Nonlinear Plant Research Articles

Design of fuzzy dynamic decoupler for a class of Two-Inputs Two-Outputs nonlinear systems

This paper deals with the problem of designing a dynamic decoupler for a class of Two-Inputs Two-Outputs nonlinear MIMO systems with experimentally modeled dynamics. The work describes the well-known linear theory of dynamic decoupling of TITO plants and discusses problems related to its application to nonlinear systems. The solution of constructing a fuzzy dynamic decoupler with two possible approaches is proposed. The paper gives a practical example of the synthesis of such a system for the air heater, which is an example of nonlinear thermal plant.

Relaxed Stability and Non-weighted $$L_2$$-Gain Analysis for Asynchronously Switched Polynomial Fuzzy Systems

AbstractThis paper concerns the stability and non-weighted $$L_2$$ L 2 -gain analysis issues for the switched systems subject to asynchronous switching and external disturbance. By taking full advantage of the admissible edge-dependent average dwell time (AED-ADT) switching signal, a stability criterion of asynchronously switched systems is proposed to achieve a lower non-weighted $$L_2$$ L 2 -gain index than the existing results. Furthermore, the dynamics of switched systems are described by using the polynomial fuzzy model instead of the T-S fuzzy model, which can represent a wider range of nonlinear plants. For such asynchronously switched polynomial fuzzy systems, the relaxed conditions are derived through the membership-function-dependent (MFD) technique and novel high-order multiple Lyapunov functions (MLFs) construction method to guarantee less conservative stability and non-weighted $$L_2$$ L 2 -gain results. Finally, the superiority of the proposed approaches are verified through two simulation examples.

Stability enhancement for seamless control in networked microgrids with energy storage: Nonlinear spatio-temporal control perspective

The integration of distributed energy resources into modernized networked microgrids, combined with the increasing variability in load dynamics, presents significant stability challenges. This research offers a comprehensive analysis of the stability of cascaded interactions in nonlinear multi-timescale systems, including grid-following and grid-forming inverters. The proposed grid-forming controller, integrated with energy storage systems and a nonlinear Lyapunov function, facilitates seamless control and stabilization of these inverters. This approach addresses challenges related to nonlinear plant and network dynamics, uncertainties in state variables, and unmodeled system dynamics. The closed-loop control system ensures asymptotic spatio-temporal dynamical stability through constrained time state convergence to stable equilibrium points while minimizing control oscillations. Comparative analysis and high-fidelity hardware-in-loop emulations demonstrate the superior performance of the proposed controller over traditional ones in diverse dynamic scenarios. Its ability to rapidly reject disturbances, minimize overshoot, converge efficiently, and enhance power quality confirms its effectiveness and highlights its potential for real-world applications.

Energy-efficient semi-continuous distillation of a ternary mixture using combined tracking-economic model predictive control

Distillation is an energy-intensive separation technique. Semicontinuous distillation has gained attention as a cost-effective alternative to conventional multi-column distillation of multi-component mixtures. However, the cyclic behavior of semicontinuous distillation poses operational challenges considering cost of energy and need for maintaining consistent product purity. The challenge is addressed in this work by proposing a dual-objective Model Predictive Controller (MPC) that handles both product purity and energy consumption through a combined tracking-economic objective function. The proposed MPC features Extended Kalman Filter for state estimation and the successive linearization technique for building the prediction model. The nonlinear plant model is implemented in OpenModelica, which is linked to Matlab for MPC implementation. The effectiveness of the proposed MPC is demonstrated on semicontinuous distillation of Benzene, Toluene, and o-Xylene. The dual-objective MPC is shown to yield an energy saving of 8% per feed processed compared with conventional tracking MPC, while also performing well under process disturbances. It is also shown that the feed processed during a certain time period is 8% higher in the dual-objective MPC than the tracking MPC. The considerable economic improvement is gained without degrading the product purities, indicating that dual-objective MPC is an effective approach to energy-efficient operation of semicontinuous distillation.

Enhancement of DDST-MFAC for tracking performance by using dynamic data reconciliation

Abstract Model-free adaptive control (MFAC) stands out as an effective data-driven method for addressing nonlinear problems in industrial processes. To maintain good control performance, a data-driven set-point tuning (DDST) method is used to update the virtual set-point of the MFAC system. The DDST-based MFAC (i.e. DDST-MFAC) constantly approaches the target of the process through the nonlinear set-point tuning method. However, due to equipment errors and external interference, industrial sensors often suffer from measurement noise, which can have adverse effects on the control performance. In this article, an available dynamic data reconciliation (DDR) technique is adopted to improve the tracking performance of the DDST-MFAC, which suppresses the impact of process noise by using predicted information and measured data to achieve high-precision requirements for controlling nonlinear processes. Finally, considering both Gaussian and non-Gaussian distribution of measurement noise, the effectiveness of the proposed method was verified through the simulation of a nonlinear nonaffine plant. It is also applied to the steam-water heat exchange process, the control result is improved ultimately.

Improved-equivalent-input-disturbance-based preview repetitive control for Takagi–Sugeno fuzzy system with state delay

This paper designs a preview repetitive control (PRC) policy for a class of Takagi–Sugeno (T–S) fuzzy systems with time-varying delay and external disturbances. First, the T–S fuzzy model is employed to represent a nonlinear plant, once the nonlinear plant is represented by a T–S fuzzy model, a fuzzy improved-equivalent-input-disturbance (IEID)-based PRC law can be designed to achieve better tracking performance and disturbance rejection. Next, based on a new equality constraint, we derive a continuous-discrete two-dimensional (2D) system that paves the way to solve the design problem of the IEID-based PRC law using linear matrix inequality (LMI) approach. Then, by solving LMIs, the gains of the controller and state observer can be obtained. Finally, a numerical example is included to show the effectiveness of the proposed method.

Online Adaptive Neural Observer for Prescribed Performance Hyper-Chaotic Systems

This paper proposes a new neural-based algorithm applied to online identifying, observing, and adaptively controlling of uncertain nonlinear systems via which the system transient and residual values independently regulated. The Lyapunov stability concept is used for enhancing the control performance. Especially, distinguished from recent related studies, not only identified model but the learning method and control rules are also innovatively implemented through which it independently separates the transient-time regulation from residual error adjustment.Sequentially, an advanced adaptive neural controller for an uncertain nonlinear plant with state feedback is implemented using the open-loop estimation result. The key contribution of the online estimator will be verified in this proposed control algorithm. Eventually, as to verify the prescribed performance and the flexibility of the suggested control approach, the estimation and control of an uncertain hyper-chaotic weld plant will be tested.

Real time adaptive probabilistic recurrent Takagi-Sugeno-Kang fuzzy neural network proportional-integral-derivative controller for nonlinear systems

This paper presents an adaptive probabilistic recurrent Takagi-Sugeno-Kang fuzzy neural PID controller for handling the problems of uncertainties in nonlinear systems. The proposed controller combines probabilistic processing with a Takagi-Sugeno-Kang fuzzy neural system to proficiently address stochastic uncertainties in controlled systems. The stability of the controlled system is ensured through the utilization of Lyapunov function to adjust the controller parameters. By tuning the probability parameters of the controller design, an additional level of control is achieved, leading to enhance the controller performance. Furthermore, it can operate without relying on the system's mathematical model. The proposed control approach is employed in nonlinear dynamical plants and compared to other existing controllers to validate its applicability in engineering domains. Simulation and experimental investigations demonstrate that the proposed controller surpasses alternative controllers in effectively managing external disturbances, random noise, and a broad spectrum of system uncertainties.

Simulation and Controller Design for a Fish Robot with Control Fins.

In this paper, a nonlinear simulation block for a fish robot was designed using MATLAB Simulink. The simulation block incorporated added masses, hydrodynamic damping forces, restoring forces, and forces and moments due to dorsal fins, pectoral fins, and caudal fins into six-degree-of-freedom equations of motion. To obtain a linearized model, we used three different nominal surge velocities (i.e., 0.2 m/s, 0.4 m/s, and 0.6 m/s). After obtaining output responses by applying pseudo-random binary signal inputs to a nonlinear model, an identification tool was used to obtain approximated linear models between inputs and outputs. Utilizing the obtained linearized models, two-degree-of-freedom proportional, integral, and derivative controllers were designed, and their characteristics were analyzed. For the 0.4 m/s nominal surge velocity models, the gain margins and phase margins of the surge, pitch, and yaw controllers were infinity and 69 degrees, 26.3 dB and 85 degrees, and infinity and 69 degrees, respectively. The bandwidths of surge, pitch, and yaw control loops were determined to be 2.3 rad/s, 0.17 rad/s, and 2.0 rad/s, respectively. Similar characteristics were observed when controllers designed for linear models were applied to the nonlinear model. When step inputs were applied to the nonlinear model, the maximum overshoot and steady-state errors were very small. It was also found that the nonlinear plant with three different nominal surge velocities could be controlled by a single controller designed for a linear model with a nominal surge velocity of 0.4 m/s. Therefore, controllers designed using linear approximation models are expected to work well with an actual nonlinear model.

Stability analysis of interval type-2 sampled-data polynomial fuzzy-model-based control system with a switching control scheme

The stability of an interval type-2 (IT2) sampled-data (SD) polynomial fuzzy-model-based control system with a switching control scheme is studied in this paper. The uncertain nonlinear plant is depicted via an IT2 polynomial fuzzy model. To realize control, a switching IT2SD polynomial fuzzy controller is generated. This paper adopts a switching control scheme with a variable sampling period. The modeling domain consists of several sub-domains, and each sub-domain corresponds to a local IT2SD polynomial fuzzy controller. These local IT2SD polynomial fuzzy controllers form the switching IT2SD polynomial fuzzy controller. To aid in the stability analysis, this paper adopts a looped-functional-based technique. The imperfect premise matching concept is brought in to solve the mismatch dilemma caused by the SD control strategy and uncertainties. For decreasing the conservativeness, this paper takes into account the state information as well as the information of IT2 membership functions. The stability analysis is performed for each sub-domain, providing the potential for further relaxation. As polynomials exist in the stability conditions, this paper employs the sum-of-squares method for the stability investigation. The simulation outcomes confirm the efficacy of the proposed method.

Neural Network Iterative Learning for SISO Non-Affine Control Systems

This work introduces an identification scheme capable of obtaining the unknown dynamics of a nonlinear plant process. The proposed method employs an iterative algorithm that prevents confinement to a sole trajectory by fitting a neural network over a series of trajectories that span the desired subset of the state space. At the core of our contributions lie the applicability of our method to open-loop unstable systems and a novel way of generating the system’s reference trajectories, which aim at sufficiently stimulating the underlying dynamics. Following this, the prescribed performance control (PPC) technique is utilized to ensure accurate tracking of the aforementioned trajectories. The effectiveness of our approach is showcased through successful identification of the dynamics of a two-degree of freedom (DOF) robotic manipulator in both a simulation study and a real-life experiment.

Online learning of stable robust adaptive controllers design based on data-dependent feedback linearization with application to rotary inverted pendulum

This study introduces an online (supervised) learning method to design nonlinear auto-regressive moving average (NARMA) controllers for feedback-linearized nonlinear single-input single-output (SISO) systems. The algorithm ensures Schur stability of the overall closed-loop system and provides adaptiveness and robustness for the NARMA controllers. The first stage of the method derives, in a data-dependent way, a feedback-linearized model of the nonlinear plant by using its input and output sample pairs. The method’s second stage, which constitutes the novel part of the presented study, builds up an online learning scheme for the linear auto-regressive moving average (ARMA) controller based on an already learned feedback-linearized model of the nonlinear plant. During online supervised learning, ARMA parameters of the feedback-linearized SISO plant model and the closed-loop ARMA model are computed by minimizing the plant identification and the closed-loop system tracking errors. Both errors are defined as ℓ1,ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\ell}}_{1,{\\varvec{\\varepsilon}}}$$\\end{document}, namely ε-insensitive loss functions that provide NARMA controller the robustness against noise and outliers. The proposed online learning control algorithm is applied to a rotary inverted pendulum model and to a real rotary inverted pendulum setup. The tracking performance of the developed controller is compared with those of the linear quadratic regulator and coupled sliding mode controller in terms of mean square error.

Iterative real-time optimization of a membrane pilot plant

In this paper, we describe the implementation and experimental validation of iterative real-time optimization (RTO) at a continuously operated membrane separation pilot plant. The objective is to achieve an economically optimal operation using the transmembrane pressure and the feed flow rate as adjustable operational parameters (set-points for the lower-level plant controllers). In spite of the popularity of RTO based on rigorous nonlinear plant models in the research literature, its practical use so far remains limited to large scale plants in the petrochemical industries. The main issue behind the limited application of RTO schemes is the necessary effort to derive and maintain sufficiently accurate models of the plants. In case of a significant plant-model mismatch, the results are not reliable, the optimal performance is not reached and even systematic violations of constraints may occur. The applicability of RTO could be extended significantly if simple process models sufficed for its successful application. Then an adaptation of the model or of the optimization problem to the real behavior of the plant is necessary to achieve an optimal operation. For this example, we tackle this issue by applying an iterative scheme called modifier-adaptation with quadratic approximation in combination with model adaptation to ensure the convergence of the plant to the true process optimum despite the fact that the model has deficiencies. The experimental results show that, in spite of a considerable plant-model mismatch, the presented RTO scheme is capable of boosting the process economics.

Nonlinear feedforward controller design of gasoline engine air-path system for reducing engine torque overshoot

In gasoline engines, the amount of fresh air in the cylinder becomes temporarily excessive owing to the slow response in exhaust gas recirculation (EGR) gas under a high EGR ratio. This phenomenon should be avoided, as it causes an engine torque overshoot because the amount of fuel also increases to follow the stoichiometric ratio, and can cause discomfort to the driver. In this study, we investigate reducing torque overshoot using a feedforward controller, which is a simple and effective method for improving the response of a control system. The feedforward controller is typically designed based on the inverse of the plant model. However, designing a feedforward controller for a high-order and nonlinear plant, such as an engine air-path system, can be challenging. Therefore, we exploit the fact that if a given nonlinear system satisfies the flatness property, a feedforward controller based on the inverse model can be easily obtained. The effectiveness of the proposed feedforward controller is evaluated through simulations.

A comparison of alternative models for solving a non-linear single plant Hydro Unit Commitment problem

A wide range of real world optimization problems involves continuous decisions and non-linearities. Each non-linear component of such problems can be modeled either linearly or non-linearly, considering or not additional integer variables. This results into different modeling choices that can drastically impact the solution time and quality. In this paper, we evaluate representative modeling alternatives, including common models from the literature as well as new models featuring less common functions. The single plant Hydro Unit Commitment problem (1-HUC) is the considered non-linear use case. Among the non-linearities of the 1-HUC, we focus on those involved in the power production, more precisely the head effect and the turbines efficiency. The power is defined as a two-dimensional non-convex and non-concave function of the water flow and head decision variables, the latter being itself a one-dimensional concave function of the turbined volume. We consider both the general problem and a common special case, assuming that the water head is fixed. Several available solvers are used for each non-linear model and the best virtual solver is retained to focus on the model capabilities rather than on the solver performance. Based on the numerical experiments, three models stand out as the most efficient in terms of computational time, solution quality and feasibility, sometimes in a counter-intuitive manner. For each of these models, a solver is highlighted as the most adequate.

Optimal finite-dimensional controller of the stochastic differential object’s state by its output II. Stochastic measurements and separation theorem

Consideration is continued of the problem of the inertial control law by the output synthesis of a continuous nonlinear stochastic plant, which is optimal on average and on a finite time interval, and works with the desired speed. An algorithm for synthesizing the optimal structure of a dynamic controller of a selected finite order, obtained in the first part of the article for the case of accurate measurements of a of the control object’s state variables part, is presented. Its application is demonstrated in detail for the case when the state variables of an object are measured with random errors. Using the example of a linear-quadratic-Gaussian problem, it is shown that the proposed controller of the corresponding order also satisfies the well-known separation theorem.

Adaptive control for shape memory alloy actuated systems with applications to human-robot interaction.

Shape memory alloy (SMA) actuators are attractive options for robotic applications due to their salient features. So far, achieving precise control of SMA actuators and applying them to human-robot interaction scenarios remains a challenge. This paper proposes a novel approach to deal with the control problem of a SMA actuator. Departing from conventional mechanism models, we attempt to describe this nonlinear plant using a gray-box model, in which only the input current and the output displacement are measured. The control scheme consists of the model parameters updating and the control law calculation. The adaptation algorithm is founded on the multi-innovation concept and incorporates a dead-zone weighted factor, aiming to concurrently reduce computational complexities and enhance robustness properties. The control law is based on a PI controller, the gains of which are designed by the pole assignment technique. Theoretical analysis proves that the closed-loop performance can be ensured under mild conditions. The experiments are first conducted through the Beckhoff controller. The comparative results suggest that the proposed adaptive PI control strategy exhibits broad applicability, particularly under load variations. Subsequently, the SMA actuator is designed and incorporated into the hand rehabilitation robot. System position tracking experiments and passive rehabilitation training experiments for various gestures are then conducted. The experimental outcomes demonstrate that the hand rehabilitation robot, utilizing the SMA actuator, achieves higher position tracking accuracy and a more stable system under the adaptive control strategy proposed in this paper. Simultaneously, it successfully accommodates hand rehabilitation movements for multiple gestures. The adaptive controller proposed in this paper takes into account both the computational complexity of the model and the accuracy of the control results, Experimental results not only demonstrate the practicality and reliability of the controller but also attest to its potential application in human-machine interaction within the field of neural rehabilitation.

Event‐triggered model reference adaptive control system design for SISO plants using meta‐learning‐based physics‐informed neural networks without labeled data and transfer learning

SummaryThis paper examines the controllability of a novel Lyapunov‐based model reference adaptive control (MRAC) system designed with a meta‐learning‐based physics‐informed neural network (MLPINN) for linear and nonlinear single‐input and single‐output (SISO) plants without labeled data (MLPINN‐MRAC system). It is devised with the benefits of several techniques: the integration of the identification process in a training mode into an online control mode (straightforward design); no labeled data generation for online identification by a physics‐informed neural network; the prevention of degradation in tracking performance by meta‐learning, as the system triggers a meta‐learning process only when an error threshold detects the deterioration (high efficiency and the reduction of computation cost); quick adaptation to new inputs and an updated control input for each sub‐time span by transfer learning. It is worth noting that the frequency of the meta‐learning event detection significantly affects the step response stability of the nonlinear plant. To achieve a better quality of the stabilization, more frequent event detection is necessary for both beginning and end intervals in control. Sixteen triggering events are enough to shape the acceptable step response of the nonlinear plant, and 44 triggering events achieve the plant's desired step response with its minor modeling error. While, as for the linear plant, a single triggering event is sufficient to attain its tolerable step response and modeling error, implying that intensive event detection is not critical in the identification. It is obvious that the MLPINN‐MRAC system functions well and is more beneficial and efficient for the nonlinear plant.

On the Global Stability of Nonlinear Hurwitz Control Systems

The problem of designing nonlinear control systems by the algebraic polynomial-matrix method using quasilinear models is considered. The quasilinear models of nonlinear plants are easily created on the basis of their nonlinear equations in the Cauchy form. To create these models only the differentiability of the plants nonlinearities is required. The solution to the design problem of the nonlinear Hurwitz control systems using the algebraic polynomial-matrix method is available if the quasilinear model of the plant is controllable. The design with application of this method consists of creating the quasilinear model of the nonlinear plant, generating several polynomials, composing and solving a system of linear algebraic equations. The theorem about the global stability of the equilibrium of the nonlinear systems, represented in the quasilinear model, is proved by the method of Lyapunov functions. The numerical examples of the design of nonlinear Hurwitz control systems are given. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article is concerned with the creation of stable nonlinear control systems with nonlinear elements since the linear systems can’t fulfill the quality requirements demanded from modern control systems. Additionally, the known design methods of nonlinear systems, such as the input-state feedback linearization, backstepping, passivity and others, require the transformation of the original nonlinear equations of the plant into some special form. These transformations are often very difficult to find and to execute. A new algebraic polynomial-matrix design method of the nonlinear control systems using the quasilinear models of nonlinear plants is proposed in the article. This method can be applied if the nonlinearities of the plant are differentiable, and the quasilinear model of the plant is controllable. The theorem about global stability of the equilibrium is proved for the systems designed with this approach. The quasilinear models are easily created on the basis of the original equations in the Cauchy form for a given nonlinear plant. The algebraic polynomial-matrix design method is very simple: the quasilinear model is created; several polynomials are calculated with the use of this model and the linear algebraic equations system is composed. The solution of this system allows us to write down the expression which defines the control law as a nonlinear function of the plant’s state variables. This system will be globally or locally stable if the conditions of the theorem or the corollaries, proved in this article, are satisfied. The numerical examples illustrate the application of the suggested approach to the design of nonlinear Hurwitz control systems for the nonlinear plants. The main advantages of this approach: the quasilinear models are created quite easily; the nonlinear control law is found as a solution to the system of linear equations. The results can be applied to the creation of nonlinear control systems of nonlinear plants in many industries: shipbuilding, aircraft construction, automobile construction, agriculture and many others.

PI Tracking Control of a Nonlinear plant

The tracking control design for nonlinear plants by model inversion, following the Linear Algebra Based methodology, usually assumes a proportional to the error approaching of the process variables to the references evolution as a design criterion for the control. In this paper, by using the well-known properties of the integral action, a PI-like control is assumed, countering constant disturbances and model parameters uncertainty. The application to a simple mass-spring nonlinear system illustrates the procedure.