Integral Compensation Research Articles

Robust Position Control of VTOL UAVs Using a Linear Quadratic Rate-Varying Integral Tracker: Design and Validation

This article presents an optimal tracking controller retrofitted with a nonlinear adaptive integral compensator, specifically designed to ensure robust and accurate positioning of Vertical Take-Off and Landing (VTOL) Unmanned Aerial Vehicles (UAVs) that utilize contra-rotating motorized propellers for differential thrust generation. The baseline position controller is synthesized by employing a fixed-gain Linear Quadratic Integral (LQI) tracking controller that stabilizes position by tracking both state variations and pitch-axis tracking error integral, which adjusts the voltage to control each coaxial propeller’s speed accurately. Additionally, the baseline tracking control law is supplemented with a rate-varying integral compensator. It operates as a nonlinear scaling function of the tracking-error velocity and the braking acceleration to enhance the accuracy of reference tracking without sacrificing its robustness against exogenous disruptions. The controller’s performance is analyzed by performing experiments on a tailored hardware-in-the-loop aero-pendulum testbed, which is representative of VTOL UAV dynamics. Experimental results demonstrate significant improvements over the nominal LQI tracking controller, achieving 17.9%, 61.6%, 83.4%, 43.7%, 35.8%, and 6.8% enhancement in root mean squared error, settling time, overshoot during start-up, overshoot under impulsive disturbance, disturbance recovery time, and control energy expenditure, respectively, underscoring the controller’s effectiveness for potential UAV and drone applications under exogenous disturbances.

A robust time synchronization algorithm for GNSS/IMU integrated navigation in urban environments

Abstract Global navigation satellite systems (GNSS) are often integrated with inertial measurement units (IMU) for navigation in urban environments. The ability of these integrated systems to achieve precise positioning and navigation is highly dependent on accurate time synchronization. While the current time synchronization algorithms are capable of achieving millisecond-level synchronization in open environments, their performance deteriorates significantly in complex urban environments due to the impact on GNSS measurements of non-line-of-sight (NLOS) signals and multipath effects. Here we propose a loosely coupled GNSS/IMU integration time synchronization error modeling and compensation algorithm to tackle this problem in the context of urban vehicle navigation. In the algorithm, the time synchronization error is augmented as a state variable in the Robust Extended Kalman Filter (REKF), with the robustness factor threshold being dynamically adjusted based on the time synchronization error. Furthermore, we have designed a system time synchronization detection scheme based on two detection factors, with the aim of achieving high-precision GNSS/IMU time synchronization in complex urban environments. Experimental results show that the proposed algorithm synchronizes data time to the millisecond level in urban positioning environments. This represents an improvement of more than 90% in time synchronization precision compared to the traditional EKF-based time synchronization algorithm, and an improvement of more than 60% compared to the REKF-based time synchronization algorithm. Furthermore, compared to the EKF-based GNSS/IMU fusion algorithm, the proposed algorithm enhances the accuracy of the determination of both position and velocity in the horizontal and 3D directions by more than 50% and heading accuracy by 85%.

Path Following Control for Unmanned Surface Vehicles: A Reinforcement Learning-Based Method With Experimental Validation.

In this article, a reinforcement learning (RL)-based strategy for unmanned surface vehicle (USV) path following control is developed. The proposed method learns integrated guidance and heading control policy, which directly maps the USV's navigation states to motor control commands. By introducing a twin-critic design and an integral compensator to the conventional deep deterministic policy gradient (DDPG) algorithm, the tracking accuracy and robustness of the controller can be significantly improved. Moreover, a pretrained neural network-based USV model is built to help the learning algorithm efficiently deal with unknown nonlinear dynamics. The self-learning and path following capabilities of the proposed method were validated in both simulations and real sea experiments. The results show that our control policy can achieve better performance than a traditional cascade control policy and a DDPG-based control policy.

Towards backward compatibility of ADRC: revisiting classical state-feedback control with integral compensator

In this paper, the problem of backward compatibility of active disturbance rejection control (ADRC) is investigated. The goal is to contextualize ADRC to deliver its interpretations from the established field of linear control systems. For this study, a control algorithm, denoted here as integral disturbance rejection control (IDRC), is considered that combines classical state-feedback control with an integral compensator. At first, an interpretation of ADRC is involved in terms of existing state-space control approaches. Next, a transition to the frequency domain is performed, which is justified as a significant part of practical control engineering is conducted in that domain. For assumed specific plant structures, both ADRC and IDRC are then holistically compared in terms of transfer function representation and frequency characteristics, as well as steady-state convergence conditions. Such a juxtaposition helps to highlight the similarities and differences of both approaches, whereas the utilized bandwidth parameterization is shown to bring the control system to the same form, thus indicating some interesting practical aspects. Finally, the theoretical results concerning both considered control structures are validated in a set of numerical simulations and experiments conducted on a laboratory hardware testbed.

Design Method of Museum Cultural and Creative Products Based on Multi sensory Experience

To explore the design method of museum cultural and creative products based on multi sensory experience, improve product level and user experience, and provide new directions for the development of museum cultural and creative design. The method first introduces the cognitive principles and sensory expression methods of sensory experience, and then focuses on the study of three common multi sensory phenomena: multi sensory integration, synesthesia, and sensory compensation. It analyzes their application in the design of cultural and creative products, summarizes the transformation process of user generated multi sensory experience, and establishes a multi sensory experience cultural and creative product design process based on this. Conclusion: Product design with multi sensory experience can bring users a more comprehensive and profound experience, help promote the inheritance and development of museum culture, and improve the serious problem of homogenization in the cultural and creative industry.

Coupled hysteresis and resonance control of three-degree-of-freedom tip-tilt-piston piezoelectric stage

In order to solve the coupled hysteresis and resonance problems in three-degree-of-freedom tip-tilt-piston piezoelectric stage, a coupled hysteresis model and a coupled integral resonance compensation model are designed. The inverse coupled hysteresis feedforward control combined multi-axis coupled resonance control and high-gain integral tracking controller are used to improve the tracking speed and positioning accuracy of the stage. Firstly, a kinematic model of the stage is built to translate the three-degree-of-freedom motion of the end-effector into the outputs of three piezoelectric actuators. Then, a coupled hysteresis model based on the rate-dependent Prandtl–Ishlinskii model is established and parameterized to simultaneously compensate for the hysteresis of a single piezoelectric actuator and the coupled hysteresis between multiple piezoelectric actuators. The effectiveness of the model is verified by open-loop and closed-loop inverse model feedforward control experiments. Afterwards, a coupled integral resonance compensation model is also established and parameterized to suppresses the resonance and expand the system bandwidth. Finally, the proposed controller is used to conduct tracking experiments on a composite signal, and the results show that the accuracy and speed of trajectory tracking are further improved, and the mechanical coupling between axes are significantly reduced.

Research on laser communication ranging Integration and VLC nonlinear compensation technology

Abstract Visible light communication (VLC) is a new spectrum communication technology that provides a new direction to solve spectrum resource problems. The nonlinearity problem in VLC will lead to a significant reduction in the performance of the communication system. To solve this problem, this paper studies the integration of laser communication ranging and VLC nonlinear compensation technology based on analyzing the principles of ranging methods and factors affecting ranging performance. Aiming at the problem that the complexity of the Random Fourier Features Kernel adaptive filter (RFF-KAF) method will increase significantly as the dimension of the mapping space increases, we introduce some second-order Volterra series square terms into the input vector of RFF-KAF and propose an improved prediction method. Experimental simulation results show that the method proposed in this article can greatly improve the performance of the RFF-KAF method while maintaining the same mapping space dimension. Compared with obtaining similar performance by increasing the mapping space dimension, the cost of this method is greatly reduced.

High-precision and Large-Scale Vat Photopolymerization Printing based on "Spatial-Pixel Integration Compensation" method

Vat photopolymerization (VPP) is widely known for its exceptional printing accuracy, but effectively controlling stitching errors to achieve high-precision, large-scale printing remains a significant challenge. This study introduces a novel compensation method, termed "Spatial-Pixel Integration Compensation" (SPIC), to address this key obstacle. SPIC combines Spatial Motion Compensation to initially control stitching errors between adjacent sub-images to be within 100 µm and Pixel Compensation for precise adjustments, further reducing stitching errors. Integrating SPIC with our high-precision printing system resulted in a remarkable reduction of stitching errors by a factor exceeding 40. Crucially, this method minimizes the stitching error between any two sub-images to be less than one pixel point, specifically below 4 µm. Notably, SPIC is the first method specifically focused on effectively controlling and reducing stitching errors to achieve large-scale printing while maintaining high precision. To validate the practical applicability of the SPIC method, we used SPIC to print both Zig-Zag and herringbone structures (HBS) and achieved high-precision large-scale manufacturing with dimensions of 44 mm × 33 mm. In the HBS structure, the minimum feature size was 14.2 µm, and the printing error was less than 1 µm. These printed structures were used as molds to fabricate proof-of-concept polydimethylsiloxane (PDMS) microfluidic chips, demonstrating the successful mixing of rhodamine B and ethanol within the microfluidic channels. Furthermore, SPIC was extended to the printing of complex three-dimensional (3D) Triple-Periodic Minimal Surface (TPMS) structures, successfully producing TPMS-Gyroid and TPMS-Diamond structures with a minimum feature size of 20 µm and a printing error below 1.5 µm. These results demonstrate that the SPIC algorithm effectively enables high-precision, large-scale printing. This work significantly advances the application of VPP technology in fields requiring complex, high-precision, and large-scale 3D structures and provides valuable insights for future research in high-precision and large-scale printing.

Adaptive neural event-triggered consensus control for unknown nonlinear second-order delayed multi-agent systems

In this paper, we discuss event-triggered consensus control for a heterogeneous second-order multi-agent systems with unknown nonlinear functions and state delays (SODMASs). Firstly, a broad adaptive dynamic event-triggered mechanism (ETM), which includes many existing ETM, is proposed. Based on this ETM and the approximation property of neural networks, an adaptive event-triggered protocol with weight estimation of neural network and time-varying integral gain compensation is designed to reduce communication frequency and to eliminate the uncertainty of nonlinear function and state delays. Then, the consensus problem for the heterogeneous SODMASs under the protocol is solved successfully by selecting a suitable Lyapunov–Krasovskii functional. In addition to these, it is also proved that all agents can exclude Zeno behavior under the proposed event-triggered protocol. Finally, a numerical example is given to verify the effectiveness of the proposed consensus protocol algorithm.

A fast-response RBCOT buck converter with second-order differential and integrator compensation based on FVF

A second-order differential and integration circuit based on a flipped voltage follower (SDI-FVF) is proposed in the paper, providing compensation ripple for the buck convert with ripple-based constant on-time (RBCOT). Additionally, an adaptive conduction time module is designed which stabilizes the operating frequency of the converter in continuous conduction mode (CCM) and guarantees stable conduction time in discontinuous conduction mode (DCM). The proposed RBCOT buck convert has been designed using 180 nm process. It operates with an input voltage range of 2.5 V–5 V and an output voltage range of 0.8 V–5 V, accommodating a load current range of 0 A to 3 A. It operates at a frequency of 4 MHz, exhibiting an output ripple of 1.4 mV, achieving a peak efficiency of 91.5 %. The efficiency exceeds 85 % under a load current of 1 mA. The undershoot and overshoot voltage are only 0.13 mV and 7.1 mV with a load current variation rate of 3 A/μs.

Sliding Mode Speed Control in Synchronous Motors for Agriculture Machinery: A Chattering Suppression Approach

Synchronous motors have extended their presence in different applications, specifically in high-demand environments such as agronomy. These uses need advanced and better control strategies to improve energy efficiency. Within this context, sliding mode control has demonstrated effectiveness in electric machine control due to its advantages in robustness and quick adaptation to uncertain dynamic system disturbances. Nevertheless, this control technique presents the undesirable chattering phenomenon due to the discontinuous control action. This paper introduces a novel speed integral control scheme based on sliding modes for synchronous motors. This approach is designed to track smooth speed profiles and is evaluated through several numeric simulations to verify its robustness against variable torque loads. This approach addresses using electric motors for different applications such as irrigation systems, greenhouses, pumps, and others. Moreover, to address the chattering problem, different sign function approximations are evaluated in the control scheme. Then, the most effective functions for suppressing the chattering phenomenon through extensive comparative analysis are identified. Integral compensation in this technique demonstrates improvement in motor performance, while sign function approximations show a chattering reduction. Different study cases prove the robustness of this control scheme for large-scale synchronous motors. The simulation results validate the proposed control scheme based on sliding modes with integral compensation, by achieving chattering reduction and obtaining an efficient control scheme against uncertain disturbances in synchronous motors for agronomy applications.

Event-based adaptive active disturbance rejection control for nonlinear large-scale systems with input delay

This paper explores the active disturbance rejection control (ADRC) issue for interconnected large-scale systems with unmeasured states, input delay and a total disturbance composed of unknown constrained external disturbances. An enhanced extended state observer is built via fuzzy logic systems to identify system uncertainties and states and keep restraining the total disturbance of uncertain systems. When the triggering condition is met, the tracking differentiator component of the ADRC is able to reduce the communication overhead by successfully applying the backstepping control approach and the dynamic event-triggered mechanism. Meanwhile, the integral compensation method eliminates the negative effect cased by the input delay. Furthermore, the developed decentralised fuzzy control scheme can ensure that all signals in the closed-loop systems are semiglobally uniformly ultimately bounded and Zeno behaviour does not occurs. Finally, an example is used to depict the validity of the control approach.

Frequency Integration and Spatial Compensation Network for infrared and visible image fusion

Infrared and visible image fusion aims to synthesize a fused image that emphasizes the salient objects while retaining the intricate texture and visual quality from both infrared and visible images. In opposite to the majority of existing deep learning-based fusion approaches, which predominantly focus on spatial information and neglect the valuable frequency information, we propose a novel method that delves into both domains simultaneously to tackle the infrared and visible image fusion task. Specifically, we first analyze the frequency characteristics of the two modality images via Fourier transform, and observe that fusion results with complementary attributes from source images can be effectively attained by directly incorporating their phase components. To this end, we propose a Frequency Integration and Spatial Compensation Network (FISCNet), consisting of two core designs: a frequency integration component and a spatial compensation component. The former integrates prominent objects from the source images while maintaining the visual perception from the visible image in the frequency domain, and the latter improves the detailed texture and emphasizes the salient objects through a meticulous compensation mechanism in the spatial domain. Extensive experiments on various benchmarks demonstrate the superiority of our method over state-of-the-art alternatives in terms of both salience preservation and texture fidelity. Code is available at https://github.com/zheng980629/FISCNet.

Consensus-based secondary frequency control for parallel virtual synchronous generators

In off-grid operating modes, microgrids with Virtual Synchronous Generators (VSG) controlled inverters are limited to primary frequency control capabilities. When operating under the primary frequency control, if VSG's output frequency exceeds the safe operational range, it can adversely affect stable operation. Consequently, there is a need to implement a secondary frequency control strategy. This paper presents an analysis of the conventional secondary frequency regulation in VSGs. It reveals that when multiple VSGs in parallel to the Point of Common Coupling (PCC) with varied line impedances, the proportionate distribution of each VSG's active power output, post frequency control, does not align with predetermined ratios. In response to this challenge, the paper introduces a quasi-distributed secondary frequency control approach, tailored for systems with multiple feed-in points. This approach modifies the traditional method of compensating for frequency deviation through average ratio integral compensation, replacing it with a compensation based on a consensus algorithm. This negates the need for global communication and additional impedance measuring equipment. By facilitating information exchange between neighboring converters, it enables global control, effectively resolving the issue of line impedance parameters impacting the distribution of VSG's active power output. This decouples the previously strong correlation between line impedance and VSG's active power. The proposed method is characterized by its strong adaptability, scalability, and swift dynamic adjustments, significantly enhancing the fault tolerance of information exchange and the stability of microgrid operations. Finally, the correctness and effectiveness of the proposed improved control strategy are verified by simulation and HIL-based platform.

A New Design and Embedded Implementation of a Low‐Cost Maximum Power Point Tracking Charge Controller for Stand‐Alone Photovoltaic Systems

This article presents a low‐cost maximum power point tracking (MPPT) charge controller designed to efficiently charge solar batteries using a simple and robust MPPT method, while providing protection against over‐currents and over‐voltages. The proposed MPPT approach utilizes a modified Incremental Conductance (INC) algorithm adapted to low‐cost embedded controllers, as it avoids all the mathematical division calculations typically used in the conventional INC algorithm. It also introduces a modified step size based only on photovoltaic (PV) power change to enhance tracking accuracy and convergence speed. Furthermore, to reduce the stress and switching losses of DC–DC converter, a feedback control with two proportional and integral (PI) compensators is also used to control both the PV voltage and to protect the battery from over‐currents using PV power limitation technique. Simulation results, carried out under MATLAB/Simulink, demonstrate the good performance of the proposed control scheme regarding any variations in atmospheric conditions, both for the MPPT control and for the battery charge control. Finally, a processor‐in‐the‐loop (PIL) test using a low‐cost Arduino MKR ZERO board is also performed to verify the hardware implementation of the proposed method. PIL results are in totally accordance with MATLAB/Simulink simulation results, which further proves the effectiveness of the proposed method.

A conservative implicit scheme for three-dimensional steady flows of diatomic gases in all flow regimes using unstructured meshes in the physical and velocity spaces

A conservative implicit scheme in the finite volume discrete velocity method framework is proposed for solving the three-dimensional steady flows of molecular gases in all flow regimes from continuum one to free-molecular one. This work is based on the Boltzmann–Rykov model equation, which is a nonlinear relaxation model and can describe the thermodynamic non-equilibrium of diatomic gas flows. The macroscopic equations are solved implicitly together with the Rykov model equation to find a predicted equilibrium distribution first at each iteration step. As a result, the collision term of the Rykov model equation can be discretized in a fully implicit way for fast convergence in all flow regimes. At the cell interface, an asymptotic preserving simplified multi-scale numerical flux is developed to relieve the limitation of grid size and time step in all flow regimes, which can keep the multi-scale property and achieve high computational efficiency. The integral error compensation technique is used to keep the scheme conservative and greatly reduce the number of unstructured discrete velocity space (DVS) meshes. Furthermore, an empirical criterion based on the numerical experiments of the Apollo 6 command module is suggested to guide the generation of three-dimensional unstructured DVS. The accuracy and efficiency of the present method are demonstrated by a number of three-dimensional classic cases, covering different flow regimes.

Evaluation of intelligent PPI controller for the performance enhancement of speed control of induction motor

Induction motor control for high dynamic performance industrial applications is often difficult due to parameters sensitivity and its non-linearity. Through independent manipulation of the flux and torque producing components, Field Oriented Control (FOC) methodologies have been used to improve dynamic performance, widen speed range, and torque/flux quality. Studies have shown that the Parallel Proportional Integral (PPI) compensation method produces responses of higher quality than the traditional cascaded Proportional Integral (PI) type though tuning gains for PPI controller is time consuming and inaccurate. In this research work, modeling of control strategy for Induction motor and tuning of four parameters (Ki, Ki1, Kp, Kp1) of PPI controller at the outer speed control loop have been conducted using GA and PSO algorithms. The speed and torque responses' performances of the proposed controller, PPI-PSO and PPI-GA, have been contrasted with each other. For simulation, SIMULINK and a programming environment of a MATLAB software were employed. The simulation result illustrated that PSO based tuning out performs the GA based tuning in terms of dynamic speed response, torque quality and disturbance rejection capability in the newly control mechanism. Although the speed trajectory tracking performance of both the controllers presented in this study is comparable, comparatively low dynamic performance was found for PPI-GA controller at both high and low speed tests inside the same search space. The PPI-PSO controller yields an optimal result having 0.270 % overshoot, a settling time of 8.185 s, and a rise time of 8.037 s in comparison with PPI-GA controller which exhibits overshoot of 0.640 %, a settling time of 9.596 s, and a rise time of 8.615 s with high-speed trajectory tracking test.

Deadbeat Predictive Current Control for Surface-Mounted Permanent-Magnet Synchronous Motor Based on Weakened Integral Sliding Mode Compensation

Deadbeat predictive current control (DPCC) has excellent dynamics and can achieve current control with less computational effort. However, its control performance relies on the precision of the parameters of the motor. Current static error will be generated and control performance will be decreased when the predictive model parameters do not correspond to the practical parameters of the motor. In this article, a weakened integral sliding mode compensation method is proposed which converts the current error into a voltage compensation term and adds it to the prediction control output to effectively compensate for the steady-state error. In addition, a boundary layer is introduced to weaken the integral so as to solve the problems of integral saturation and overshoot caused by the introduction of the integral term when the error is large. Moreover, weight factors are introduced to optimize the feedback current, which enhances the robustness of the system. In the end, the effectiveness of this method is verified via simulation and experimental results.

Model-based neuroadaptive event-triggered tracking consensus control for nonlinear multiagent systems with input delay

In this article, a neuroadaptive event-triggered control methodology is proposed to tackle the leader-following tracking consensus issue of uncertain nonlinear multiagent systems (MASs) with input delay and external disturbances. The proposed approach incorporates radial bias function neural networks (RBF NNs) and the integral compensation technique, effectively addressing the issues of nonlinear uncertainty and input delay, respectively. For the sake of reducing the transmission of information, we adopt the strategy that the neural network (NN) weight update law is only changed at the event-triggered instant, and a novel adaptive model and related controller are constructed. Simultaneously, this paper establishes an impulsive dynamic system to analyze the stability of the closed-loop system by extending the Lyapunov theorem to continuous and reset dynamics. Sufficient conditions for achieving leader-following tracking consensus are derived without the Zeno behavior. Finally, a numerical example is presented to illustrate the validity of the proposed method.

Cooperative control of velocity and heading for unmanned surface vessel based on twin delayed deep deterministic policy gradient with an integral compensator

This paper addresses cooperative control of velocity and heading for an unmanned surface vessel (USV) utilizing a twin delay deep deterministic policy gradient (TD3) reinforcement learning algorithm. The utilization of a deep neural network establishes a direct correlation between the USV’s state parameters and motor control quantities. A reward function is devised to update the network parameters and which acquires the trained model. The introducing of an integral compensator effectively eliminates the steady-state error of the system, thereby significantly enhancing the precision of both velocity control and heading control. Furthermore, a two-stage training algorithm comprising offline learning and online learning has been devised. Through offline learning, a deep neural network model for the USV controller is obtained. Subsequently, the optimization of the controller strategy is conducted during the online learning phase. Ultimately, the simulation results demonstrate the exceptional control performance attained by the proposed algorithm.