Integrator Backstepping Research Articles

Sensorless integral backstepping control of a single-stage photovoltaic system connected to the single-phase grid using a multi-level NPC inverter with an LCL filter

In this paper, the control problem of a single-phase, grid-tied photovoltaic (PV) system consisting of a three-level neutral point clamped (3L-NPC) inverter and an LCL filter is considered. The proposed controller aims at achieving threefold control objectives: (i) guaranteeing the PF correction (PFC) objective by enforcing the current of the grid to track a sinusoidal reference signal in phase with the grid voltage; (ii) controlling the DC bus capacitor voltages to follow a reference value provided by the maximum power point tracking (MPPT) algorithm to achieve the maximum available PV power; (iii) ensuring a balanced power exchange through the regulation of the two input capacitor voltages to the same values. To achieve these aims, a multi-loop nonlinear controller is synthesized, including three control loops, specifically the inner PFC requirement loop designed through the integral backstepping approach, the outer voltage control loop formulated using a filtered proportional integral (PI) regulator, and the power balance loop built up using a PI regulator. The control problem under consideration entails several difficulties as the existence of numerous state variables that are inaccessible to measurements. This challenge is addressed by adding a high-gain observer to estimate the current of the solar panels. The performance of the proposed controller against climate changes is demonstrated via numerical simulations using the MATLAB/Simulink platform.

Advanced control of an autonomous torpedo-type underwater vehicle with integral backstepping techniques in the yaw plane

Advanced control of an autonomous torpedo-type underwater vehicle with integral backstepping techniques in the yaw plane

Robust Braking Pressure Control for an Electrohydraulic Brake System under Friction and Disturbance Conditions

This paper addresses the challenges in hydraulic pressure control for an electrohydraulic brake (EHB), considering nonlinearities and uncertainties such as friction and parameter variations. The proposed solution is a robust integral backstepping control (IBC) strategy, which incorporates motor current dynamics and the LuGre friction model. A nonlinear observer is introduced to estimate the unmeasurable internal state of the LuGre model. The IBC is applied to pressure control for the EHB, resulting in improved steady-state behavior and robustness. The paper concludes with a global stability analysis using Lyapunov theory and performance validation through simulation using MATLAB/Simulink.

Advanced control of an autonomous torpedo-type underwater vehicle with integral backstepping techniques in the yaw plane

Advanced control of an autonomous torpedo-type underwater vehicle with integral backstepping techniques in the yaw plane

Robust trajectory tracking of quadrotors using adaptive radial basis function network compensation control

Radial Basis Function Neural Networks (RBFNN) methods have gained incredible efficiency and applicability in control. This paper presents a nested control strategy for robust trajectory tracking of a quadrotor using adaptive RBF compensation and NN-supervised control embedded with Integrator BackStepping (IBS). The approach addresses the robustness in the presence of modeling uncertainties, sensing noise, and bounded disturbances. The control design is derived from the decentralized inverse dynamics, using adaptive RBFNN for outer-loop disturbance approximation and compensation. In conjunction with an Inner-loop supervised control that stabilizes the quadrotor attitude, preventing initial instability during NN convergence. In addition, an adaptive Extended Kalman Filter (EKF) attenuates noisy signals. Simulation results demonstrate strong adaptability to changes in model parameters, and superior performance when compared to Proportional Integral Derivative (PID), Integrator BackStepping (IBS), and offline decentralized Multi-Layer Perceptron (MLP) algorithms, in terms of parameter convergence, disturbance compensation control, and noise attenuation.

Robust and Adaptive Stabilization Controllers of State-Constrained Nonholonomic Chained Systems: A Discontinuous Approach

In this paper, two systematic control design strategies are proposed for strict-feedback nonholonomic systems with full-state constraints to solve stabilization and adaptive stabilization problems. The stabilization schemes involve the introduction of state scaling, the barrier Lyapunov function (BLF), the integrator backstepping method, and the tuning function approach. In addition, a discontinuous switching control strategy is proposed to achieve the control goal if the first system state’s initial state is confined to zero. In both stabilization and adaptive stabilization control, the system states can be regulated at the origin, and meanwhile, the full-state constraints are realized. Finally, it is shown that the simulation results are consistent with the theory analysis results, which further demonstrates the effectiveness of the proposed control schemes.

Adaptive terminal synergetic-backstepping technique based machine learning regression algorithm for MPPT control of PV systems under real climatic conditions

This paper deals with a comparative evaluation of nonlinear controllers based on the linear regression technique, which is a machine learning algorithm for maximum power point tracking. In the past decade, most photovoltaic systems have been equipped with classical algorithms such as perturb and observe, hill climbing, and incremental conductance. The simplicity of these techniques and their ease of implementation were seen as the main reasons for their utilization in photovoltaic systems. However, researchers’ attention has recently been attracted by artificial intelligence-based techniques such as linear regression, which offer better performance within the bounds of the nonlinearity of photovoltaic system characteristics. An adaptive terminal synergetic backstepping controller is developed in this paper for a single-ended primary inductance converter. This control scheme is based on the combination of a non-singular terminal synergetic technique with an integral backstepping technique and equally a neural network for the approximation of unmeasured or inaccessible variables that guarantees the finite-time convergence. The proposed controller was further verified under virtual and real environmental conditions, and the numerical results obtained from Matlab/Simulink software under various test conditions, including load variations, show that the adaptive terminal synergetic backstepping controller gives satisfactory performance compared to the adaptive integral backstepping controller used in the same climatic conditions.

Coordinated Control of Quadrotor Suspension Systems Based on Consistency Theory

This paper designs a cooperative control method for the multi-quadrotor suspension system based on consistency theory and realizes the cooperative formation trajectory tracking control of the multi-quadrotor suspension system by designing a consistent formation cooperative algorithm of virtual piloting and a nonlinear controller. First, a new quadrotor suspension system model is established based on the traditional quadrotor model using the Newton–Euler method. This model can accurately reflect the influence of the load on the quadrotor while obtaining the swing of the load. Then, the vertical and horizontal positions are designed separately based on the quadrotor motion characteristics, and the formation algorithm based on the virtual pilot consistency theory ensures that the final convergence of each position is consistent. An integral backstepping controller and an integral backstepping sliding mode controller are designed for quadrotor position, attitude, and load swing control to achieve accurate and fast quadrotor trajectory tracking control while reducing load swing. The stability of all the controllers is demonstrated using Lyapunov functions. Finally, a multi-quadrotor suspension system formation cooperative simulation experiment is designed to verify the designed control method.

Robust nonlinear 3D control of an inverted pendulum balanced on a quadrotor

This paper addresses the nonlinear control problem of balancing an inverted pendulum on an underactuated unmanned aerial vehicle. In view of the system’s slow and quick transients, a convenient error transformation is employed to render the attitude subsystem less sensitive to translational errors. Linearizations are not involved, making this controller suitable beyond the limited scope of trim maneuvers. Furthermore, the controller features an adaptive bounded law that is used to compensate for unknown exogenous perturbations. The Lyapunov-based control design is rooted in an integral backstepping process, wherein the origin of the closed-loop total system error is shown to be almost globally asymptotically stable. Simulation results are presented to validate our strategy, and experimental results are also provided to demonstrate its accuracy and robustness.

Nonlinear position control of electro-hydraulic servo system based on lyapunov robust integral backstepping controller

In electro-hydraulic servo systems (EHSS), high nonlinearity and time-varying features limit the hydraulic actuator performance. In feedback-based systems, linearization reduces nonlinearities. Their cancellation may produce instability when modeling uncertainty exists. This work uses a robust nonlinear controller based on Lyapunov theory to control the nonlinear position of the electro-hydraulic servo system (EHSS). The dynamics of the system were modeled as extensively as possible, and then a simplified mathematical model based on the EHSS dynamics was created for the controller design. Integral backstepping was used to design the nonlinear robust controller utilizing the Lyapunov theory of nonlinear systems. Lyapunov functions theoretically ensured closed-loop stability. Comparative simulation analysis and experimental investigation in real-time with the proportional integral derivative (PID) controller optimized offline for position tracking control were carried out. Besides tracking performance and steady-state error, the mean square error (MSE), the root mean square error (RMSE), the maximum absolute value of tracking errors and the standard deviation of tracking errors (σ) was utilized to evaluate the controllers’ performance. The simulation analysis and experimental verification were accomplished under various sinusoidal trajectories using different testing conditions (amplitudes, frequencies, and external disturbance), in all testing conditions the effectiveness of the robust nonlinear integral backstepping controller was demonstrated.

Nonlinear dynamics and chaos control of circular dielectric energy generator

The current study focuses on the nonlinear dynamics of the dielectric elastomer generator (DEG). To begin with, we will go through DEG’s operating principles, parameters, materials, and deformation modes. On this basis, the dynamical modeling for the nonlinear behavior of the DEG system is described, and the second-order nonlinear ordinary differential equation representing radially symmetric motion is derived using Hamilton’s variational principle. A static applied electric field allows the DEG system to attain two equilibrium states: thick and thin. The effects of the stiffening phenomenon on the dynamics of the DEG system are investigated. The system converges to a stable equilibrium point under constant loads, and the convergence position and velocity are closely related to both the initial states. Subjected to periodic loads, certain phenomena such as quasiperiodicity and chaos are detected, and the chaotic phenomena are explored using the bifurcation diagram and 0-1 chaos test. Furthermore, parametric studies are carried out using numerical analyses to demonstrate the influence of load amplitude and external frequency on the dynamics of the DEG system. Once the DEG enters the chaotic regime, the chaotic zone is transformed into a stable manifold using established chaos control techniques such as system parameter change and parametric perturbation. However, because these techniques require changes in system design, we proposed a chaos control by using a non-linear controller, specifically, adaptive integral backstepping sliding mode control (AIBSMC) as one demonstrative candidate. The controller also enables the DEG system to follow motion along a predefined trajectory. The current work may be expected to substantially impact the future design and performance of energy harvesters.

Improved Robust Control of a New Morphing Quadrotor UAV Subject to Aerial Configuration Change

Over these last years, morphing Unmanned Aerial Vehicles (UAVs) control became one of the critical problems, which has not been properly solved by the researchers. This is due to their particular and complex features compared to the ordinary ones as: morphology change, flight transition, model asymmetry, geometric variation, different dynamics, over-actuation and high nonlinearity. To deal with such challenges, this paper addresses the control of a new over-actuated morphing drone that changes its arms in different orientations to form various morphology and configuration models. First, the present system is divided into two principal parts: an attitude subsystem and a position subsystem. Furthermore, an improved Adaptive Nonsingular Fast Terminal Sliding Mode Controller (ANFTSMC) is proposed to stabilize the attitude loop. While the position loop is controlled by Integral Backstepping Controller (IBC) using Lyapunov theory. Second, with the aim to better adjust the control gains, a recent metaheuristic technique based on the Whale Optimization Algorithm (WOA) is adopted. At last, a comparative study with the standard control algorithms is accomplished to evaluate the effectiveness and robustness of the proposed methods.

POSITION CONTROL OF ELECTRO-HYDRAULIC SERVO SYSTEM WITH FRICTION COMPENSATION

This work presents a model-based friction compensation technique and an integral adaptive backstepping controller to improve the position control of the electrohydraulic servo system. The controller design uses a continuous approximation of the LuGre friction model and the Lyapunov theory of nonlinear systems. The friction compensation enhances system performance, and comparison tests are conducted on a hydraulic servo test bench to validate the control strategy's tracking performance under various conditions. KEYWORDS: Electrohydraulic servo systems; Position control; Integral adaptive backstepping controller; LuGre dynamic friction model; Lyapunov theory; Friction compensation.

Robust nonlinear MPPT controller for PV energy systems using PSO-based integral backstepping and artificial neural network techniques

Robust nonlinear MPPT controller for PV energy systems using PSO-based integral backstepping and artificial neural network techniques

Adaptive Robust Terminal Sliding Mode Control with Integral Backstepping Synthesized Method for Autonomous Ground Vehicle Control

Autonomous ground vehicles (AGVs) operating in complex environments face the challenge of accurately following desired paths while accounting for uncertainties, external disturbances, and initial conditions, necessitating robust and adaptive control strategies. This paper addresses the critical path-tracking task in AGVs through a novel control framework for multilevel speed AGVs, considering both structured and unstructured uncertainties. The control system introduced in this study utilizes a nonlinear adaptive approach by integrating integral backstepping with terminal sliding mode control (IBTSMC). By incorporating integral action, IBTSMC continuously adjusts the control input to minimize tracking errors, improving tracking performance. The hybridization of the terminal sliding mode method enables finite time convergence, robustness, and a chatter-free response with reduced sensitivity to initial conditions. Furthermore, adaptive control compensators are developed to ensure robustness against unknown but bounded external disturbances. The Lyapunov stability theorem is employed to guarantee the global asymptotic stability of the closed-loop system and the convergence of tracking errors to the origin within finite time. To validate the effectiveness of the proposed control scheme, high-fidelity cosimulations are conducted using CarSim and MATLAB. Comparative analysis is performed with other methods reported in the literature. The results confirm that the proposed controller demonstrates competitive effectiveness in path-tracking tasks and exhibits strong efficiency under various road conditions, parametric uncertainties, and unknown disturbances.

Robust integral backstepping control microgrid connected photovoltaic System with battery energy storage through multi-functional voltage source inverter using direct power control SVM strategies

This paper proposes a robust control based on the integral backstepping control (IBC) for power quality enhancement of micro-grid-connected photovoltaic (PV) system with battery energy storage systems (BESS), The DC side consists of a PV system and battery storage. As for the AC side, it consists of three phases of a multi-functional two-level voltage source inverter (MVSI) coupled to the electrical grid via an inductive filter, all feeding a non-linear load. The MVSI is controlled by a nonlinear direct power control (DPC) strategy with space vector modulation (SVM) and the proposed IBC technique. Using the proposed IBC technique to control the voltage of the DC link voltage loop, the active/reactive power loops of the grid, the compensation of the harmonic currents of the network, and the injection of the power of the PV battery into the grid, loop of the maximum power point tracking (MPPT) regardless of the random nature of weather changes and guarantees optimal power management system battery storage. Using simulation under the MATLAB environment, the proposed control system was validated and compared to the conventional strategies (proportional–integral controller and backstepping controller) in terms of success, performance, robustness, and efficiency. In addition to its ability to respond under any irradiation distortion and non-linear load unbalance.

Adaptive neural network based compensation control of quadrotor for robust trajectory tracking

SummaryNeural network (NN) methods have become increasingly efficient and applicable in control. This article presents a novel nested control strategy based on adaptive radial basis function neural networks (RBFNN) and NN supervised control embedded with integrator back stepping (IBS) for a robust position and attitude trajectory tracking of quadrotor aerial robot in presence of modeling uncertainties, sensing noise, and external bounded disturbance. The control philosophy is derived from the decentralized inverse dynamics, where the adaptive RBFNN is adopted for the outer loop to approximate the unknown external disturbance, and adaptively compensate for their effect. In conjunction with a supervised control that stabilizes the attitude in the inner loop by adaptively compensating the unknown and unmodeled uncertainties, avoiding initial instability of the attitude during NN convergence. Furthermore, noise is attenuated by an adaptive extended Kalman filter. Stability analysis was elaborated using Lyapunov stability theory. Simulation of adaptive RBFNN control philosophy proved robustness and effectiveness compared to proportional integral derivative, IBS, and offline decentralized convolution neural network algorithms as it generates the control law by guarantying a fast convergence of parameters, better external disturbance compensation, and noise attenuation. The proposed scheme of robust tracking was validated.

Switched step integral backstepping control for nonlinear motion systems with application to a laboratory helicopter

In this paper, the energy efficiency of the widespread application of backstepping control to a class of nonlinear motion systems is investigated. A Switched Step Integral Backstepping Control (SSIBC) scheme is introduced to improve immunity to measurement noise and to increase the energy efficiency of conventional backstepping in practice. The SSIBC is realized by switching between two candidate controllers obtained at different steps of the iterative backstepping design process. A bi-state dependent hysteresis rule is developed to supervise stable switching between the different regimes in the presence of noise. The proposed method is experimentally verified on a MIMO twin rotor laboratory helicopter involving coupled nonlinear dynamics, inaccessible states and uncertainties. Experimental results show that in addition to a reduction in power consumption, the SSIBC reduces saturation of the control signal and visible motor jerking in contrast with conventional backstepping. Additional comparisons with a previously proposed optimized decoupling PID controller also show significant improvement in precision achieved with higher energy efficiency. Experimental results obtained with the introduction of an external disturbance into the system also show the robustness of the proposed SSIBC.

Prescribed-time constrained feedback control for an uncertain twin rotor helicopter

This article presents a prescribed-time adaptive constraint feedback control strategy for an unmanned twin rotor helicopter system in the presence of parametric uncertainties. The integrator backstepping technique and adaptive estimator are employed to handle these unknown parameters. Additionally, a constrained function is utilized to prevent the possibility of signal amplification as the appointed settling time approaches. Through rigorous mathematical analysis employing Lyapunov theory, we prove that the proposed adaptive time-varying constraint feedback control and parameter estimator ensure the boundedness of all signals in the closed-loop system, promoting stability and preventing erratic behavior. One notable benefit of the proposed approach is that the convergence can be achieved within the time specified in advance. Finally, simulations and experiments are carried out to verify the efficacy of the proposed adaptive prescribed-time constraint feedback control strategy.

Nonlinear Robust Control by a Modulating-Function-Based Backstepping Super-Twisting Controller for a Quadruple Tank System.

In this paper, a robust nonlinear approach for control of liquid levels in a quadruple tank system (QTS) is developed based on the design of an integrator backstepping super-twisting controller, which implements a multivariable sliding surface, where the error trajectories converge to the origin at any operating point of the system. Since the backstepping algorithm is dependent on the derivatives of the state variables, and it is sensitive to measurement noise, integral transformations of the backstepping virtual controls are performed via the modulating functions technique, rendering the algorithm derivative-free and immune to noise. The simulations based on the dynamics of the QTS located at the Advanced Control Systems Laboratory of the Pontificia Universidad Católica del Perú (PUCP) showed a good performance of the designed controller and therefore the robustness of the proposed approach.