Nonlinear Control Design Research Articles

Nonlinear recursive gain asymptotic tracking controller design for hydraulic turbine regulating systems

AbstractThis paper focuses on the nonlinear asymptotic tracking control for a hydraulic turbine regulating system (HTRS). The proposed control approach combines a recursive gain control scheme with an adaptive technique to achieve asymptotic tracking. An important characteristic feature of the proposed controller is the incorporation of a smooth function with a time‐varying function that is integrable and positive. This function provides the developed controller with sufficient power to achieve asymptotic tracking, whereas the recursive gain control alone can ensure that tracking errors converge exponentially to zero within balls of any arbitrarily small radii. The simulation results demonstrate the efficacy of the presented control technique, which outperforms backstepping, command‐filtered backstepping, dynamic surface, synergetic control designs; deals with the “explosion of complexity” problem; and simultaneously achieves asymptotic tracking. Furthermore, even though the HTRS parameters vary, the proposed technique is capable of providing consistent control performance. As a result, the presented controller is unaffected by changes in the system's parameters.

Lyapunov-based nonlinear boundary control design with predefined convergence for a class of 1D linear reaction-diffusion equations

In this paper, we treat the problem of Lyapunov-based nonlinear boundary stabilization of a class of one-dimensional reaction-diffusion systems with any predefined convergence (asymptotic or non-asymptotic). As an application, we focus on the non-asymptotic notions (finite-time and fixed-time) for which we give some particular explicit control designs followed by some numerical simulations. The key idea of our approach is to use a “spatially weighted L2-norm” as a Lyapunov functional to design a nonlinear controller and to ensure stability with any desired convergence.

Generalized robust MPC with zone-tracking

We propose a robust nonlinear model predictive control design with generalized zone tracking (ZMPC) in this work. The proposed ZMPC has guaranteed convergence into the target zone in the presence of bounded disturbance. The proposed approach achieves this by modifying the actual target zone such that the effect of disturbances is rejected. A control invariant set (CIS) inside the modified target zone is used as the terminal set, which ensures the closed-loop stability of the proposed controller. Closed-loop stability analysis is presented. Simulation studies based on a continuous stirred tank reactor (CSTR) are performed to validate the effectiveness of the proposed ZMPC.

Fault-tolerant design of non-linear iterative learning control using neural networks

The design of neural-network-based iterative learning control for non-linear systems is addressed in the setting of a fault tolerant control regime. Taking advantage of the repetitive character of the control task, the inherent uncertainty related to a potential faulty system state can be properly accommodated in terms of a data-driven iterative learning scheme with neural networks used for forward/inverse modeling as well as for controller synthesis. The resulting control technique is supposed to be flexible enough to accurately compensate the faults occurring on both the sensors and actuators and, additionally, take into account the disturbances and noise acting on the system. A complete characterization of the novel fault-tolerant iterative learning scheme is provided including system identification, fault detection and accommodation. Also, the painstaking convergence analysis is presented and the resulting sufficient conditions can be constructively used to determine the update of control law in the consecutive process trial. The excellent performance of the developed control scheme is illustrated by a nontrivial example of tracking control for a magnetic brake system on various scenarios involving actuator and/or sensor faults.

Laplace transform and nonlinear control design for quasi‐projective synchronization for Caputo inertial delayed neural networks

The quasi‐projective synchronization problems for Caputo inertial neural networks (INNs) with delays are analyzed in this article. The considered model is transformed into two subsystems by selecting a suitable variable substitution. To realize synchronization, a novel fractional differential inequality is established, and the new lemma is derived via Laplace transform. Applying the given lemmas and inequality techniques, the synchronization conditions are inferred through different nonlinear feedback controllers. From the derivation of the theorems, it can be seen that the designed controllers are more extensive and efficacious. Furthermore, the error bound is validly estimated, and the validity of obtained theorems is illustrated by the numerical simulations.

Design of a Takagi–Sugeno Fuzzy Exact Modeling of a Buck–Boost Converter

DC–DC converters are used in many power electronics applications, such as switching power supply design, photovoltaic, power management systems, and electric and hybrid vehicles. Traditionally, DC–DC converters are linearly modeled using a typical operating point for their control design. Some recent works use nonlinear models for DC–DC converters, due to the inherent nonlinearity of the switching process. In this sense, a standout modeling technique is the Takagi–Sugeno fuzzy exact method due to its ability to represent nonlinear systems over the entire operating range. It is more faithful to system behavior modeling, and allows a nonlinear closed-loop control design. The use of nonlinear models allows the testing of controllers obtained by linear methods to operate outside their linearization point, corroborating with robust controllers for specific applications. This work aims to perform the exact fuzzy Takagi–Sugeno modeling of a buck–boost converter with non-ideal components, and to design a discrete proportional–integral–derivative (PID) controller from the pole cancellation technique, obtained linearly, to test the controller at different operating points. The PID control ensured a satisfactory result compared with the stationary value of the different operating points, but it did not reach the desired transient response. Since the proposed model closely represents the operation of the buck–boost converter by considering the components’ non-idealities, other control techniques that consider the system’s nonlinearities can be applied and optimized later.

Quadrotor Neural Network Adaptive Control: Design and Experimental Validation

This letter presents the design and experimental study of an adaptive nonlinear controller for Unmanned Aerial Vehicles (UAVs) in the presence of unknown time-varying disturbances, and model parametric uncertainty. We employ an adaptive Neural Network (NN), used to approximate the partially unknown system, in tandem with a simple controller designed for trajectory tracking, not of the center of mass, but of a point located along the UAV's vertical body axis. This strategy allows: (i) to avoid the two-subsystems control paradigm generally adopted by conventional UAV controllers; (ii) all control inputs to be defined at once; and (iii) to lump all unknown dynamics from both translational and rotational levels into a single vector term. The weights of the NN are determined online by an adaptive law based on the Lyapunov synthesis method. The tracking and adaptation errors are shown to be uniformly ultimately bounded. Simulation and experimental results, including comparison data, are provided to validate and assess the proposed control solution.

Boundary Fuzzy Output Tracking Control of Nonlinear Parabolic Infinite-Dimensional Dynamic Systems: Application to Cooling Process in Hot Strip Mills

This paper utilizes a combination of integral control, fuzzy control, and observer-based output feedback control to deal with the issue of nonlinear output tracking control (OTC) design for nonlinear infinite-dimensional dynamic systems. The system dynamics model is represented by a semi-linear parabolic partial differential equation (PDE) with boundary control and non-collocated boundary measurement. Initially, a Takagi-Sugeno (T-S) fuzzy parabolic PDE model is constructed to surmount the OTC design difficulty from the infinite-dimensional nonlinear system dynamics. Subsequently, a fuzzy-observer-based OTC law is proposed via the T-S fuzzy PDE model and the integral control approach. Here, the integral control ensures asymptotic output regulation, and the observer-based output feedback control is employed to conquer the stabilizing control design difficulty caused by the non-collocation between control actuation and measurement. It is shown via the Lyapunov technique with variants of vector-valued Poincaré-Wirtinger's inequality that the suggested fuzzy OTC law drives the measurement output to asymptotically track the desired reference signal and ensures the boundedness of the resulting closed-loop system, provided that a sufficient condition given in the form of linear matrix inequalities is fulfilled. Moreover, the proposed fuzzy-model-based OTC design is also revised for the exponential stabilization case. Finally, extensive simulation results for a numerical example and a cooling process in hot strip mills are provided to examine the effectiveness and merit of the proposed fuzzy OTC scheme.

Nonlinear controller design for hydraulic turbine regulating systems via immersion and invariance

This paper proposes a nonlinear controller strategy for the frequency regulation of a hydraulic turbine regulating system (HTRS). An immersion and invariance (I&I) technique is utilised to develop the desired control law. The derived control method is used to guarantee that the equilibrium point is asymptotically stable. Furthermore, it can ensure that all overall closed-loop system trajectories are bounded. The feasibility and effectiveness of the technique are demonstrated using a nonlinear dynamical system of an HTRS connected to a single-machine infinite bus (SMIB) power system. The simulation results demonstrate that the technique is capable of regulating the frequency and improving dynamic performance despite large disturbances. It is capable of rapidly reducing oscillations and surpasses two known nonlinear controllers, namely the synergetic control and the backstepping control techniques. Additionally, despite the fact that the HTRS's parameters vary, the proposed technique is capable of providing consistent control performance. As a result, the presented controller is insensitive to variations in the system's parameters.

Design of Auto-Tuning Nonlinear PID Tracking Speed Control for Electric Vehicle with Uncertainty Consideration

This study presents a new auto-tuning nonlinear PID controller for a nonlinear electric vehicle (EV) model. The purpose of the proposed control was to achieve two aims. The first aim was to enhance the dynamic performance of the EV regarding internal and external disturbances. The second aim was to minimize the power consumption of the EV. To ensure that these aims were achieved, two famous controllers were implemented. The first was the PID controller based on the COVID-19 optimization. The second was the nonlinear PID (NPID) optimized controller, also using the COVID-19 optimization. Several driving cycles were executed to compare their dynamic performance and the power consumption. The results showed that the auto-tuning NPID had a smooth dynamic response, with a minimum rise and settling time compared to other control techniques (PID and NPID controllers). Moreover, it achieved low continuous power consumption throughout the driving cycles.

Computationally Efficient Stability-Based Nonlinear Model Predictive Control Design for Quadrotor Aerial Vehicles

This article presents the design of a stability-guaranteed nonlinear model predictive controller for quadrotor-type microaerial vehicles to operate robustly on fast trajectories. The basic controller structure operates without having to use terminal conditions in the optimization problem. As a result, the controller is computationally less demanding and provides more stable closed-loop performance than traditional nonlinear predictive control schemes. This article presents a detailed stability analysis without terminal costs or terminal constraints and proves the asymptotic stability and necessary conditions for the recursive feasibility of the system. This article derives the growth-bound sequence that enables obtaining the shortest possible prediction horizon for stability. The proposed analysis provides the necessary conditions to implement the controller while using the shortest stabilizing prediction horizon compared to major traditional predictive control schemes reported in the literature. This particular feature enables the proposed controller to perform fast optimization and, hence, the capability to implement fast trajectories using feedback regularization. In order to demonstrate the validity of this new proposed control scheme, first, several MATLAB simulations are conducted to demonstrate the improved performance of the controller especially when the quadrotor vehicle follows fast trajectories. Real-time lab experiments are also conducted to validate the performance of the proposed scheme for point stabilization (hovering) and trajectory tracking problems. The results show that the proposed scheme can stabilize the system with a relatively short prediction horizon, a fast convergence rate, and a small tracking error.

Least Square Support Vector Machines Laguerre Hammerstein Model Identification and Non-linear Model Predictive Controller Design for pH Neutralization Process

The ability to describe the nonlinear process dynamics is an essential feature of the Hammerstein model that paved more research and application studies in system identification and control. Using the Hammerstein model, this study shows an alternative approach to identify and control the highly nonlinear pH neutralization process. This Hammerstein model called Laguerre Least Square Support Vector Machines (LLSSVM) models the static nonlinearity with LSSVM and the linear part with Laguerre filter. The identified LLSSVM Hammerstein model performance evaluation with Mean Squared Error (MSE) and Variance Accounted For (VAF) is better than the Linear Laguerre model. We apply the identified LLSSVM Hammerstein model to implement a Nonlinear Model Predictive Controller (NMPC) to control the pH neutralization process. Then evaluated NMPC performance in terms of Integral Squared Error (ISE), Integral Absolute Error (IAE), and Total Variation (TV) and Control Effort (CE) parameters to verify its effectiveness in set-point tracking and disturbance rejection problems. The comparison of the NMPC with the Linear Laguerre Model-based Predictive Controller (LMPC) shows better performance of the NMPC than the LMPC. Results show that the LLSSVM Hammerstein model replicates the pH neutralization process well than the Linear Laguerre model. Also, the identified LLSSVM Hammerstein model provides an efficient NMPC than the LMPC for the pH neutralization process.

Accounting for magnetic saturation in designing a SRM speed controller for torque ripple minimization

This study established a nonlinear control design for switched reluctance motor (SRM) vehicle applications, using the backstepping approach. The suggested controller is established according to a model that consider magnetic saturation while reducing torque ripple and resulting in less vibrations. To optimize torque ripple, control angles are adjusted based on the machine speed and torque measurements. Indeed, a lookup table is constructed, offering the efficient control angles for various motor operating points. The suggested control technique was validated through simulation, exploiting an accurate MATLAB SRM model considering magnetic saturation effects. To illustrate the superiority of the suggested regulator, a comparison of its performance with a proportional-integral (PI) controller was performed. The acquired findings indicate the suggested regulator’s effectiveness.

An LMI framework for contraction-based nonlinear control design by derivatives of Gaussian process regression

Contraction theory formulates the analysis of nonlinear systems in terms of Jacobian matrices. Although this provides the potential to develop a linear matrix inequality (LMI) framework for nonlinear control design, conditions are imposed not on controllers but on their partial derivatives, which makes control design challenging. In this paper, we illustrate this so-called integrability problem can be solved by a non-standard use of Gaussian process regression (GPR) for parameterizing controllers and then establish an LMI framework of contraction-based control design for nonlinear discrete-time systems, as an easy-to-implement tool. Later on, we consider the case where the drift vector fields are unknown and employ GPR for functional fitting as its standard use. GPR describes learning errors in terms of probability, and thus we further discuss how to incorporate stochastic learning errors into the proposed LMI framework.

ACTUATOR AND SENSOR FAULT COMPENSATION USING PROPORTIONAL-PROPORTIONAL INTEGRAL OBSERVER FOR FUZZY TRACKING CONTROL OF PENDULUM-CART SYSTEM

The pendulum-cart system is a popular system plant as a case study in nonlinear control design and implementation. The controllability and system performance can be influenced by the effectivity of the actuator and sensor. However, actuator and sensor fault sometimes is inevitable and can be occurred during operation. This paper considers fault-tolerant control (FTC) to minimize the actuator and sensor fault. The control objective is to track the sinusoidal reference position of the cart while the pendulum is maintained upright in which the faulty actuator and sensor occurred. Takagi-Sugeno (T-S) fuzzy tracking control is designed based on a compensator scheme where the Proportional-Proportional Integral Observer (PPIO) is utilized for this scheme. The Linear Matrix Inequalities (LMIs) are used to calculate the controller and observer gains. The performance of the proposed controller is verified through simulation and experimental validation. The effectiveness of FTC in the case of actuator and sensor fault is given. The system responses for the compensated and uncompensated controllers (to track the reference signal) are compared. In the case of a sensor fault, only the compensated controller can converge to the reference signal. However, in the case of actuated fault, both compensated and uncompensated controllers converge to the reference signal but the error of the compensated controller is better than the other one.

Nonlinear Adaptive Optimal Controller Design for Anti-Angiogenic Tumor Treatment.

Angiogenesis is an important process in tumor growth as it represents the regime when the tumor recruits blood vessels from the surrounding tissue to support further tumor growth. Anti-angiogenic treatments aim to shrink the tumor by interrupting the vascularization of the tumor; however, the anti-angiogenic agents are costly and the tumor response to these agents is nonlinear. Simple dosing schemes, e.g., a constant dose, may yield higher cost or lower efficacy than an approach that considers the tumor system dynamics. Hence, in this study, the administration of anti-angiogenic treatment is considered as a nonlinear control problem. The main aim of the controller design is to optimize the anti-angiogenic tumor therapy, specifically, to minimize the tumor volume and drug dose. Toward this aim, two nonlinear optimal controllers are presented. The first controller ensures exponential tracking of a desired, optimal tumor volume profile under the assumption that all parameters in the system model are known. The second controller, on the other hand, assumes all the parameters are unknown and provides asymptotic tracking. Both controllers take pharmacokinetics and pharmacodynamics into account, as well as the carrying capacity of the vascular network. Lyapunov based arguments are used to design the controllers, using stability arguments, and numerical simulation results are presented to demonstrate the effectiveness of the proposed method.

Direct Output-Voltage Control of Nonminimum Phase Higher Order DC–DC Converters

This article addresses a fundamental issue in power converter control. Namely, the direct output-voltage control of power converters with higher order dynamics. We argue that despite of the burst in the development of new topologies, legacy control design principles—inherited from second-order converter analysis— have been unduly adopted as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">de facto</i> rules of procedure. In particular, we refer to the minimum-phase requirement on the feedback variable, as the underlying stabilizing mechanism. In this article, we demonstrate that the requirement of minimum-phaseness for higher order converters and the legacy <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ad hoc</i> solution via ancillary current control, can be bypassed without compromising closed-loop performance. To prove this, we unveil important differences between stability properties of second-order and higher order converters. Then, we introduce new linear and nonlinear control design strategies that permit direct output-voltage control. Experimental results are provided to validate the theory.

Hybrid Backstepping-Super Twisting Algorithm for Robust Speed Control of a Three-Phase Induction Motor

This paper proposes a Hybrid Backstepping Super Twisting Algorithm for robust speed control of a three-phase Induction Motor in the presence of load torque uncertainties. First of all, a three-phase squirrel cage Induction Motor is modeled in MATLAB/Simulink. This is then followed by the design of different non-linear controllers, such as sliding mode control (SMC), super twisting SMC, and backstepping control. Furthermore, a novel controller is designed by the synergy of two methods, such as backstepping and super twisting SMC (Back-STC), to obtain the benefits of both techniques and, thereby, improve robustness. The sigmoid function is used with an exact differentiator to minimize the high-speed discontinuities present in the input channel. The efficacy of this novel design and its performance were evidenced in comparison with other methods, carried out by simulations in MATLAB/Simulink. Regression parameters, such as ISE (Integral Square error), IAE (Integral Absolute error) and ITAE (Integral Time Absolute error), were calculated in three different modes of operation: SSM (Start-Stop Mode), NOM (Normal Operation Mode) and DRM (Disturbance Rejection Mode). In the end, the numerical values of the regression parameters were quantitatively analyzed to draw conclusions regarding the tracking performance and robustness of the implemented non-linear control techniques.

Nonlinear Vibration Control Experimental System Design of a Flexible Arm Using Interactive Actuations from Shape Memory Alloy.

The flexible arm easily vibrates due to its thin structural characteristics, which affect the operation accuracy, so reducing the vibration of the flexible arm is a significant issue. Smart materials are very widely used in the research topic of vibration suppression. Considering the hysteresis characteristic of the smart materials, based on previous simulation research, this paper proposes an experimental system design of nonlinear vibration control by using the interactive actuation from shape memory alloy (SMA) for a flexible arm. The experiment system was an interactive actuator-sensor-controller combination. The vibration suppression strategy was integrated with an operator-based vibration controller, a designed integral compensator and the designed n-times feedback loop. In detail, a nonlinear vibration controller based on operator theory was designed to guarantee the robust stability of the flexible arm. An integral compensator based on an estimation mechanism was designed to optimally reduce the displacement of the flexible arm. Obtaining the desired tracking performance of the flexible arm was a further step, by increasing the n-times feedback loop. From the three experimental cases, when the vibration controller was integrated with the designed integral compensator, the vibration displacement of the flexible arm was much reduced compared to that without the integral compensator. Increasing the number of n-times feedback loops improves the tracking performance. The desired vibration control performance can be satisfied when n tends to infinity. The conventional PD controller stabilizes the vibration displacement after the 7th vibration waveform, while the vibration displacement approaches zero after the 4th vibration waveform using the proposed vibration control method, which is proved to be faster and more effective in controlling the flexible arm's vibration. The experimental cases verify the effectiveness of the proposed interactive actuation vibration control approach. It is observed from the experimental results that the vibration displacement of the flexible arm becomes almost zero within less time and with lower input power, compared with a traditional controller.

Nonlinear Adaptive Fuzzy Control Design for Wheeled Mobile Robots with Using the Skew Symmetrical Property

This research presents a nonlinear adaptive fuzzy control method as an analytical design and a simple control structure for the trajectory tracking problem in wheeled mobile robots with skew symmetrical property. For this trajectory tracking problem in wheeled mobile robots, it is not easy to find an analytical adaptive fuzzy control solution due to the complicated error dynamics between the controlled wheeled mobile robots and desired trajectories. For deriving the analytical adaptive fuzzy control law of this trajectory tracking problem, a filter link is firstly adopted to find the solvable error dynamics, then the research is based on the skew symmetrical property of the transformed error dynamics. This proposed nonlinear adaptive fuzzy control solution has the advantages of low computational resource consumption and elimination of modeling uncertainties. From the results for tracking two simulation scenarios (an S type trajectory and a square trajectory), the proposed nonlinear adaptive fuzzy control method demonstrates a satisfactory trajectory tracking performance for the trajectory tracking problem in wheeled mobile robots with huge modeling uncertainties and outperforms the existing H2 control method.