Simple Feedback Control Research Articles

Synchronization of a nonlinear 4D hyperchaotic system using linear feedback control strategy

Abstract This paper uses a linear feedback control strategy to discuss the synchronization analysis of the nonlinear 4D hyperchaotic system. Targeting four control schemes, namely four, three, two, and one simple linear feedback controller, respectively, the synchronization of this hyperchaotic system was achieved through the Backstepping method. By using some simpler controllers, global asymptotic synchronization has been achieved. Among these four schemes, sufficient conditions for the synchronization of two identical hyperchaotic systems were derived using linear feedback control and the Lyapunov stability theorem. Finally, these results were validated through numerical simulation examples, demonstrating the correctness and effectiveness of the theoretical analysis.

Robust finite-time output feedback stabilisation for a class of uncertain planar systems with asymmetric output constraints

This paper considers the finite-time output feedback stabilisation (FTOFS) problem for a class of uncertain planar systems with asymmetric output constraints. The presence of unknown control coefficients, unknown measurement sensitivity and asymmetric output constraints makes the system under consideration essentially different from those in the existing related works. By constructing a new barrier Lyapunov function and applying homogeneous system theory, a simple proportional-derivative like finite-time output feedback controller is explicitly constructed, which only utilises the output information. A rigorous proof demonstrates that not only the closed-loop system is finite time stable, but also the requirement of asymmetric output constraint can be achieved. The novelty of the control approach lies in that it is capable to handle the FTOFS problem for uncertain planar systems with or without asymmetric output constraints in a unified manner, without changing the control structure. The efficiency of the proposed theoretical results are confirmed by simulation results.

Fish couple forecasting with feedback control to chase and capture moving prey.

Predator-prey interactions are fundamental to ecological and evolutionary dynamics. Yet, predicting the outcome of such interactions-whether predators intercept prey or fail to do so-remains a challenge. An emerging hypothesis holds that interception trajectories of diverse predator species can be described by simple feedback control laws that map sensory inputs to motor outputs. This form of feedback control is widely used in engineered systems but suffers from degraded performance in the presence of processing delays such as those found in biological brains. We tested whether delay-uncompensated feedback control could explain predator pursuit manoeuvres using a novel experimental system to present hunting fish with virtual targets that manoeuvred in ways that push the limits of this type of control. We found that predator behaviour cannot be explained by delay-uncompensated feedback control, but is instead consistent with a pursuit algorithm that combines short-term forecasting of self-motion and prey motion with feedback control. This model predicts both predator interception trajectories and whether predators capture or fail to capture prey on a trial-by-trial basis. Our results demonstrate how animals can combine short-term forecasting with feedback control to generate robust flexible behaviours in the face of significant processing delays.

Advanced Feedforward Controller for a Molten Salt Receiver in Star Design Based on Real-Time Flux Measurement

This paper presents a control system with a panel-wise applied feedforward temperature controller for a molten salt receiver in star design utilizing temperature measurements in the connecting pipes between the panels and a real-time flux density measurement as inputs. It is tested in realistic cloud passage scenarios and the results are compared to the results from an earlier developed control system for the same receiver, in which the temperature controller is based on a simple feedback controller (PID) supported by a simple feedforward controller. The results show that the performance of the new feedforward controller is outstanding and could be applied to common cylindrical receiver designs as well. Nevertheless, the highly increased actuator movement of the control valves is to be further investigated.

Advances in Coupling Computational Fluid Dynamics and Discrete Element Method in Geotechnical Problems

In some cases, the water content in granular soil increases to the extent that it becomes saturated, which noticeably alters its responses. For example, the pore water pressure within saturated granular soil would increase rapidly under sudden external loading, which is equivalent to undrained or constant volume conditions. This reduces the effective stress in soil dramatically and may result in catastrophic failure. There have been different numerical approaches to analyse such a failure mechanism of soil to provide a deeper understanding of soil behaviour at the microscopic level. One of the most common numerical tools for such analysis is the discrete element method (DEM) due to its advantage in obtaining microscopic properties (e.g., statistics on particle contacts and fabric), reproducibility and simple feedback control. However, most DEM studies ignore the fluid phase and merely consider the solid particles while the fluid pressure is indirectly calculated by mimicking undrained condition to a constant volume condition. Note that fluid’s influence does not limit to the change of pore water pressure. For example, the external loading would induce the movement of fluid, and the fluid-solid interaction could subsequently drag the solid particles to shift within the system. In addition, the state of soil could change from solid to suspension under an excess hydraulic gradient. Therefore, the study of the fluid-solid mixture is essential as it is a typical scenario in geotechnical practice, and the simulations of saturated sand should be conducted in numerical forms in which both the solid and fluid phases can be modelled.

Three-dimensional motion control of an untethered magnetic object using three rotating permanent magnets

Magnetic motion control has been actively studied mainly for the purpose of biomedical applications. However, in many cases, many actuator magnets surround a small magnet to be moved, and they consume large electric power. In some cases, complex calculations are required to estimate the control input of the actuator magnets. This study proposes a simple method to move a small magnet to the desired positions. For this, three cylindrical permanent magnets magnetized in the radial direction were positioned as the sides of a triangle; these actuator magnets were rotated using motors. By monitoring the position of the small magnet and through simple feedback control based on the angles of the three actuator magnets, the untethered small magnet could be moved along arbitrary three-dimensional (3D) paths. The control principle was established by calculating the magnetic force and torque acting on the small magnet for some sets of actuator-magnet angles.

Taming chaos in generalized Liénard systems by the fractional-order feedback based on Melnikov analysis

The dynamical behavior of Liénard systems has always been a hot topic in nonlinear analysis. In the present study, a simple fractional-order feedback controller is put forward to tame chaos for a class of forced generalized Liénard systems. Adopting harmonic balance method, the first-order approximate equivalent integer-order system of the original fractional-order system is deduced. Then the criterion for taming chaos is established by employing the Melnikov approach. Duffing-Rayleigh chaotic oscillator is taken as an example to illustrate the validity of the proposed method. Firstly, the critical feedback intensity and differential order for taming chaos are obtained by the proposed criterion. Then, multiple numerical indicators such as phase portrait, time history plot, Lyapunov exponent and bifurcation diagram are provided to assist in analyzing theoretical results.

Feedback Control of Electrospray with and without an External Liquid Pump Using the Spray Current and the Apex Angle of a Taylor Cone for ESI-MS.

An electrospray operated in the steady cone-jet mode is highly stable but the operating state can shift to pulsation or multijet modes owing to changes in flow rate, surface tension, and electrostatic variables. Here, a simple feedback control system was developed using the spray current and the apex angle of a Taylor cone to determine the error signal for correcting the emitter voltage. The system was applied to lock the cone-jet mode operation against external perturbations. For a pump-driven electrospray at a regulated flow rate, the apex angle of the Taylor cone decreased with increasing voltage. In contrast, for a voltage-driven electrospray with low flow resistance, the angle was found to increase with the emitter voltage. A simple algorithm based on iterative learning control was formulated and implemented using a personal computer to automatically correct the emitter voltage in response to the error signal. For voltage-driven electrospray ionization (ESI), the feedback control of the spray current can also be used to regulate the flow rate to an arbitrary value or pattern. Electrospray ionization-mass spectrometry (ESI-MS) with feedback control was demonstrated to produce ion signal acquisition with long-term stability that was insusceptible to the emulated external disturbances.

Krasovskii and shifted passivity based output consensus

Motivated by current sharing in power networks, we consider a class of output consensus (also called agreement) problems for nonlinear systems, where the consensus value is determined by external disturbances, e.g., power demand. This output consensus problem is solved by a simple distributed output feedback controller if a system is either Krasovskii or shifted passive, which is the only essential requirement. The effectiveness of the proposed controller is shown in simulation on an islanded DC power network.

Hydraulic Power System Control using State Feedback Controller (SFC)

In an electrical network, generators work and provide power to the loads. When the load on the generator increases, the speed of the generator decreases then resulting in a reduction in the frequency of the network. This paper was designed within the state feedback controller (SFC) to improve the hydraulic power system performance. The performance of the proposed controller is compared with simple feedback controller (FC) in the simulation environment. The load variation was tested which is 5%, 10%, and 20% variation. The testing results show that in terms of steady state error (SSE) and overshoot, the SFC is superior. In terms of settling time, the FC method is faster. Since it quickly reaches steady event not getting into set-point. The overall, it can be concluded that SFC can give better performance than FC in the frequency control of a hydraulic power system.

Linear Stability of Reversing a Car-trailer Combination

In this paper, we investigate the reverse motion of a car-trailer combination. The single track model of the vehicle is used with quasi-static tire model to design a simple linear feedback controller that can achieve stable reversing motion along a straight path. The linear stability of the closed-loop system is analyzed by constructing stability charts in the plane of the control gains. The effect of the reversing speed of the vehicle on the stability is also shown. In order to validate the theoretical results, laboratory experiments are carried out using a small-scale vehicle and a conveyor belt.

The impact of personal preference-based thermal control on energy use and thermal comfort: Field implementation

Recent research efforts on modeling personal thermal comfort support the integration of personalized preferences in optimal building control and further implementation in real buildings. This paper presents the development and field implementation of personal preference-based thermal control (i.e., a controller that provides thermal conditions to satisfy personal preferences) in real offices, emphasizing the role of model predictive control (MPC) and low-cost local sensing. Probabilistic thermal preference profiles were developed from experiments collected in identical private offices with controllable VAV systems. A low-cost thermal sensing network and a MPC framework were integrated into a centralized building management and control system. Customized, preference-based HVAC control was then experimentally implemented in the offices to (i) quantify the personal comfort penalty when using conventional wall thermostat versus local sensing-based operation for two distinct thermal preference profiles; (ii) evaluate the impact of personalized MPC (dynamic setpoint) on energy use and personal comfort compared with personalized simple feedback control (static setpoint), using local sensing; (iii) compare the personalized MPC performance for two distinct thermal preference profiles under different weather conditions. The results indicate the comfort benefits of monitoring local thermal conditions (vs wall thermostats) for different preference profiles and showed 28–35% energy savings with personalized MPC (vs personalized static setpoint control). The overall personalized MPC performance (and energy consumption) depends on the personal thermal preference characteristics and outdoor conditions.

Direct Power Control of a Surface-Mounted Permanent Magnet Synchronous Generator Wind Turbine for Offshore Applications

This paper proposes a direct power control scheme for an offshore wind turbine-driven surface-mounted permanent magnet synchronous generator with a full back-to-back converter situated onshore to decentralize the weight of the turbine. The proposed model is designed in a stationary reference frame and does not require a phase-locked loop as opposed to the traditional vector current control method. Simple feed-forward and feedback control loops are used in the proposed model to extract the maximum available wind power, maintain constant voltage at the coupling DC link, and ensure power injection into the electric network at unity power factor. Simulation results carried out in MATLAB/SIMULINK show that the proposed model has fast transient response and steady-state performance consistent with the vector current control model. Furthermore, eigenvalue analysis results demonstrate that the proposed method’s performance is robust to variations in different system parasitic elements, even under both stiff and weak electric network conditions. These results also indicate that the back-to-back converter can operate effectively when located onshore close to the load center, while the turbine is in close proximity offshore. This can be suitable for multiple specific offshore applications as it has the potential to reduce the overall weight, volume, and cost of the offshore wind turbine infrastructure.

ASPR-based Output Feedback Control with Virtual PFC for Output Tracking

Nowadays, the output feedback control method based on the Almost Strictly Positive Real (ASPR) property gets many attentions and has been researched widely. ASPR models can be stabilized by applying simple output feedback control; so the designed controllers have a simple structure. However, the systems have to satisfy quite strict conditions in order to obtain ASPR-ness, although almost all practical systems do not have the ASPR property. Therefore, for relaxing those conditions, the introduction of a Parallel Feedforward Compensator (PFC) has been proposed. This method can render the resulting augmented system ASPR. Up to now, several PFC design methods have been proposed, and one of them is an adaptive PFC design scheme. This technique has a feature that it can design a PFC automatically by utilizing online data. Furthermore, for the purpose of output regulation, the control design methods with an adaptive PFC have been proposed. Unfortunately, however, in almost all schemes, the discussion on the convergence of actual errors has not been conducted. Therefore, in this paper, introducing a virtual PFC model and an auxiliary input for ensuring ASPR-ness, a new ASPR-based output feedback control method is proposed, and the stability analysis and convergence of the actual error are discussed. Finally, the effectiveness of the proposed method is confirmed via numerical simulations.

Minimum-Time Escape from a Circular Region for a Dubins Car

We investigate the problem of finding paths that enable a robot modeled as a Dubins car (i.e., a constant-speed finite-turn-rate unicycle) to escape from a circular region of space in minimum time. This minimum-time escape problem arises in marine, aerial, and ground robotics in situations where a safety region has been violated and must be exited before a potential negative consequence occurs (e.g., a collision). Using the tools of nonlinear optimal control theory, we show that a surprisingly simple closed-form feedback control law solves this minimum-time escape problem, and that the minimum-time paths have an elegant geometric interpretation.

COM Shifter and Body Rotator for Step-by-Step Teleoperation of Bipedal Robots

This paper presents a controller for step-by-step teleoperation of bipedal robots, in which the user commands the robot’s foot motions in a step-by-step manner through a pair of handheld 3-dimensional pointing devices. The proposed controller is intended to allow users to precisely manipulate the swing foot motions to traverse rough terrains by avoiding obstacles. It aims to realize quick response to user commands and stable automatic balancing even under erroneous user commands. The main components of the proposed controller are a COM (center-of-mass) shifter and a body rotator, which are simple sensory feedback controllers that do not involve first-in first-output (FIFO) buffers, time-series generation, or online optimization. The COM shifter is a controller to produce a COM motion according to a reference zero moment point (ZMP). The body rotator complements the COM shifter to produce an appropriate angular momentum rate to enhance the regulation of ZMP. The proposed controller is validated in our interactive/realtime simulation environment.

Aiding reinforcement learning for set point control

While reinforcement learning has made great improvements, state-of-the-art algorithms can still struggle with seemingly simple set-point feedback control problems. One reason for this is that the learned controller may not be able to excite the system dynamics well enough initially, and therefore it can take a long time to get data that is informative enough to learn for good control. The paper contributes by augmentation of reinforcement learning with a simple guiding feedback controller, for example, a proportional controller. The key advantage in set point control is a much improved excitation that improves the convergence properties of the reinforcement learning controller significantly This can be very important in real-world control where quick and accurate convergence is needed. The proposed method is evaluated with simulation and on a real-world double tank process with promising results.

Parallel Learning-Based Steering Control for Autonomous Driving

Steering control for autonomous vehicles at high speeds is challenging due to the highly nonlinear vehicle dynamics. The traditional model-based controllers usually degrade significantly in this case. With the development of artificial intelligence, learning-based control methods are emerging as promising alternatives. These methods require a tremendous amount of training data to achieve acceptable performances. However, the data collection process is costly or inefficient. To solve this problem, we propose a parallel learning-based steering control method. Specifically, we first build a neural network (NN) based trajectory generative model (GeneratingNN) based on limited steering-trajectory raw data. The GeneratingNN can efficiently generate sufficient steering-trajectory data by enumerating the allowable steering actions sequences. Then, based on the raw data and generated data, we train another NN (RecallingNN) to learn the inverse mapping relationship between steering actions and trajectories. Hence, the RecallingNN can efficiently recall appropriate steering actions once given the previewed trajectory points. In addition, to further enhance the control accuracy and robustness, we use a simple feedback controller to handle the unmodeled dynamics and external disturbance. Testing results validate that the proposed method can achieve better tracking accuracy, stability and computational efficiency.

Convergence criteria for nonhomogeneous linear nonautonomous real‐order time‐delay systems

Nonhomogeneous linear nonautonomous real‐order time‐delay systems where the coefficient matrices involve time‐varying elements and state variables are dependent on constant multiple delays are considered. Is it possible to determine the limiting behavior of unknown solutions to such systems? We introduce a new comparison inequality, and then by using Laplace transform, we develop some new asymptotic convergence criteria when the coefficient matrices of such systems are constants. We show that it is possible to ensure the limiting behavior of such systems by establishing some new convergence criteria. For an application of interest, we introduce a simple nonhomogeneous linear feedback control and demonstrate that unstable real‐order time‐delay systems can be effectively controlled by using the proposed approach.

Optimal production of microalgae in the presence of grazers

Zooplankton contamination represents a major constraint in large-scale microalgal cultivation systems. While zooplankton contamination cannot be avoided, their development can be controlled by regulating the dilution rate. However, it is not straightforward to find the best control strategy for the dilution rate. Low dilution rates (or long retention times) favor grazer development and high dilution rates avoid their establishment at the risk of reducing microalgal productivity. Furthermore, the presence of periodic regimes arising from the interaction predator–prey makes it unclear if the presence of grazers must be completely avoided. In this paper, we study the role of the dilution rate in the control of zooplankton populations and in the optimization of biomass productivity. We show that in the long-term operation (static optimal control problem or SOCP), the optimal constant dilution rate must ensure the eradication of the zooplankton population. In the case of time-varying dilution rate, we numerically solve an optimal control problem (OCP) over a finite interval of time. We find that the optimal solution approaches the solution for the SOCP most of the time, except when zooplankton actively avoid the pond outflow. Based on these results, we propose a simple sub-optimal feedback control that approximately matches the solution of the OCP when the initial concentration of grazers is low.