Nonlinear Plant Research Articles

PI control of stable nonlinear plants using projected dynamical systems

This paper presents a novel anti-windup proportional–integral controller for stable multi-input multi-output nonlinear plants. We use tools from projected dynamical systems theory to force the integrator state to remain in a desired (compact and convex) region, such that the plant input steady-state values satisfy the operational constraints of the problem. Under suitable monotonicity assumptions on the plant steady-state input–output map, we use singular perturbation theory results to prove the existence of a sufficiently small controller gain ensuring closed-loop (local) exponential stability and reference tracking for a feasible set of constant references. We suggest a particular controller design, which embeds (when possible) the right inverse of the plant steady-state input–output map. The relevance of the proposed controller scheme is validated through an application in the power systems domain, namely, the output (active and reactive) power regulation for a grid-connected synchronverter.

Membership-Function-Dependent Control Design of Interval Type-2 Sampled-Data Fuzzy-Model-Based Output-Feedback Tracking Control System

This article focuses on the stability analysis and control design of an interval type-2 sampled-data fuzzy-model-based output-feedback (IT2SDFMBOF) tracking control system, which is formed by the interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy model, the stable reference model, and the interval type-2 sampled-data output-feedback (IT2SDOF) fuzzy controller. The design goal is to establish a proper IT2SDOF fuzzy controller that is able to drive the states of the nonlinear plant subject to uncertainties to track those of the stable reference model, and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> performance index is adopted to optimize the tracking control performance. To improve the robustness of the IT2SDOF fuzzy controller against uncertainties of the nonlinear plant, IT2 fuzzy sets are utilized. Considering that the tracking control system is sampled-data (SD) type, a two-sided looped-functional-based approach exploiting the information on the interval from time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$t_k$</tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$t$</tex-math></inline-formula> and the interval from time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$t$</tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$t_{k+1}$</tex-math></inline-formula> is applied to enhance the stability analysis. The imperfect premise matching (IPM) concept permits the number of rules and the premise membership functions of the IT2 T-S fuzzy model and the IT2SDOF fuzzy controller to be different, which can be employed to promote the design flexibility. The tracking control system with the SD type and IPM design will cause the membership grades between the IT2 T-S fuzzy model and the IT2SDOF fuzzy controller to be mismatched. In addition, the membership-function-dependent stability analysis approach that can introduce the boundary information of membership functions into the stability analysis is used to relax the stability conditions. The relaxed stability conditions subject to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> performance building on the Lyapunov stability theory are developed in terms of linear matrix inequalities. Simulation results demonstrate the effectiveness of the proposed IT2SDFMBOF tracking control system.

A Novel Mixed Control Approach for Fuzzy Systems via Membership Functions Online Learning Policy

This article focuses on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {L}_{2}-\mathcal {L} _{\infty}/ \mathcal {H}_{\infty}$</tex-math></inline-formula> optimization control issue for a family of nonlinear plants by Takagi–Sugeno (T–S) fuzzy approach with actuator failure. First, considering unmeasurable system states, sufficient criteria for devising fuzzy imperfect premise matching dynamic output feedback controller to maintain asymptotic stability while guaranteeing a mixed performance for T–S fuzzy systems are provided. Therewith, in the light of feasible areas of dynamic output feedback controller membership functions (MFs), a new MFs online learning policy using gradient descent algorithm is proposed to learn the real-time values of MFs to acquire a better <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {L}_{2}-\mathcal {L}_{\infty}/ \mathcal {H}_{\infty}$</tex-math></inline-formula> control effect. Different from the traditional method using an imperfect premise matching scheme, under the proposed optimization algorithm, the trajectory of mixed performance index is lowered effectively. Afterward, a sufficient criterion is presented for assuring the convergence of the error of the cost function. Finally, the superiority of this online optimization learning policy is confirmed via simulations.

Relaxed Fault Estimation of Discrete-Time Nonlinear System Based on a New Multi-Instant Real-Time Scheduling Fuzzy Observer

Relaxed fault estimation (FE) criteria of a class of discrete-time nonlinear plants are proposed based on a new multi-instant real-time scheduling fuzzy FE observer. Compared with the existing methods given in the recent literature, the newly developed fuzzy observer is capable of providing much freedom for reducing the conservatism of designing feasible FE criteria. At each sampling point, the information of adjacent groups of normalized fuzzy weighting functions can be updated and utilized for deciding the activated mode of our developed fuzzy FE observer. Based on this, an exclusive pair of gain matrices can be given by introducing a set of well-designed free matrices into the designed FE criteria for every activated mode. Moreover, it can be found that the proposed result will include the previous one as a special case if all of those free matrices are removed. Finally, the well-known nonlinear truck–trailer plant with actuator fault is utilized to validate the superiority of our approach over the existing ones reported in the literature.

Use of multilayer recursive model for non-linear dynamic system identification

In practice, the dynamics of the system are uncertain due to nonlinear and dynamic characteristics. It is difficult to establish accurate identification and prediction of the nonlinear plants that require dynamic modelling of the system. Extreme learning machine (ELM) as the recursive model due to its fast training and convergence speed is utilized in this work. However, its limitation is that it has only 1 hidden neuron which tends to make evolution speed low. Further, Multi-layer ELM (ML-ELM) model is applied on a nonlinear Auto-regressive complex benchmark system. The performance of ML-ELM is compared with dynamic recurrent functional link neural network (DRFLNN), functional link neural network (FLNN), nonlinear auto-regressive moving average (NARAX), multi-layer perception (MLP), radial basis function network (RBFN), Elman recurrent neural network (ERNN), and basic ELM models. From the comparison table, it can be seen that ML-ELM has better performance as compared with other models.

Real-Time Metaheuristic Algorithm for Dynamic Fuzzification, De-Fuzzification and Fuzzy Reasoning Processes

This paper presents a systematic approach to designing a dynamic metaheuristic fuzzy logic controller (FLC) to control a piece of non-linear plant. The developed controller is a multiple-input–multiple-output (MIMO) system. However, with the proposed control mechanism is possible to adapt it to single-input–single-output (SISO) systems as well. During real-time operation, the dynamic behavior of the proposed fuzzy controller is influenced by a metaheuristic particle swarm optimization (PSO) mechanism. Nevertheless, to analyze the performance of the developed dynamic metaheuristic FLC as a piece of non-linear plant, a 1 kW four-wheel independent-drive electric rover is controlled under different road constraints. The test results show that the proposed dynamic metaheuristic FLC maintains the wheel slip ratio of all four wheels to less than 0.35 and a top recorded translational speed of 90 km/h is maintained for a fixed orientation.

Economic Linear Parameter Varying Model Predictive Control of the Aeration System of a Wastewater Treatment Plant.

This work proposes an economic model predictive control (EMPC) strategy in the linear parameter varying (LPV) framework for the control of dissolved oxygen concentrations in the aerated reactors of a wastewater treatment plant (WWTP). A reduced model of the complex nonlinear plant is represented in a quasi-linear parameter varying (qLPV) form to reduce computational burden, enabling the real-time operation. To facilitate the formulation of the time-varying parameters which are functions of system states, as well as for feedback control purposes, a moving horizon estimator (MHE) that uses the qLPV WWTP model is proposed. The control strategy is investigated and evaluated based on the ASM1 simulation benchmark for performance assessment. The obtained results applying the EMPC strategy for the control of the aeration system in the WWTP of Girona (Spain) show its effectiveness.

К ОЦЕНКЕ ОБЛАСТИ ПРИТЯЖЕНИЯ ПОЛОЖЕНИЯ РАВНОВЕСИЯ НЕЛИНЕЙНЫХ СИСТЕМ УПРАВЛЕНИЯ

Designing nonlinear control systems is still difficult, so many researchers are trying to findsome useful ways and methods to solve this problem. As a result of such research, some methodshave been seen trying to design a good enough control system for nonlinear plants. But a disadvantageof these methods is the complexity, so it created a need to compare some methods to determinewhich one is the easiest method to design a control system for nonlinear plants. It wasfound a way to compare two methods, which is comparing the regions of initial conditions of thesystems which are designed using these methods. Two analytical nonlinear control systems designmethods are compared on the example of the design control systems mobile robots. The algebraicpolynomial-matrix method uses a quasilinear model, and the feedback linearization method usesparticular feedback. Both considered methods give a bounded domain of equilibrium attraction,therefore the obtained control systems can be operated only with bounded initial conditions. Thenumerical example of designing the control systems for one object by these methods and the estimatesof the attraction areas of the system’s equilibriums in these systems are given in the paper.As a result of this paper, it was found that using the algebraic polynomial-matrix method will get abigger section of initial conditions of the plant’s variable than the same section which is given bythe feedback linearization method.

Deep Learning for Robust Adaptive Inverse Control of Nonlinear Dynamic Systems: Improved Settling Time with an Autoencoder.

An adaptive deep neural network is used in an inverse system identification setting to approximate the inverse of a nonlinear plant with the aim of constituting the plant controller by copying to the latter the weights and architecture of the converging deep neural network. This deep learning (DL) approach to the adaptive inverse control (AIC) problem is shown to outperform the adaptive filtering techniques and algorithms normally used in adaptive control, especially when in nonlinear plants. The deeper the controller, the better the inverse function approximation, provided that the nonlinear plant has an inverse and that this inverse can be approximated. Simulation results prove the feasibility of this DL-based adaptive inverse control scheme. The DL-based AIC system is robust to nonlinear plant parameter changes in that the plant output reassumes the value of the reference signal considerably faster than with the adaptive filter counterpart of the deep neural network. The settling and rise times of the step response are shown to improve in the DL-based AIC system.

Remote State Estimation of Nonlinear Systems Over Fading Channels via Recurrent Neural Networks

In this article, we consider the remote state estimation for nonlinear dynamic systems with known linear dynamics and unknown nonlinear perturbations. The nonlinear dynamic plant is monitored by multiple distributed sensors over a random access wireless network with shared common radio channel. We focus on the communication strategy and remote state estimation algorithm design so as to achieve a remote state estimation stability subject to unknown nonlinearities in plant and various wireless impairments, such as multisensor interference, wireless fading, and additive channel noise. By exploiting the additive properties of the physical wireless channels, we propose a novel information fusion over-the-air mechanism to address the signal collision and interference among the sensors. Utilizing the partial knowledge on the linear dynamics of the plant, we also propose a novel recurrent neural network (RNN)-based remote state estimator aided by a virtual state estimation mean-square-error (MSE) process. We further propose a novel online training algorithm such that the RNN at the remote estimator can effectively learn the unknown plant nonlinearities. Using the Lyapunov drift analysis approach, we establish closed-form sufficient requirements on the communication resources needed to achieve almost sure stability of both state estimation and RNN online training in high signal-to-noise ratio (SNR) regime. As a result, our proposed scheme is asymptomatic optimal for large SNR in the sense that both the plant state and the unknown plant nonlinearities can be perfectly recovered at the remote estimator. The proposed scheme is also compared with various baselines and we show that significant performance gains can be achieved.

Unfalsified Adaptive Control for Nonlinear Time-Varying Plants

The Battistelli–Hespanha–Mosca–Tesi (BHMT) adaptive reset switching algorithm is enhanced to admit bumpless transfer and to control a nonlinear time-varying plant using the broad class of two-degree-of-freedom nonlinear time-varying controllers. Performance, including stability and exponential stability, is proved given only that the adaptive stabilization problem is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\lambda$</tex-math></inline-formula> -feasible, which means at every time, there exists at least one exponentially stabilizing controller. We relax two restrictive BHMT assumptions: i) the plant is linear time-invariant (LTI) over most intervals and has finite order and ii) each controller is LTI. And, we expand the scope to include a broad class of bumpless switching algorithms. An example is provided to support the improved results.

A Unified Rule-Based Small-Signal Modelling Technique for Two-Switch, Non-Isolated DC–DC Converters in CCM

The inherent non-linear behavior of switch-mode power supplies complicates the task of computing their linear models, which are essential for a model-oriented control design of DC–DC converters. In a model-oriented control design approach, the accuracy of the plant model directly influences the performance of the control system as the plant parameters tend to be linked to the controllers’ gains. Moreover, the extractions of linear dynamic models of high-order non-linear plants such as DC–DC converters are laborious and mathematically intractable. Therefore, in this paper, a generalized expression that represents either the audio-susceptibility or the control-to-output voltage transfer function for voltage-mode control is proposed. The proposed generalization reduces the task of computing the small-signal model of a given converter to simple calculations of coefficients of generalized transfer function/expression. It is shown that the coefficients of the generalized model can be deduced by inspection, directly from the circuit diagram, allowing the whole model to be computed by inspection. Additionally, the proposed modelling technique will be shown to have secondary use of verifying accuracy even when conventional modelling techniques such as state-space averaging or circuit averaging are used.

Event‐triggered control of quasi‐LPV systems with communication delays

AbstractThis paper addresses the dynamic periodic event‐triggered control for local stabilization of nonlinear networked control systems with communication delays. Based on a polytopic quasi‐linear parameter‐varying (quasi‐LPV) model of the nonlinear plant and the Lyapunov–Krasovskii stability theory, a local stability analysis condition is established. Then a constructive co‐design condition is proposed to jointly design the state‐feedback control law and the trigger rule. The local asymptotic stability of the closed‐loop equilibrium point of interest is ensured with a guaranteed region of attraction where trajectories remain inside even in the presence of communication delays. An optimization procedure is proposed to perform the co‐design considering the objectives of enlarging the guaranteed region of attraction and reducing the number of transmissions. Numerical examples indicate a trade‐off between these two objectives. Also, the examples illustrate the effectiveness of the proposed dynamic event‐triggered control co‐design approach over both its static counterpart and periodic time‐triggering mechanisms.

A stochastic optimization framework for integrated scheduling and control under demand uncertainty

Increased globalization and energy market deregulation are requiring process industries to respond more rapidly to fluctuations in demand levels, and utility and raw material prices, in order to remain competitive. In this study, a two-stage stochastic approach is proposed to account for demand uncertainty in a closed-loop dynamic real-time optimization (CL-DRTO) formulation that includes scheduling decisions. The CL-DRTO problem utilizes a prediction of the closed-loop response of the plant under the action of constrained MPC. The CL-DRTO system is executed in a rolling horizon fashion to compute economically optimal operation that is communicated to the plant through set-point trajectories assigned to the plant MPC. Nonlinear plant models are approximated using linear and piecewise affine (PWA) approximations, allowing the integrated CL-DRTO problem to be formulated as a mixed-integer linear program (MILP). Case studies demonstrate significantly higher expected profit using the proposed formulation than with a deterministic formulation utilizing the expected demand.

Adaptive event-triggered finite-time [formula omitted] control for fuzzy semi-Markovian jump systems with immeasurable premise variables

This paper addresses the adaptive event-triggered finite-time H∞ control problem of Takagi-Sugeno fuzzy semi-Markovian jump systems with immeasurable premise variables. Firstly, different from some existed works, the restrictions of measurable system states and measurable premise variables of nonlinear plant are removed and the fuzzy observer is designed to estimate unmeasurable system states. Then, a novel adaptive event-triggered scheme is firstly proposed to reduce the number of data transmission while ensuring the reliable system performance. Subsequently, the asynchronous problem about premise variables, namely, the premise variables of fuzzy system are not consistent with premise variables of fuzzy event-triggered controller is dealt with by utilizing an asynchronous method. By applying the delay system method, free-weighting matrix approach and slack matrix variables, novel sufficient conditions are derived to guarantee the finite-time H∞ performance of the closed-loop system, where the nonlinear terms caused by network-induced delay and partly unknown transition rates can be tackled by using suitable method. Finally, the single-link robot arm system is presented to affirm the efficiency of the obtained theoretical results.

An arbitrary-order continuous sliding mode control technique for nonlinear PWR-type nuclear power plants

This paper presents an arbitrary order continuous-time sliding mode controller based on the super-twisting algorithm for a nonlinear pressurized water nuclear power plant. A proportional-derivative terminal sliding surface is designed to achieve the finite time convergence and to enhanced the tracking performance. The proposed controller is chattering free, which is always preferable in most of the practical applications and, it is robust against Lipschitz in time uncertainties. The implementation of the proposed controller requires only the information about the system output, and thus, it is most suitable for large scale complex systems, such as nuclear power plants. Superiority of the proposed controller over some conventional control techniques in the presence of uncertainties is shown with the help of simulation results in the MATLAB/Simulink environment.

Control-Enabling Adaptive Nonlinear System Identification

In this article, we rely on the theoretical foundations of radial basis function neural networks to form an adaptive parameter estimation problem, which we solve using the recently introduced prescribed performance control methodology. Such combination results in a compact user-configurable adaptive nonlinear system identification methodology that can be used to retrieve the open-loop nonlinear plant dynamics in any compact region of interest.

Adaptive Critics for Decentralized Stabilization of Constrained-Input Nonlinear Interconnected Systems

This article considers the decentralized stabilization problem of continuous-time nonlinear systems subject to unmatched interconnections and asymmetric input constraints. Initially, with the nonquadratic value functions being introduced to constrained auxiliary subsystems, the decentralized stabilization problem is converted into an array of nonlinear optimal control problems. It is proved that all solutions of these nonlinear optimal control problems together assure asymptotic stability of the entire system. Then, in the framework of adaptive critics, the critic-only architecture is built to solve the Hamilton–Jacobi–Bellman equations associated with these solutions. The critic-only architecture is implemented via critic neural networks (NNs) with their weight vectors being tuned through an improved gradient descent method. A remarkable feature of the present gradient descent approach is that it simultaneously utilizes previously stored and instantaneous state data, which makes the persistence of excitation conditions relaxed. After that, with Lyapunov’s techniques being employed, asymptotic stability of the closed-loop auxiliary subsystems and uniform ultimate boundedness of the critic NNs’ weight estimation errors are demonstrated. Finally, simulations of an unmatched interconnected nonlinear plant are provided to validate the present decentralized control method.

Event-triggered output feedback dissipative control of nonlinear systems under DoS attacks and actuator saturation

This paper presents a novel event-triggered dynamic output feedback dissipative control of nonlinear systems under intermittent denial-of-service (DoS) attacks and actuator saturation. Firstly, based on attack information, a secure event-triggered mechanism (ETM) is introduced, which not only saves systems resources but also is Zeno-free and resilient to DoS attacks. Secondly, a switched T–S fuzzy closed-loop system model is built, which unifies the parameters of nonlinear plant, noises, ETM, DoS attacks, switched output feedback fuzzy controller, and actuator saturation all in one framework. Thirdly, low conservative exponential stability criteria are derived while guaranteeing strict , , -dissipativity, and hence the relationships between system performance and factors such as DoS attacks, secure ETM, noises and actuator saturation are established. Further, sufficient conditions are given for the co-design of the switched output-based fuzzy controller and the secure ETM. Finally, the effectiveness of the proposed method is confirmed by numerical examples, achieving over 92% system resources.

Shaping transient response of nonlinear systems to satisfy a class of integral constraints

AbstractWe consider the problem of shaping the transient step response of nonlinear systems to satisfy a class of integral constraints. Such constraints are inherent in hybrid energy systems consisting of energy sources and storage elements. While typical transient specifications aim to minimize overshoot, this problem is unique in that it requires the presence of an appreciable overshoot to satisfy the foregoing constraints. The problem was previously studied in the context of linear systems and this article extends that work to nonlinear systems. A combined integral and feedforward control, that requires minimal knowledge of the plant model, is shown to make the system amenable to meeting such constraints. Broadly, the compensation is effective for nonlinear plants with stable open‐loop step response and a positive DC gain. However, stability of the resulting closed‐loop system mandates bounds on the integral gain. In this regard, we state and prove generalized stability theorems for first and higher‐order nonlinear plants.