications. In this paper, an extension of a new approach to feedback stabilization based on the Hermite–Biehler theorem to the Lag/Lead controller structure is given. In addition, the problem of stabilization of uncertain systems defined by an interval plant is studied using the Kharitonov and the Hermite–Biehler theorems. The proposed method is analytical and it can be applied successfully using today’s advanced computer technology. Examples are included to illustrate the method presented.     

奇异摄动系统的边界层鲁棒控制研究及应用

研究一类非线性奇异摄动系统的边界层鲁棒控制问题。该类系统边界层的不确定项不满足一般匹配条件。鲁棒控制器的设计分为伪名义边界层系统和整个边界层系统两步进行。在满足某些条件时,设计的控制器可使该类系统的边界层仍保持渐近稳定特性。将此方法用于中程空地导弹的中制导系统,仿真结果验证了该设计方法的有效性。     

Lazy learning for local modelling and control design

This paper presents local methods for modelling and control of discrete-time unknown non-linear dynamical systems, when only input-output data are available. We propose the adoption of lazy learning, a memory-based technique for local modelling. The modelling procedure uses a query-based approach to select the best model configuration by assessing and comparing different alternatives. A new recursive technique for local model identification and validation is presented, together with an enhanced statistical method for model selection. A lso, three methods to design controllers based on the local linearization provided by the lazy learning algorithm are described. In the first method the lazy technique returns the forward and inverse models of the system which are used to compute the control action to take. The second is an indirect method inspired by self-tuning regulators where recursive least squares estimation is replaced by a local approximator. The third method combines the linearization provided by the local learning techniques with optimal linear control theory, to control non-linear systems about regimes which are far from the equilibrium points. Simulation examples of identification and control of non-linear systems starting from observed data are given.     

Distributed estimation-based tracking control of multiple uncertain non-linear systems

This paper considers the tracking control of multiple uncertain non-linear systems with a desired signal which is not available to each system. An estimation-based controller design approach is proposed. Distributed estimation-based adaptive controllers are proposed with the aid of Lyapunov techniques and results from graph theory. Simulation results show the effectiveness of the proposed controllers.     

Identification of closed-loop systems with low-order controllers

A bias correction method without noise modelling was recently proposed for indirect identification of closed-loop systems. A key assumption used in deriving this method required that the order of the controller is not less than that of the open-loop plant. A significant feature of the results presented in this paper is the removal of this assumption to enable the method to be applicable to unbiased identification of closed-loop systems with low order controllers.     

Modelling adaptive multi-agent manufacturing control with discrete event system formalism

This paper introduces an approach for modelling and designing multi-agent control architectures for agile manufacturing using a generic formalism based on a system-theoretic discrete event approach. To describe the details of the modelling strategy, we apply the proposed approach to a multi-agent network for Job flow control in a manufacturing plant. Two interacting types of autonomous controllers, Part Agents and Machine Agents, are in charge of controlling the part flow and the machine processing sequences. Both type of agents are first modelled as atomic discrete event systems and subsequently integrated in the model of the entire network of autonomous controllers. To improve the performance of the network of agents, we introduce a mechanism based on evolutionary algorithms adapting the agents’ decision laws that are encapsulated in agents’ states. Through network simulation, the algorithm continuously searches for effective decision laws, consequently adapting agent's behaviour to the current operational conditions of the manufacturing floor. Simulation results show the potentialities of the approach.     

A new specification-based qualitative metric for simulation model validity

Informal validation techniques such as simulation are extensively used in the development of embedded systems. Formal approaches such as model-checking and testing are important means to carry out Verification and Validation (V&V) activities. Model-checking consists in exploring all possible behaviors of a model in order to perform a qualitative and quantitative analysis. However, this method remains of limited use as it runs into the problem of combinatorial explosion. Testing and model-checking do not take into account the context of use objectives of the model. Simulation overcomes these problems but it is not exhaustive. Submitted to simulation scenarios which are an operational formulation of the V&V activity considered, simulation consists in exploring a subset of the state space of the model. This paper proposes a formal approach to assess simulation scenarios. The formal specification of a model and the simulation scenarios applied to that model serve to compute the effective evolutions taken by the simulation. It is then possible to check whether a simulation fulfills its intended purpose. To illustrate this approach, the application study of an intelligent cruise controller is presented. The main contribution of this paper is that combining simulation objectives and formal methods leads to define a qualitative metric for a simulation evaluation without running a simulation.     

A new approach to fuzzy estimation of Takagi-Sugeno model and its applications to optimal control for nonlinear systems

An efficient approach is presented to improve the local and global approximation and modelling capability of Takagi-Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy. The main problem is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the use of the T-S method because this type of membership function has been widely used during the last two decades in the stability, controller design and are popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S method with optimized performance in approximating nonlinear functions. A simple approach with few computational effort, based on the well known parameters’ weighting method is suggested for tuning T-S parameters to improve the choice of the performance index and minimize it. A global fuzzy controller (FC) based Linear Quadratic Regulator (LQR) is proposed in order to show the effectiveness of the estimation method developed here in control applications. Illustrative examples of an inverted pendulum and Van der Pol system are chosen to evaluate the robustness and remarkable performance of the proposed method and the high accuracy obtained in approximating nonlinear and unstable systems locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity and generality of the algorithm.     

Impact of model plant mismatch on performance of control systems: An application to paper machine control

Model-based controllers based on incorrect estimates of the true plant behaviour can be expected to perform poorly. This work studies the effect of model plant mismatch on the closed loop behaviour and system performance for a certain class of MIMO systems. Performance is measured using a minimum variance index and a closely related user-specified criterion. We study the effect of model plant mismatch on the output variance and performance indices. Under mild assumptions, the performance of each output in a MIMO system can be analysed independently. Moreover, we propose an approach to distinguish the effect of model–plant mismatch from the effect of changes in disturbance characteristics on closed-loop performance. We define a sensitivity measure that relates system performance to model–plant mismatch, and use it to explore this sensitivity for three realistic types of parametric modelling errors. Next, we suggest a quantitative method that compares a system's actual output to its desired response in a transient setting. The performance of the transient response is demonstrably more sensitive to the model–plant mismatch than the steady state performance. The results are illustrated on industrial paper machine data.     

Model-free control

‘Model-free control’and the corresponding ‘intelligent’ PID controllers (iPIDs), which already had many successful concrete applications, are presented here for the first time in an unified manner, where the new advances are taken into account. The basics of model-free control is now employing some old functional analysis and some elementary differential algebra. The estimation techniques become quite straightforward via a recent online parameter identification approach. The importance of iPIs and especially of iPs is deduced from the presence of friction. The strange industrial ubiquity of classic PIDs and the great difficulty for tuning them in complex situations is deduced, via an elementary sampling, from their connections with iPIDs. Several numerical simulations are presented which include some infinite-dimensional systems. They demonstrate not only the power of our intelligent controllers but also the great simplicity for tuning them.     

离散线性时滞系统的次优控制:逐次逼近法

A successive approximation approach for designing optimal controllers is presented for discrete linear time-delay systems with a quadratic performance index. By using the successive approximation approach, the original optimal control problem is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems without time-delay and time-advance terms. The optimal control law obtained consists of an accurate feedback terms and a time-delay compensation term which is the limit of the solution sequence of the adjoint equations. By using a finite-step iteration of the time-delay compensation term of the optimal solution sequence, a suboptimal control law is obtained. Simulation examples are employed to test the validity of the proposed approach.     

基于SMT的区域控制器同步反应式模型的形式化验证

在安全关键系统的软件开发过程中,形式化验证是一种经检验的提高软件质量的技术.然而,无论从理论上还是从应用角度来看,软件的验证都必须是完整的,数据流验证应该是对实现层软件模型进行验证的必要体现.因此,环境输入、泛型函数、高阶迭代运算和中间变量对于分析形式化验证的可用性至关重要.为了验证同步反应式模型,工程师很容易验证控制流模型(即安全状态机).现有工作表明,这类工作无法全面地验证安全关键系统的同步反应式模型,尤其是数据流模型,导致这些方法没有达到工业应用的要求,这成为对工业安全软件进行形式化验证的一个挑战.提出了一种自动化验证方法.该方法可以实现对安全状态机和数据流模型的集成进行验证.采用了一种基于程序综合的方法,其中,SCADE模型描述了功能需求、安全性质和环境输入,可以通过对Lustre模型的程序综合,采用基于SMT的模型检查器进行验证.该技术将程序合成作为一种通用原理来提高形式化验证的完整性.在轨道交通的工业级应用(近200万行Lustre代码)上评估了该方法.实验结果表明,该方法在大规模同步反应式模型长期存在的复杂验证问题上是有效的.     

Global 𝒦-exponential trackers for nonholonomic chained-form systems based on LMI

Global 𝒦-exponential controllers are constructed for the tracking control problem of nonholonomic systems in chained form. Compared to previously published papers, a difference is that the reference targets are allowed to converge to a point exponentially. By using a novel transformation and the cascade-design method, the tracking control problem is converted into a stabilisation problem composed of two simple subsystems. Then the LMI-design approach is developed for the stabilising one of the above two subsystems. Assumptions on the reference signal is much more relaxed than our previous papers. A peculiar character of the presented methodology is that global 𝒦-exponential tracking can be successfully obtained for nonholonomic chained-form systems without the popular condition of persistent excitation or not converging to zero. Simulation results on a unicycle mobile robot and an articulated vehicle are presented to show the validity of the proposed strategy.     

The First World Congress on Formal Methods in the Development of Computing Systems

Formal methods are coming of age: mathematical techniques and tools are now regarded as an important part of the development process in a wide range of industrial and governmental organisations. A transfer of technology into the mainstream of systems development is slowly, but surely, taking place. FM'99, the First World Congress on Formal Methods in the Development of Computing Systems, was a result and a measure of this new-found maturity. It brought together an impressive array of industrial and applications-oriented papers that show how formal methods have been used to tackle real problems. The proceedings are published as Volumes 1708 and 1709 in Springer-Verlag's Lecture Notes in Computer Science. These proceedings are a record of the technical symposium of FM'99. Alongside the papers describing applications of formal methods, you will find technical reports, papers, and abstracts detailing new advances in formal techniques, from mathematical foundations to practical tools. After the World Congress, we decided that many papers deserved a wider audience, and we created an opportunity for their authors to revise and extend their work. The proceedings contain over one hundred papers, and we decided to publish twelve of them simultaneously in special issues of three journals: Formal Aspects of Computing, Formal Methods in System Design, and IEEE Transactions in Software Engineering. The papers selected are among the best submitted to FM'99, and were subjected to a rigorous second review process involving leading international academic and industrial researchers.     

Direct data‐driven design of switching controllers

Switching linear models can be used to represent the behavior of hybrid, time‐varying, and nonlinear systems, while generally providing a satisfactory trade‐off between accuracy and complexity. Although several control design techniques are available for such models, the effect of modeling errors on the closed‐loop performance has not been formally evaluated yet. In this paper, a data‐driven synthesis scheme is thus introduced to design optimal switching controllers directly from data, without needing a model of the plant. In particular, the theory will be developed for piecewise affine controllers, which have proven to be effective in many real‐world engineering applications. The performance of the proposed approach is illustrated on some benchmark simulation case studies.     

Industrial applications of type-2 fuzzy sets and systems: A concise review

Data, as being the vital input of system modelling, contain dissimilar level of imprecision that necessitates different modelling approaches for proper analysis of the systems. Numbers, words and perceptions are the forms of data that has varying levels of imprecision. Existing approaches in the literature indicate that, computation of different data forms are closely linked with the level of imprecision, which the data already have. Traditional mathematical modelling techniques have been used to compute the numbers that have the least imprecision. Type-1 fuzzy sets have been used for words and type-2 fuzzy sets have been employed for perceptions where the level of imprecision is relatively high. However, in many cases it has not been easy to decide whether a solution requires a traditional approach, i.e., type-1 fuzzy approach or type-2 fuzzy approach. It has been a difficult matter to decide what types of problems really require modelling and solution either with type-1 or type-2 fuzzy approach. It is certain that, without properly distinguishing differences between the two approaches, application of type-1 and type-2 fuzzy sets and systems would probably fail to develop robust and reliable solutions for the problems of industry. In this respect, a review of the industrial applications of type-2 fuzzy sets, which are relatively novel to model imprecision has been considered in this work. The fundamental focus of the work has been based on the basic reasons of the need for type-2 fuzzy sets for the existing studies. With this purpose in mind, type-2 fuzzy sets articles have been selected from the literature using the online databases of ISI-Web of Science, ScienceDirect, SpringerLink, Informaworld, Engineering Village, Emerald and IEEE Xplore. Both the terms “type-2 fuzzy” and “application” have been searched as the main keywords in the topics of the studies to retrieve the relevant works. The analysis on the industrial applications of type-2 fuzzy sets/systems (FSs) in different topics allowed us to summarize the existing research areas and therefore it is expected be useful to prioritize future research topics. This review shows that there are still many opportunities for application of type-2 FSs for several different problem domains. Shortcomings of type-1 FSs can also be considered as an opportunity for the application of type-2 FSs in order to provide a better solution approach for industrial problems.     

Suboptimal Control for Discrete Linear Systems with Time-delay:A Successive Approximation Approach

A successive approximation approach for designing optimal controllers is presented for discrete linear time-delay systems with a quadratic performance index.By using the successive approximation approach,the original optimal,control problem is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems without time-delay and time- advance terms.The optimal control law obtained consists of an accurate feedback terms and a time-delay compensation term which is the limit of the solution sequence of the adjoint equations. By using a finite-step iteration of the time-delay compensation term of the optimal solution sequence, a suboptimal control law is obtained.Simulation examples are employed to test the validity of the proposed approach.