Control Design For Nonlinear Systems Research Articles

Robust nonlinear tracking control system design of an uncertain multivariable process driven by a distributed control system device

In this paper, by using a distributed control system (DCS) device, a robust tracking control system is proposed based on robust right coprime factorization for a heat exchanger actuated by a water level process with coupling effects and uncertainties. Firstly, nonlinear models of water level and temperature processes with coupling and uncertainties are given. Secondly, nonlinear feedback tracking control systems corresponding to a multi-input multi-output (MIMO) process are realized by using operator-based robust right coprime factorization. Meanwhile, stability of the control systems is guaranteed by using robust stability conditions compatible with the MIMO process including coupling effects, and to improve the output tracking performance, tracking controllers are designed. Finally, the effectiveness of the proposed design scheme is confirmed by simulation and experimental results.

A Nonlinear Gain-Scheduling Compensation Approach Using Parameter-Dependent Lyapunov Functions

This paper addresses the gain-scheduling control design for nonlinear systems to achieve output regulation. For gain-scheduling control, the linear parameter-varying (LPV) model is obtained by linearizing the plant about zero-error trajectories upon which an LPV controller is based. A key in this process is to find a nonlinear output feedback compensator such that its linearization matches with the designed LPV controller. Then, the stability and performance properties of LPV control about the zero-error trajectories can be inherited when the nonlinear compensator is implemented. By incorporating the exosystem, nominal input, and measured output information into the LPV model, the LPV control synthesis problem is formulated as linear matrix inequalities (LMIs) using parameter-dependent Lyapunov functions (PDLFs). Moreover, explicit formulae for the construction of the nonlinear gain-scheduled compensator have been derived to meet the linearization requirement. Finally, the validity of the proposed nonlinear gain-scheduling control approach is demonstrated through a ball and beam example.

LabVIEW based ‘nonlintool’ for analysis and design of nonlinear control system

ABSTRACTThis paper presents LabVIEW based Graphical User Interface (GUI) tool called as ‘nonlintool’. The tool provides much needed user friendly computational platform for nonlinear control system as there are very few endeavours found on computer aided tool for analysis and design of nonlinear control system. The tool is useful for analysis and design of nonlinear control system. The tool offers user friendly computational platform for the study of nonlinear control system. It has capability to carry the analysis and design for almost all type of discrete (or discontinuous) and continues nonlinearities. It aims to provide quick and effective means for the understanding of behaviour of nonlinear systems. The different modules integrated in the tool to analyse the discrete type nonlinearity with phase plane trajectory and continuous type nonlinearity with linearization. The tool enables the user to investigate the stability of the system and help to proceed for the design of nonlinear control system. The tool is converted in to executable file to make it open source package. © 2015 Wiley Periodicals, Inc. Comput Appl Eng Educ 24:195–201, 2016; View this article online at wileyonlinelibrary.com/journal/cae; DOI 10.1002/cae.21697

Design of a new nonlinear model predictive fault tolerant control system using multi-sensor data fusion technique based on UKF algorithm

Purpose– There are high expectations for reliability, safety and fault tolerance are high in chemical plants. Control systems are capable of potential faults in the plant processing systems. This paper proposes is a new Fault Tolerant Control (FTC) system to identify the probable fault occurrences in the plant.Design/methodology/approach– A Fault Diagnosis and Isolation (FDI) module has been devised based on the estimated state of system. An Unscented Kalman Filter (UKF) is the main innovation of the FDI module to identify the faults. A Multi-Sensor Data Fusion algorithm is utilized to integrate the UKF output data to enhance fault identification. The UKF employs an augmented state vector to estimate system states and faults simultaneously. A control mechanism is designed to compensate for the undesirable effects of the detected faults.Findings– The performance of the Nonlinear Model Predictive Controller (NMPC) without any fault compensation is compared with the proposed FTC scheme under different fault scenarios. Analysis of the simulation results indicates that the FDI method is able to identify the faults accurately. The proposed FTC approach facilitates recovery of the closed loop performance after the faults have been isolated.Originality/value– A significant contribution of the paper is the design of an FTC system by using UKF to estimate faults and enhance the accuracy of data. This is done by applying a data fusion algorithm and controlling the system by the NMPC after eliminating the effects of faults.

RBFNs Nonlinear Control System Design through BFPSO Algorithm

All parameters are automatically extracted by the bacterial foraging particle swarm optimization (BFPSO) algorithm to approach the desired control system. Three parameterize basis function neural networks (RBFNs) model to solve the car-pole system problem. Several free parameters of radial basis functions can be automatically tuned by the direct of the specified fitness function. In additional, the proper number of radial basis functions (RBFs) of the constructed RBFNs can be chosen by the defined fitness function which takes this factor into account. The desired multiple objectives of the RBFNs control system are proposed to simultaneously approach the smaller errors with a fewer RBFs number. Simulations show that the developed RBFNs control systems efficiently achieve the desired the setting lot as soon as possible.

Nonlinear Thf‐Fxlms Algorithm For Active Noise Control With Loudspeaker Nonlinearity

AbstractAdaptive algorithms are prevalently applied in the design of nonlinear active noise control (ANC) systems. The most important nonlinearity in ANC is the saturation effect produced by the electro‐acoustical sensors and transducers. The dominant saturation nonlinearity is in the transducers, which can be represented by a Wiener model. An effective solution to mitigate such nonlinear distortion is to employ the Nonlinear Filtered‐X Least Mean Square (NLFXLMS) algorithm. The controller compensates the nonlinearity using a model of the saturation effect represented by the scaled error function (SEF). However, the NLFXLMS is limited by two practical issues such that the degree of nonlinearity has to be known in advance and the SEF cannot be evaluated in real time. In this work, the NLFXLMS algorithm is modified by incorporating the tangential hyperbolic function (THF) to model the saturation effect of the loudspeaker. The proposed THF‐NLFXLMS algorithm, models the nonlinear secondary path and applies the estimated degree of nonlinearity in the control algorithm design. The results show that the Wiener secondary path, with saturation nonlinearity represented by SEF, can be modelled by THF with a certain degree of accuracy and can yield a reasonable estimate of the degree of nonlinearity. The performance of the proposed algorithm is comparable with the benchmark NLFXLMS and is superior to the conventional FXLMS as well as the second order Volterra algorithm of similar computational complexity with the proposed algorithm.

Optimal control for a linear quadratic neuro Takagi--Sugeno fuzzy singular system using genetic programming

Optimal control for a linear neuro Takag--Sugeno fuzzy singular system with quadratic performance is obtained using genetic programming (gp). To obtain the optimal control, the solution of a matrix Riccati differential equation is computed by solving a differential algebraic equation using the gp approach. The obtained solution is equivalent or very close to the exact solution of the problem. The accuracy of the solution computed by the gp approach is qualitatively better than the traditional Runge--Kutta method. An illustrative numerical example is presented for the proposed method. References P. Balasubramaniam, J. Abdul Samath, N. Kumaresan and A. Vincent Antony Kumar, Solution of matrix Riccati differential equation for the linear quadratic singular system using neural networks, Appl. Math. Comput. 182(2):1832–1839, 2006. doi:10.1016/j.amc.2006.06.020 G. Da Prato and A. Ichikawa, Quadratic control for linear periodic systems, Appl. Math. Opt. 18:39–66, 1988. doi:10.1007%2FBF01443614 D. E. Goldberg, Genetic algorithms in search, optimization and machine learning , Addision Wesley, 1989. http://dl.acm.org/citation.cfm?id=534133 J. Jang, ANFIS: adaptive-network-based fuzzy inference systems, IEEE T. Syst. Man. Cyb. 23(3):665–685, 1993. doi:10.1109/21.256541 J. R. Koza, Genetic programming: on the programming of computers by means of natural selection . MIT Press, 1992. http://mitpress.mit.edu/books/genetic-programming M. O'Neill and C. Ryan, Evolutionary automatic programming in an arbitrary language, Genetic Programming, Vol. 4 , Kluwer Academic Publishers, 2003. http://www.springer.com/computer/ai/book/978-1-4020-7444-8 N. Kumaresan, Optimal control for stochastic linear quadratic singular periodic neuro Takagi–Sugeno fuzzy system with singular cost using ant colony programming, Appl. Math. Model. , 35:3797–3808, 2011. doi:10.1016/j.apm.2011.02.017 T. Takagi and M. Sugeno, Derivation of fuzzy control rules from human operator's actions, IFAC-IFIP-IFORS Symp., Fuzzy information, knowledge representation and decision analysis , 55–60, 1983. http://dl.acm.org/citation.cfm?id=577582 I. G.Tsoulos and I. E. Lagaris, Solving differential equations with genetic programming, Genet. Program. Evolv. M. , 7:33–54, 2006. doi:10.1007/s10710-006-7009-y S.-J. Wu, H.-H. Chiang, H.-T. Lin and T.-T. Lee, Neural-nerwork-based optimal fuzzy controller design for nonlinear systems, Fuzzy Set. Syst. , 154:182–207, 2005. doi:10.1016/j.fss.2005.03.011

Event-triggered controller design of nonlinear discrete-time networked control systems in T-S fuzzy model

This article is concerned with event-triggered fuzzy control design for a class of discrete-time nonlinear networked control systems (NCSs) with time-varying communication delays. Firstly, a more general mixed event-triggering scheme (ETS) is proposed. Secondly, considering the effects of the ETS and communication delays, based on the T-S fuzzy model scheme and time delay system approach, the original nonlinear NCSs is reformulated as a new event-triggered networked T-S fuzzy systems with interval time-varying delays. Sufficient conditions for uniform ultimately bound (UUB) stability are established in terms of linear matrix inequalities (LMIs). In particular, the quantitative relation between the boundness of the stability region and the triggering parameters are studied in detail. Thirdly, a relative ETS is also provided, which can be seen as a special case of the above proposed mixed ETS. As a difference from the preceding results, sufficient conditions on the existence of desired fuzzy controller are derived to ensure the asymptotic stability of the closed-loop system with reduced communication frequency between sensors and controllers. Moreover, a co-design algorithm for simultaneously determining the gain matrices of the fuzzy controller and the triggering parameters is developed. Finally, two illustrative examples are presented to demonstrate the advantage of the proposed ETS and the effectiveness of the controller design method.

Successive Approximations of Model Reference Adaptive Control Design for Nonlinear Systems

In this study, model reference adaptive control algorithm with successive approximation method is suggested for nonlinear systems. The proposed method uses Linear Time Varying (LTV) approximations of the nonlinear model to design the controller. Provided that an adaptive control exists for the approximated LTV system, it is shown that the responses of the approximated LTV systems converge to the response of the nonlinear system. Then the model reference adaptive control for nonlinear system is designed by using successive LTV approximations. The proposed control design method is exemplified with a nonlinear dynamical system.

Gain-Scheduled MPC Design for Nonlinear Systems with Input Constraints

A novel methodology is proposed for discrete model predictive gain-scheduled controller design for nonlinear systems with input(hard)/output(soft) constraints for finite and infinite prediction horizons. The proposed design procedure is based on the linear parametervarying (LPV) paradigm, afine parameter-dependent quadratic stability and on the notion of the parameter-varying guaranteed cost. The obtained design procedure is in the form of BMI. Numerical examples show the benefit of the proposed approach.

On-line direct control design for nonlinear systems

An approach to design a feedback controller for nonlinear systems directly from experimental data is presented. Improving over a recently proposed technique, which employs exclusively a batch of experimental data collected in a preliminary experiment, here the control law is updated and refined during real-time operation, hence enabling an on-line learning capability. The theoretical properties of the described approach, in particular closed-loop stability and tracking accuracy, are discussed. Finally, the experimental results obtained with a water tank laboratory setup are presented.

CONTROL PREDICTIVO DE MODELO DISTRIBUÍDO PARA SISTEMAS RESTRINGIDOS DE ZONAS AFINES CON ACOPLAMIENTO DE CONTROL

ABSTRACT: To improve the model predictive controller design of nonlinear system, a cooperative distributed model predictive controller (DMPC) for a system comprised of several constrained piecewise affine (PWA) subsystems with coupled control information is proposed in this paper. Distributed scheme is applied for saving time of solving optimization. To improve the optimal performance of entire system, cooperation was promoted with consideration to a greater portion of the system-wide objective. The terminal's positively invariant set and cost of the entire closed-loop system were added to guarantee stability. The optimal problem of each subsystem was converted to mixed-integer quadratic programming (MIQP) solving for obtaining control actions. This method decomposed the optimization problem of a large-scale nonlinear system into several lower-dimension MIQPs such that solving time could be reduced dramatically. Another advantage of the distributed model predictive control strategy is non-convex nonlinear optimization could be replaced by finite MIQPs, and an approximate global optimum could be obtained rather than a local optimum. Finally, a numerical example and a quadruple-tank simulation are presented in order to assess the proposed distributed model predictive control strategy. Keywords: Piecewise affine system, distributed control, model predictive control, mixed integer quadratic programming, quadruple-tank

MIMO Tracking PI/PID Controller Design for Nonlinear Systems based on Singular Perturbation Technique

Problem of the tracking PI/PID multivariable controller design based on time-scale separation technique (singular perturbation technique) for MIMO nonlinear systems is discussed. The presented design methodology guarantees almost perfect rejection of nonlinearities, unknown external disturbances, and interactions between loops due to increase of time-scale separation degree between the fast and slow modes that are artificially forced in the closedloop system. Simulation results for trajectory tracking control of two-link robot manipulator are presented as an example of the proposed design methodology application.

Frequency-Domain Analysis and Design of Linear Feedback of Nonlinear Systems and Applications in Vehicle Suspensions

Nonlinear vibration control systems (both passive and active) always involve parameter design and performance optimization tasks. A systematic and novel frequency-domain method is established to this aim in this study based on a newly developed concept-nonlinear characteristic output spectrum (nCOS). The nCOS function can be any system output function or multiobjective performance function to be optimized. It is shown for the first time that the nCOS function can be expressed into an explicit and analytical polynomial function of any model parameters which define underlying linear dynamics of the system. A simple least square algorithm is provided for the determination of this nonlinear parametric relationship. This novel nCOS function can obviously facilitate parameter analysis and design of nonlinear vibration control systems and provide a useful tool for a simple linear control design, while simultaneously considering inherent nonlinear dynamics of a system. A case study in vehicle suspension control demonstrates these new results.

Data-driven inversion-based control of nonlinear systems

In this paper, we introduce the Data-Driven Inversion-Based Control (D2-IBC) method for nonlinear control system design. The method relies on a two degree-of-freedom architecture, with a nonlinear controller and a linear controller running in parallel, and does not require any detailed physical knowledge of the plant to control. Specifically, we use input/output data to synthesize the control action by employing convex optimization tools only. We show the effectiveness of the proposed approach on a simulation example, where the D2-IBC performance is also compared to that of the Direct FeedbacK (DFK) design approach, a benchmark method for nonlinear controller design from data.

Multiobjective control system controllers design based on switching and applications

Many systems operate in an uncertain environment of limitations such as temperature, pressure, and physical acceleration/deceleration limitation, etc. Whatever the linear or nonlinear control system design methods are, the aircraft engine will encounter limitations on some occasions. So the aircraft engine control system consists of a family of continuous-time subsystems and switches from one to another depending on various environmental factors (see Figure 1). When the system switches from one subcontrol loop to another, the stability of the system is the basic performance that must be considered. The traditional control method is to switch slowly to avoid the dangers. Therefore, there is much space to improve the dynamic performance of the control system.

PID Controller Design of Nonlinear System using a New Modified Particle Swarm Optimization with Time-Varying Constriction Coefficient

The proportional integral derivative (PID) controllers have been widely used in most process control systems for a long time. However, it is a very important problem how to choose PID parameters, because these parameters give a great influence on the control performance. Especially, it is difficult to tune these parameters for nonlinear systems. In this paper, a new modified particle swarm optimization (PSO) is presented to search for optimal PID parameters for such system. The proposed algorithm is to modify constriction coefficient which is nonlinearly decreased time-varying for improving the final accuracy and the convergence speed of PSO. To validate the control performance of the proposed method, a typical nonlinear system control, a continuous stirred tank reactor (CSTR) process, is illustrated. The results testify that a new modified PSO algorithm can perform well in the nonlinear PID control system design in term of lesser overshoot, rise-time, settling-time, IAE and ISE.Keywords: PID controller, Particle Swarm Optimization (PSO),constriction factor, nonlinear system.

Adaptive fuzzy output-feedback controller design for nonlinear systems via backstepping and small-gain approach.

This paper focuses on an input-to-state practical stability (ISpS) problem of nonlinear systems which possess unmodeled dynamics in the presence of unstructured uncertainties and dynamic disturbances. The dynamic disturbances depend on the states and the measured output of the system, and its assumption conditions are relaxed compared with the common restrictions. Based on an input-driven filter, fuzzy logic systems are directly used to approximate the unknown and desired control signals instead of the unknown nonlinear functions, and an integrated backstepping technique is used to design an adaptive output-feedback controller that ensures robustness with respect to unknown parameters and uncertain nonlinearities. This paper, by applying the ISpS theory and the generalized small-gain approach, shows that the proposed adaptive fuzzy controller guarantees the closed-loop system being semi-globally uniformly ultimately bounded. A main advantage of the proposed controller is that it contains only three adaptive parameters that need to be updated online, no matter how many states there are in the systems. Finally, the effectiveness of the proposed approach is illustrated by two simulation examples.

Neural Networks Predictive Controller Using an Adaptive Control Rate

A model predictive control design for nonlinear systems based on artificial neural networks is discussed. The Feedforward neural networks are used to describe the unknown nonlinear dynamics of the real system. The backpropagation algorithm is used, offline, to train the neural networks model. The optimal control actions are computed by solving a nonconvex optimization problem with the gradient method. In gradient method, the steepest descent is a sensible factor for convergence. Then, an adaptive variable control rate based on Lyapunov function candidate and asymptotic convergence of the predictive controller are proposed. The stability of the closed loop system based on the neural model is proved. In order to demonstrate the robustness of the proposed predictive controller under set-point and load disturbance, a simulation example is considered. A comparison of the control performance achieved with a Levenberg-Marquardt method is also provided to illustrate the effectiveness of the proposed controller.

H∞ Control of Polynomial Fuzzy Systems: A Sum of Squares Approach

This paper proposes the control design ofa nonlinear polynomial fuzzy system with H∞ performance objective using a sum of squares (SOS) approach. Fuzzy model and controller are represented by a polynomial fuzzy model and controller. The design condition is obtained by using polynomial Lyapunov functions that not only guarantee stability but also satisfy the H∞ performance objective. The design condition is represented in terms of an SOS that can be numerically solved via the SOSTOOLS. A simulation study is presented to show the effectiveness of the SOS-based H∞ control designfor nonlinear polynomial fuzzy systems.