Linear Feedback Research Articles

Model Simplification for Asymmetric Marine Vehicles in Horizontal Motion—Verification of Selected Tracking Control Algorithms

This paper addresses a trajectory tracking control algorithm for underactuated marine vehicles moving horizontally in which the current in the North–East–Down frame is constant. This algorithm is a modification of a control scheme based on the input-output feedback linearization method, for which the application condition was that the vehicle was symmetric with respect to the left and right sides. The proposed control scheme can be applied to a fully asymmetric model, and, therefore, the geometric center can be different from the center of mass in both the longitudinal and lateral directions. A velocity transformation to generalized vehicle equations of motion was used to develop a suitable controller. Theoretical considerations were supported by simulation tests performed for a model with 3 degrees of freedom, in which the performance of the proposed algorithm was compared with that of the original algorithm and the selected control scheme based on a combination of backstepping and integral sliding mode control approaches.

Gaussian process-based nonlinearity compensation for pneumatic soft actuators

Abstract Highly compliant Pneumatic Soft Actuators (PSAs) have the potential to perform challenging tasks in a broad range of applications that require shape-adaptive capabilities. Achieving accurate tracking control for such actuators with complex geometries and material compositions typically involves many time-consuming and laborious engineering steps. In this work, we propose a data-driven learning-based control approach to address reference tracking tasks, incorporating self-adaptation in situ. We utilize a short interaction maneuver, recorded a priori, to collect the quasi-static data affected by severe hysteresis. Besides a linear feedback controller, we use two Gaussian process models to predict the feedforward control input to compensate for the nonlinearity in a one-shot learning setting. The proposed control approach demonstrates accurate tracking performance even under realistic varying configurations, such as alterations in mass and orientation, without any parameter tuning. Notably, training was achieved with only 25–50 s of experimental interaction, which emphasizes the plug-and-play capabilities in diverse real-world applications.

Adaptive PMSM Control of Ship Electric Propulsion with Energy-Saving Features

Electric ship propulsion is considered one of the most promising alternatives to conventional combustion systems. Its goal is to reduce the carbon footprint and increase a ship’s maneuverability, operational safety, and reliability. The high requirements for ship propulsion make permanent magnet synchronous motors (PMSMs) an attractive solution due to their characteristics. This paper discusses the control problem of a PMSM based on the input–output feedback linearization method combined with the optimal and adaptive control techniques. The method presented here integrates the parameter tuning process with the optimal design of the baseline controller. Since the load disturbances are treated as an additional unknown parameter, there is no need to introduce an integral action to deal with the resulting steady-state error. An important feature of the designed controller is the so-called energetic optimization of the system; i.e., in addition to the aforementioned adaptive and optimal controller, it has a feature of ensuring zero reactive power consumed by the system. The performed simulations of the machine speed stabilization process confirmed the high efficiency of the proposed controller despite the assumed uncertainty of the system parameters and environmental (load) disturbances. Besides achieving high-quality control, an essential feature of this approach is the elimination of the tuning problem.

An Atraumatic Mock Loop for Realistic Hemocompatibility Assessment of Blood Pumps.

Conventional mock circulatory loops (MCLs) cannot replicate realistic hemodynamic conditions without inducing blood trauma. This constrains in-vitro hemocompatibility examinations of blood pumps to static test loops that do not mimic clinical scenarios. This study aimed at developing an atraumatic MCL based on a hardware-in-the-loop concept (H-MCL) for realistic hemocompatibility assessment. The H-MCL was designed for 450 ± 50 ml of blood with the polycarbonate reservoirs, the silicone/polyvinyl-chloride tubing, and the blood pump under investigation as the sole blood-contacting components. To account for inherent coupling effects a decoupling pressure control was derived by feedback linearization, whereas the level control was addressed by an optimization task to overcome periodic loss of controllability. The HeartMate 3 was showcased to evaluate the H-MCL's accuracy at typical hemodynamic conditions. To verify the atraumatic properties of the H-MCL, hemolysis (bovine blood, n = 6) was evaluated using the H-MCL in both inactive (static) and active (minor pulsatility) mode, and compared to results achieved in conventional loops. Typical hemodynamic scenarios were replicated with marginal coupling effects and root mean square error (RMSE) below 1.74 ± 1.37 mmHg while the fluid level remained within ±4% of its target value. The normalized indices of hemolysis (NIH) for the inactive H-MCL showed no significant differences to conventional loops ( ∆NIH = -1.6 mg/100 L). Further, no significant difference was evident between the active and inactive mode in the H-MCL ( ∆NIH = +0.3 mg/100 L). Collectively, these findings indicated the H-MCL's potential for in-vitro hemocompatibility assessment of blood pumps within realistic hemodynamic conditions, eliminating inherent setup-related risks for blood trauma.

Nonlinear model predictive control—Cross-coupling control with deep neural network feedforward for multi-hydraulic system synchronization control

This paper studies a multi-hydraulic system (MHS) synchronization control algorithm. Firstly, a general nonlinear asymmetric MHS state space entirety model is established and subsequently the model form is simplified by nonlinear feedback linearization. Secondly, an entirety model-type solution is proposed, integrating a nonlinear model predictive control (NMPC) algorithm with a cross-coupling control (CCC) algorithm. Furthermore, a novel disturbance compensator based on the system's inverse model is introduced to effectively handle disturbances, encompassing unmodeled errors and noise. The proposed innovative controller, known as nonlinear model predictive control—cross-coupling control with deep neural network feedforward (NMPC-CCC-DNNF), is designed to minimize synchronization errors and counteract the impact of disturbances. The stability of the control system is rigorously demonstrated. Finally, simulation results underscore the efficacy of the NMPC-CCC-DNNF controller, showcasing a remarkable 60.8% reduction in synchronization root mean square error (RMSE) compared to other controllers, reaching up to 91.1% in various simulations. These results affirm the superior control performance achieved by the NMPC-CCC-DNNF controller.

Active and passive heave compensation system based on feedback linearization sliding mode variable structure control

This study presents a novel electric-hydraulic servo system with an active–passive lift compensation feature designed for a lifting crane used in offshore operations. Additionally, the study explores the control methodology of this system. Firstly, the principle of the combined active–passive lift-compensated system is explained, and the mathematical model of the response is established. To eliminate the strong nonlinearities inherent and mismatched term, the method of exact input-state linearization is employed. For observing the uncertain disturbance terms in the model, a new type of expanded state sliding mode observer(ESSMO) is designed. Subsequently, a control strategy of sliding mode with variable structure is designed using the method of hyperbolic convergence law. The stability of the controller is proved based on Lyapunov’s stability theorem. Finally, the control method is simulated and analyzed under different working conditions and compared with traditional PID control and sliding mode control strategies directly designed by the nonlinear model. The simulation results demonstrate that the feedback linearized hyperbolic convergence law sliding mode control strategy not only reduces dependence on exact parameters of the original system but also exhibits strong robustness and suppression of model nonlinearities and parameter uncertainty.

Robust tracking and model following of uncertain nonlinear systems with some uncertainties and dead-zone inputs

The problem of robust tracking and model following is reconsidered for a class of uncertain nonlinear systems with some uncertainties and dead-zone input constraints. In this paper, the system uncertainties are regarded as some nonlinear functions which are not required to must satisfy the matching conditions. That is, being different from traditional robust control theory, the matched structures of uncertainties are sufficient, but not necessary, for being able always to design some types of robust tracking control schemes. In addition, the external disturbances of dynamical systems are assumed to be any bounded functions which is not also required to satisfy the matching condition. By making use of the integral inequality, instead of Lyapunov function, a class of robust tracking control schemes is constructed to guarantee the uniform exponential boundedness of the model tracking errors. Moreover, the upper bounds of nonlinear uncertainties are not required to be known, and it is also unnecessary to know or estimate the characteristic parameters of dead-zone functions. Therefore, the resulting robust tracking control schemes have a simple structure. Actually, the resulting robust tracking control scheme is a linear feedback control one with a self-tuning control gain. Finally, an illustrative numerical example is provided to demonstrate the validity of the presented theoretical results.

Redundant Space Manipulator Autonomous Guidance for In-Orbit Servicing via Deep Reinforcement Learning

The application of space robotic manipulators and heightened autonomy for In-Orbit Servicing (IOS) represents a paramount pursuit for leading space agencies, given the substantial threat posed by space debris to operational satellites and forthcoming space endeavors. This work presents a guidance algorithm based on Deep Reinforcement Learning (DRL) to solve for space manipulator path planning during the motion-synchronization phase with the mission target. The goal is the trajectory generation and control of a spacecraft equipped with a 7-Degrees of Freedom (7-DoF) robotic manipulator, such that its end effector remains stationary with respect to the target point of capture. The Proximal Policy Optimization (PPO) DRL algorithm is used to optimize the manipulator’s guidance law, and the autonomous agent generates the desired joint rates of the robotic arm, which are then integrated and passed to a model-based feedback linearization controller. The agent is first trained to optimize its guidance policy and then tested extensively to validate the results against a simulated environment representing the motion synchronization scenario of an IOS mission.

Constrained State Regulation Problem of Descriptor Fractional-Order Linear Continuous-Time Systems

This paper deals with the constrained state regulation problem (CSRP) of descriptor fractional-order linear continuous-time systems (DFOLCS) with order 0<α<1. The objective is to establish the existence of conditions for a linear feedback control law within state constraints and to propose a method for solving the CSRP of DFOLCS. First, based on the decomposition and separation method and coordinate transformation, the DFOLCS can be transformed into an equivalent fractional-order reduced system; hence, the CSRP of the DFOLCS is equivalent to the CSRP of the reduced system. By means of positive invariant sets theory, Lyapunov stability theory, and some mathematical techniques, necessary and sufficient conditions for the polyhedral positive invariant set of the equivalent reduced system are presented. Models and corresponding algorithms for solving the CSRP of a linear feedback controller are also presented by the obtained conditions. Under the condition that the resulting closed system is positive, the given model of the CSRP in this paper for the DFOLCS is formulated as nonlinear programming with a linear objective function and quadratic mixed constraints. Two numerical examples illustrate the proposed method.

A fully actuated system approach: Desired compensation adaptive robust control for uncertain nonlinear systems

A desired compensation adaptive robust control (DCARC) framework is presented for two types of fully actuated systems (FASs) subject to both parametric and nonlinear uncertainties based on the Lyapunov theory. The designed controller consists of three parts: (i) a fundamental linear state error feedback term; (ii) an adaptive feedforward compensation term; (iii) a robust compensation term. Different from the existing FAS approaches, the adaptive compensation in the proposed controller relies on the noise-free desired trajectory and online parameter estimate only. A better overall tracking performance with an accelerated transient response is expected, arising from significantly reducing interaction between the robustness part and the adaptation part. Through theoretical analysis, the proposed controller ensures that the estimation error of the unknown parameter vector and the tracking error finally converge to a bounded ellipsoid. The comparative simulation of a permanent magnet (PM) stepper motor demonstrates the effectiveness of the presented approach.

Time-optimal coordinated detumbling and pose adjusting control of a non-cooperative target with model uncertainties

In this paper, a novel post-capture takeover control strategy of non-cooperative target with model uncertainties by the dual-arm space manipulator is proposed. Two mission objectives of target detumbling and pose adjusting are comprehensively considered. First, the motion trajectory of the target is parameterized with normalized time by a Bezier shape-based function. On this basis, by considering the resultant external force and moment constraint and the model uncertainties of the target, the mission duration is optimized to obtain the time optimal detumbling and pose adjusting the trajectory of the target. Furthermore, the desired trajectory in manipulator joint space is obtained by introducing the arm angle inverse kinematics method, and a joint trajectory tracking controller is designed based on the feedback linearization theory to track the desired joint trajectory. Simulation results show that detumbling and pose adjusting can be simultaneously achieved by one control action, which verifies the effectiveness of the proposed integrated control strategy.

Fin failure tolerant control of agile air vehicle using feedback linearization

The probability of actuator lock, control surface damage, and thermal insulation failure on supersonic aircraft due to high speed and temperature is significant. Additionally, foldable fins are often used in missiles to increase the number of missiles that can be loaded onto a launcher and facilitate transportation, but this design presents the potential for malfunction and failure to open during flight. This study focuses on scenarios where control surfaces do not open or are partially damaged, leading to asymmetries and changes in the vehicle’s dynamics and aerodynamic model. The aim is to detect such failures and design a control system that can withstand these issues. To achieve this, the paper proposes an equivalent aerodynamic model representing the vehicle’s dynamics. The health of each fin is monitored using a nonlinear filter to estimate a parameter. Using separation theory, the dynamic system is divided into fast and slow subsystems, and a control signal for the faulty dynamics is designed based on back-stepping theory principles. Furthermore, the control allocation method is modified to accommodate the condition of the fins and generate the desired control moment. The proposed technique can quickly detect and isolate fin failures within seconds, while the designed controller effectively compensates for these failures.

Research on decoupling greenhouse temperature and humidity based on feedback linearization

In order to improve the control effect of each environmental factor of conventinal glasshouse, a realistic nonlinear glasshouse system feedback linearization decoupling control arithmetic has been reported. The multi-input, multi-output system which is nonlinear is turned into two detached single-input, single-transport stepwise linear systems by implementing the encoder algorithm, and the relation of the ambient components, which is strong coupling, such as the temperature and humidity, is alleviated. The simulation results show that if the target value of the environmental factor is within a proper controllable range, the controlled system of greenhouse temperature and humidity can achieve a good following effect, eliminate the coupling between temperature and humidity, and improve the accuracy of temperature and humidity control, which can effectively reduce energy consumption and improve the comprehensive benefit of greenhouse production. Precision of temperature and humidity control, which can effectively reduce energy consumption and improve the comprehensive benefits of greenhouse production

Communication topology for AUV formation consensus based on optimal cost control under time-varying communication and input delays

This study investigates the optimal communication topology for consensus in autonomous underwater vehicle (AUV) formations, considering both leader-following and leaderless scenarios. Initially, a second-order dynamic model of the AUV is established using the feedback linearization method. To address time-varying delays, a universal predictor-based consensus protocol is introduced, capable of operation with or without a designated leader. Subsequently, two global quadratic cost functions are formulated based on distinct consensus errors. Utilizing linear quadratic regulator (LQR) theory and matrix theory, the optimal communication topologies and associated gain matrices are deduced. Specifically, for leader-following AUV formations, the optimal communication topology is identified as an unevenly weighted star-shaped directed spanning tree. Conversely, for leaderless formations, the optimal topology adopts a complete digraph, which indicates high interaction requirements. To accommodate practical constraints, a suboptimal topology is devised, featuring a directed spanning tree. These findings offer a theoretical framework for selecting communication topologies in AUV formations, with numerical examples provided to validate the proposed approaches.

Using a Flywheel to Stabilize a Self-Balancing Bicycle

The designs of two linear control systems approach to stabilize the balance of an unmanned bicycle system are presented. Both approaches are based on the use of a reaction wheel or flywheel to balance the bicycle. The two linear control approaches, based on the linearization of a nonlinear model obtained using Lagrange formalism, are the classic linear controllers, PID and State Feedback control. The performance of both controllers is verified by digital simulation and real-time experimental results.

A simultaneous area, delay and leakage current reduction method for Linear Feedback Shift Register (LFSR) using pulsed latches and DTMOS transistors

In digital circuits, the shift registers are the significant elements having the ability of storing and transmitting the data in sequential manner.The linear feedback shift register (LFSR) uses large number of flips-flops that consumes maximum amount of power. To overcome this issue, this research work concentrates on the design of LFSR for the area efficient, power reduction, minimization of delay and leakage current. By replacing the d-flip-flop with the bi-enabled pulsed latch to reduce the power consumption and delay of the proposed LFSR design. For the minimization of area, leakage current and delay, the hybrid body bias generator with dynamic threshold MOS (BBG-DTMOS) is used. Moreover, the pulsed clock signal is generated in the digital circuit with the aid of hybrid BBG-DTMOS technique. The proposed LFSR design is implemented in the tanner EDA tool with the available CMOS model libraries. Based on the implementation result, the proposed LFSR area is 1824 μm2and its power consumption is 172μW at a 100 MHz clock frequency withVDD=5V. Furthermore, having the better performance in different corners of the method, reduces the propagation delay and leakage current in the digital circuit. The proposed LFSR design is compared with some of the shift registers such as unidirectional and bidirectional shift registers. The existing clock pulse generator such as conventional, delayed clock pulse, TIMBER logic, PTL-AND logic and multiplexer based clock pulse generator (MCPG) are compared with the proposed BBG-DTMOS technique.

Torque modulation mechanism of the knee joint during balance recovery

Exploring the torque modulation mechanisms of human joints is critical for analyzing the human balance control system and developing natural human-machine interactions for balance support. However, the knee joint is often overlooked in biomechanical models because of its limited range of motion during balance recovery. This poses a challenge in establishing mathematical models for the knee joint's torque modulation mechanisms using computer simulations based on the inverted pendulum model. This study aims to provide a simplified linear feedback model inspired by sensorimotor transformation theory to reveal the torque modulation mechanism of the knee joint. The model was validated using data from experiments involving support-surface translation perturbations. The goodness-of-fit metrics of the model, including R2 values and root mean square errors (RMSE), demonstrated strong explanatory power (R2 ranged from 0.77 to 0.90) and low error (RMSE ranging from 0.035 to 0.072) across different perturbation magnitudes and directions. Through pooling samples across various perturbation conditions and conducting multiple fits, this model revealed that knee torque is modulated using a direction-specific strategy with adaptable feedback gains. These results suggest that the proposed simplified linear model can be used to develop assistive systems and retrieve insights on balance recovery mechanisms.

Dynamic model of high-speed maglev train-guideway bridge system with a nonlinear suspension controller

To improve the anti-interference ability of maglev trains, a dynamic model of the high-speed maglev train with a nonlinear suspension controller for the guideway system is proposed in this paper. Based on the nonlinear characteristics of the magnetic suspension system, a nonlinear decoupling controller is designed using the feedback linearization theory. Then, a high-speed maglev train model is refined with a guideway coupling system, consisting of a maglev train simulated as a multi-body dynamics model with 537 degrees of freedom and a spatial finite element model of the guideway. Taking the Shanghai high-speed maglev train as an example, the correctness of the computational model is verified by comparing the modeling results with field measurement data, and the control effectiveness of the nonlinear controllers and the traditional PD controllers is compared considering different train speeds and disturbance forces. The results show that the suspension gap under the decoupling control is smaller than that under the PD control during the train operations. Under the same disturbance force, the decoupling control exhibits better control performance than the PD control. The variation amplitudes of the magnetic pole gaps are generally linearly related to the disturbance force.

FPGA-Based Speed Control Strategy of PMSM Using Improved Beetle Antennae Search Algorithm

To improve performance in terms of overshoot and motor response speed when a permanent-magnet synchronous motor (PMSM) with a proportional–integral (PI) controller is subjected to external disturbances, this paper proposes a speed control strategy based on an enhanced Beetle Antennae Search algorithm, which allows for adjustable parameters of the PI controller within a certain range. Firstly, to enhance the global and local search capabilities of each individual beetle, the step size was improved by linearly decreasing it. Secondly, a simulation model of a PMSM closed-loop control system was built to verify the effectiveness of the improved Beetle Antennae Search (BAS) algorithm. Finally, a linear feedback shift register model that generates four random numbers was developed on a field-programmable gate array (FPGA). The improved BAS algorithm for the PMSM control system was implemented on an FPGA using the Verilog hardware description language, and the feasibility of the system was verified through hardware simulation. Additionally, the hardware resource consumption on different FPGA platforms was analyzed. The simulation results demonstrate that the proposed new speed control strategy can reduce the overshoot and improve the motor response speed.

Robust Direct Power Control of Three-Phase PWM Rectifier with Mismatched Disturbances

To effectively eliminate the impacts of both matched and mismatched power disturbances in a three-phase PWM rectifier, this paper proposes a robust direct power control (RDPC) method with a single-loop control structure. Firstly, a nonlinear power model of the three-phase PWM rectifier is established. Then, using the exact feedback linearization method, a linearized power model including matched and mismatched power disturbances is derived and achieves the decoupling of active and reactive power. Secondly, to regulate the DC bus voltage, a sliding-mode controller (SMC) combined with a nonlinear disturbance observer (NDO) is proposed. The proposed SMC combined with an NDO (SMC + NDO) method features a single-loop control structure, which enables a faster response and simpler structure compared to the dual-loop DPC method. By incorporating estimated mismatched power disturbance into the sliding-mode surface, it overcomes the SMC’s defect in incompletely suppressing mismatched disturbances and enables the simultaneous regulation of voltage and active power. Additionally, it effectively reduces sliding-mode chattering. To regulate reactive power, a sliding-mode controller based on the exponential convergence law is designed to suppress matched reactive power disturbances. Finally, the simulation and experimental comparative results demonstrate that the proposed controller exhibits stronger robustness against matched and mismatched power disturbances, as well as a better performance under the constant power load (CPL).