Bang-bang Control Research Articles

Adaptive Virtual Inertia Control Strategy of VSG for Micro-Grid Based on Improved Bang-Bang Control Strategy

With the increasing capacity of new energy in the power system, new energy cannot provide support for the system frequency directly. This characteristic of new energy affects the frequency stability of the power system. Therefore the control strategy of a virtual synchronous generator (VSG) is proposed to improve the frequency stability of the system. An adaptive virtual inertia control strategy based on an improved bang-bang control strategy for a micro-grid is presented. On one hand, it can make full use of the variability of virtual inertia to reduce dynamic frequency deviation. On the other hand, the steady-state interval of frequency and the steady-state inertia are set to improve the system frequency stability. Then the stability analysis of the value range of the virtual inertia is performed by the small signal model of the VSG for the micro-grid. Meanwhile, the ranges of virtual inertia and steady-state inertia are determined. Finally, Matlab/Simulink is applied to accomplish simulation experiments to compare various virtual inertia control strategies. The results indicate the effectiveness of the proposed strategy.

About modeling and control strategies for scheduling crop irrigation

Abstract We propose a new simplified crop irrigation model and study the optimal control which consists in maximizing the biomass production at harvesting time, under a constraint on the total amount of water used. Under water scarcity, we show that a strategy with a singular arc can be better than a simple bang-bang control as commonly used. The gain is illustrated on numerical simulations. This result is a promising first step towards the application of control theory to the problem of optimal irrigation scheduling.

Communications and Control for Wireless Drone-Based Antenna Array

In this paper, the effective use of multiple quadrotor drones as an aerial antenna array that provides wireless service to ground users is investigated. In particular, under the goal of minimizing the airborne service time needed for communicating with ground users, a novel framework for deploying and operating a drone-based antenna array system whose elements are single-antenna drones is proposed. In the considered model, the service time is minimized by minimizing the wireless transmission time as well as the control time that is needed for movement and stabilization of the drones. To minimize the transmission time, first, the antenna array gain is maximized by optimizing the drone spacing within the array. In this case, using perturbation techniques, the drone spacing optimization problem is addressed by solving successive, perturbed convex optimization problems. Then, according to the location of each ground user, the optimal locations of the drones around the array’s center are derived such that the transmission time for the user is minimized. Given the determined optimal locations of drones, the drones must spend a control time to adjust their positions dynamically so as to serve multiple users. To minimize this control time of the quadrotor drones, the speed of rotors is optimally adjusted based on both the destinations of the drones and external forces (e.g., wind and gravity). In particular, using bang–bang control theory, the optimal rotors’ speeds as well as the minimum control time are derived in closed-form. Simulation results show that the proposed approach can significantly reduce the service time to ground users compared with a fixed-array case in which the same number of drones form a fixed uniform antenna array. The results also show that, in comparison with the fixed-array case, the network’s spectral efficiency can be improved by 32% while leveraging the drone antenna array system. Finally, the results reveal an inherent tradeoff between the control time and transmission time while varying the number of drones in the array.

Coupling a sunspace to a hyper insulated building: Field tests of different configurations to optimize the energy and comfort performance

An experimental study was conducted on a hyper insulated building coupled with a sunspace, to investigate the role of the major design parameters (depth, glass percentage and typology, etc.) and mechanically controlled convective transfer (VMC) on the energy performance. Based on 132 dynamic simulations, a modifiable sunspace was built on the sun-exposed side of a nZEB mock-up in Central Italy and monitored via an extensive sensor network. The conditioning system tracked the seasonal set point via a bang-bang controller, while the VMC was governed by a bespoke temperature-driven logic. In a previous run, irradiative and combined irradiative-convective modes were tested on a 30% glazed sunspace: VMC was found to dump the daily energy consumption to -27%. Then; a second monitoring campaign compared the 30% and 50% configurations. The former guaranteed very stable indoor conditions (20.1±0.3°C), yet the latter still preserved global comfort at a remarkably lower (-40%) energy expenditure.

Switching Control of GSC of DFIGWTs for Disturbance Rejection Based on Bang–Bang Control

This letter proposes a switching controller (SC) for the grid-side converter (GSC) of doubly-fed induction generator-based wind turbines (DFIGWTs) to improve the disturbance rejection capability of the GSC based on bang–bang funnel control. A bang–bang funnel controller (BBFC) is designed and activated in the cases where the dc-link voltage of a DFIGWT is disturbed far away from its nominal value. A conventional vector controller (VC) is switched on operation when the tracking error of dc-link voltage converges within a prespecified error funnel. The BBFC and the VC constitute a SC. The disturbance rejection performance of the SC was tested through hardware-in-the-loop experiments.

A novel feedrate planning and interpolating method for parametric toolpath in Frenet-Serret frame

In practical machining areas, since parametric toolpath can ensure smaller approximation error in computer-aided design/computer-aided manufacturing (CAD/CAM) systems and provide stable feedrate in computer numerical control (CNC) systems, it can improve machining efficiency and machining quality simultaneously compared to linear and circular segments. Therefore, it is necessary to improve the performance of feedrate planning and interpolating for parametric toolpath. In this paper, the parametric toolpath is re-parameterized by the displacement to analyze the feedrate, acceleration, and jerk constraints in the Frenet-Serret frame, and a novel motion method including feedrate planning and interpolating is presented. Afterwards, a time-optimal method for the parametric trajectory is proposed based on linear programming algorithm to limit the multi-constraints and obtain Bang-Bang control. To improve machining accuracy further, a feedback interpolation method is introduced to eliminate the feedrate fluctuation. Finally, experiments are conducted to demonstrate the efficiency and contour performance of the proposed method compared to the conventional methods. The results show that the proposed method can ensure better contour performance and the cycling time is also reduced by 10.46% and 2.86% for 2D and 3D toolpath respectively.

Near time-optimal controller based on analytical trajectory planning algorithm for satellite attitude maneuver

Near time-optimal controller based on analytical trajectory planning algorithm for satellite attitude maneuver is proposed in this paper. The attitude maneuver issue is constructed as three successive attitude maneuvers and the desired trajectory is derived by calculating the minimum rotate angle, meanwhile each maneuver process is optimized by Bang–Bang control logic so that the system could have near time optimal character. The constraint on control torque is discussed and the relationship between system upper bound and control parameters is given. A special case of attitude maneuver is discussed and system acceleration and deceleration process is optimized inspired by Hohmann transfer of orbit control. The analytical solution of desired trajectory is given hence the computation is largely reduced. The attitude tracking controller is designed so that system could maneuver along the designed trajectory. System stability is proved by Lyapunov method and system performance is demonstrated by numerical simulation.

Robust optimal control during feedback disruption for nonlinear systems controlled by an observer-based output feedback controller

ABSTRACT In this paper, a robust optimal control problem during feedback disruption is considered for a class of nonlinear systems which have been controlled by an observer-based output feedback controller. It is shown that during feedback disruption, there exists an optimal control input which keeps both system states and observer errors within a specified bound for the longest time. Then, it is shown that such an optimal control input can be practically implemented by using a bang-bang control input in terms of control performance. One numerical and one practical examples are given for clear illustration.

Experimental study of semi-active magnetorheological elastomer base isolation system using optimal neuro fuzzy logic control

Abstract In this paper, a “smart” base isolation strategy is proposed in this study utilising a semi-active magnetorheological elastomer (MRE) isolator whose stiffness can be controlled in real-time and reversible fashion. By modulating the applied current, the horizontal stiffness of the MRE isolator can be controlled and thus the control action can be generated for the isolated structure. To overcome the inherent nonlinearity and hysteresis of the MRE isolator, radial basis function neural network based fuzzy logic control (RBF-NFLC) was developed due to its inherent robustness and capability in coping with uncertainties. The NFLC was optimised by a non-dominated sorting genetic algorithm type II (NSGA-II) for better suited fuzzy control rules as well as most appropriate parameters for the membership functions. To evaluate the effectiveness of the proposed smart base isolation system, four scenarios are tested under various historical earthquake excitations, i.e. bare building with no isolation, passive isolated structure, MRE isolated structure with Bang-Bang control, MRE isolated structure with proposed NFLC. A three-storey shear building model was adopted as the testing bed. Through the testing results, limited performance of passive isolation system was revealed. In contrast, the adaptability of the proposed isolation strategy was demonstrated and it is proven that the smart MRE base isolation system is able to provide satisfactory protection for both structural and non-structural elements of the system over a wide range of hazard dynamic loadings.

Dynamic Pricing Control for Open Queueing Networks

Pricing control is an important problem in service systems and it aims to control customer behaviors through an economic way, instead of administrative commands. In this paper, we study a dynamic pricing and service rate control problem in an open Jackson network with limited capacity. The goal is to determine the optimal admission prices and the optimal service rates at every state such that the long-run average social welfare is maximized. The original problem is decomposed into a rate-setting problem plus a price-setting problem. To solve the rate-setting problem, we derive a difference formula based on the sensitivity-based optimization theory. When the cost rate function is convex in service rates and the value rate function is concave in arrival rates, we decompose the rate-setting problem into a series of convex optimization subproblems. When the rate functions have linear structure, these subproblems are even simpler and a bang–bang control is optimal. For the price-setting problem, we determine the state-dependent prices so as to induce the optimal arrival rates obtained by the rate-setting problem. We propose a recursive algorithm to numerically compute the conditional expected delays at every state. Finally, we conduct numerical experiments to explore the optimality properties and some useful insights for this dynamic pricing control problem.

Stability for bang-bang control problems of partial differential equations

ABSTRACTIn this paper, we investigate solution stability for control problems of partial differential equations with the cost functional not involving the usual quadratic term for the control. We first establish a sufficient optimality condition for the optimal control problems with bang-bang controls. Then we obtain criteria for solution stability for the optimal control problems of bang-bang controls under linear perturbations. We prove Hölder stability of optimal controls in.

A robust homotopic approach for continuous variable low-thrust trajectory optimization

This paper presents an improved understanding of the interaction of hybrid optimization method with variable low-thrust trajectory optimization requirements. To analyze fuel-optimal bang-bang control problem, a new version of homotopic algorithm, termed robust homotopic method, is investigated with the prospect of improving the efficiency and automation of the homotopic approach to achieve a high-level of robustness, and consequently enlarge its range of application. Such desired characteristics are promoted via a combination of several techniques. As an effective approach, a modified methodology of the switching detection process is presented for the bang-bang optimal-control problem. Moreover, the value of unknown costates and switching functions are mapped to new normalized intervals throughout the computational process. As a result, the optimal solution is rapidly designed to obtain the global robust-convergence to satisfy all constraints without any ambiguity. The fitting process of all iterations robustly find the unknown variables with the percent of converged solutions to maximum, and the penalty terms are quickly satisfied with predetermined high-accuracy, from the energy-optimal to the fuel-optimal solution, especially close to zero point as a critical point. Accordingly, two advanced interplanetary trajectories are optimized using two dynamic modeling approaches for the instantaneous and constant maximal thrust magnitude as a way to analyze and substantiate the robustness of the proposed algorithm. Results and performances are compared with existing solutions of the same mission problem.

Stochastic Model Predictive Control of Air Conditioning System for Electric Vehicles: Sensitivity Study, Comparison, and Improvement

A stochastic model predictive controller (SMPC) of air conditioning (AC) system is proposed to improve the energy efficiency of electric vehicles (EVs). A Markov-chain based velocity predictor is adopted to provide a sense of the future disturbances over the SMPC control horizon. The sensitivity of electrified AC plant to solar radiation, ambient temperature, and relative air flow speed is quantificationally analyzed from an energy efficiency perspective. Three control approaches are compared in terms of the electricity consumption, cabin temperature, and comfort fluctuation, which include the proposed SMPC method, a generally used bang-bang controller, and dynamic programming as the benchmark. Real solar radiation and ambient temperature data are measured to validate the effectiveness of the SMPC. Comparison results illustrate that SMPC is able to improve the AC energy economy by 12% compared to the rule-based controller. The cabin temperature variation is reduced by more than 50.4%, resulting with a much better cabin comfort.

Fast Transient Fully Standard-Cell-Based All Digital Low-Dropout Regulator With 99.97% Current Efficiency

A fully standard-cell-based digital low-dropout (D-LDO) regulator with low-level quiescent current and fast load transient response is proposed for efficient power management in a system-on-a-chip. For the design of a fast and accurate voltage comparator, we propose a logic-threshold triggered comparator (LTTC) based on a standard CMOS digital inverter. The LTTC is employed to implement the binary voltage comparator for a bang-bang loop control and a multimode detector, which senses the output voltage with three segmented ranges during its transition, is also employed. Further, we implement a multiloop controller composed of components, such as a fixed-gain accumulator, successive approximation register, and variable-gain accumulator (VG-ACC), which accelerate the transient response while being switched over adaptively to the finely segmented voltage range. In particular, the proposed VG-ACC enables a constant unity-gain frequency overload current variation such that it enhances the load transient response in terms of over/undershoot and settling time. The proposed D-LDO is fabricated using a 65-nm CMOS process technology with an active area of 0.014 mm2. The measurement results show a peak current efficiency of 99.97% with the enhanced load-transient response and load regulation of 2.08 μs and 0.040 mV/mA, respectively, with a 20-MHz clock.

Incentive Design for Operations-Marketing Multitasking

A firm hires an agent (e.g., store manager) to undertake both operational and marketing tasks. Marketing tasks boost demand, but for demand to translate into sales, operational effort is required to maintain adequate inventory. The firm designs a compensation plan to induce the agent to put effort into both marketing and operations while facing “demand censoring” (i.e., demand in excess of available inventory is unobservable). We formulate this incentive-design problem in a principal-agent framework with a multitasking agent subject to a censored signal. We develop a bang-bang optimal control approach, with a general optimality structure applicable to a broad class of incentive-design problems. Using this approach, we characterize the optimal compensation plan, with a bonus region resembling a “mast” and “sail,” such that a bonus is paid when either all inventory above a threshold is sold or the sales quantity meets an inventory-dependent target. The optimal “mast and sail” compensation plan implies non-monotonicity, where the agent can be less likely to receive a bonus for achieving a better outcome. This gives rise to an ex post moral hazard issue where the agent may “hide” inventory to earn a bonus. We show this ex post moral hazard issue is a result of demand censoring. If available information includes a waitlist (or other noisy signals) to gauge unsatisfied demand, no ex post moral hazard issues remain.

Adaptive vibration suppression of time-varying structures with enhanced FxLMS algorithm

Abstract Filtered-x least mean square (FxLMS) control algorithm has been widely used for adaptive noise and vibration control. Yet, classical FxLMS controller is not applicable for time-varying system since the secondary path identified offline cannot reflect the system characteristics in real-time. In order to overcome this challenge, here online modelling of secondary path is realized by existing signals, i.e. no noise injection. In addition, FxLMS is further enhanced with variable step size that is adaptively adjusted via bang-bang controller. The adaptation of step size is aimed to achieve the balance between control efficiency and system stability. To verify the feasibility of proposed control algorithm, numerical and experimental efforts are undertaken for the buffeting suppression of vertical tail which is a typical time-varying system. Both results demonstrate that the proposed method is able to reduce the vibration response effectively for varied structures under harmonic and random excitations, while the classical FxLMS cannot. This performance improvement indicates that the online modeling of secondary path captures the system characteristics accurately and timely. Moreover, compared with the FxLMS controller with fixed step size, the control efficiency of the proposed method is also strengthened. These multiple enhancements of the performance of FxLMS controller reveal that online modeling and variable step size are favorable for adaptive vibration control of time-varying structures.

The particle swarm modified quasi bang-bang controller for seismic vibration control

The frequent occurrence of seismic events results in the damage to the structures. Structural control is one of the popular methods to prevent these damages. In structural control, the main objective is to impart an adequate counterforce. This required counter force is determined by a suitable control algorithm. In this work, an optimized and adaptive control algorithm is proposed based on modified quasi bang-bang control algorithm to generate the adequate counterforce. The constant output weights used in the modified quasi bang-bang controller are optimized for best performance in dynamic loading such as earthquake using the particle swarm optimization (PSO). The proposed optimized controller is then applied to a three storey prototype structure fixed with an MR damper. This structure has been subjected to various seismic events for performance evaluation. The results thus obtained are compared with best performing clipped optimal linear quadratic Gaussian (LQG) controller, quasi bang-bang and modified quasi bang-bang controller. The results establish that the PSO modified quasi bang-bang controller is superior to the other controller in reducing the structural responses i.e. relative displacement, interstorey drift and the absolute accelerations. Further, the voltage comparison shows that the power consumption is less for the proposed controller in attaining better performance.

Metric Regularity Properties in Bang-Bang Type Linear-Quadratic Optimal Control Problems

The paper investigates the Lipschitz/Hölder stability with respect to perturbations of optimal control problems with linear dynamic and cost functional which is quadratic in the state and linear in the control variable. The optimal control is assumed to be of bang-bang type and the problem to enjoy certain convexity properties. Conditions for bi-metric regularity and (Hölder) metric sub-regularity are established, involving only the order of the zeros of the associated switching function and smoothness of the data. These results provide a basis for the investigation of various approximation methods. They are utilized in this paper for the convergence analysis of a Newton-type method applied to optimal control problems which are affine with respect to the control.

Periodic sampling: maximising the sampling period

The process of periodic sampling is investigated for a class of nonlinear systems. The objective is to achieve the longest sampling period that is compatible with a specified error bound. It is shown that there are robust optimal controllers that achieve this objective. It is also shown that the performance of such optimal controllers can be approximated by bang-bang controllers – controllers that are relatively easy to design and implement.

Optimal curvature-smooth transition and efficient feedrate optimization method with axis kinematic limitations for linear toolpath

In industrial areas, the machining performance with linear G01 code is a crucial indicator to evaluate the computer numerical control (CNC) systems and many researchers have presented various methods to deal with the corner tracking issue. However, the axis jerk limitations are not satisfied well and the different axis kinematic limitations are not considered in most researches, which will reduce the machining efficiency and machining quality simultaneously. In this paper, a novel method including trajectory planning, feedrate scheduling, and interpolating is proposed to obtain better machining quality and higher machining efficiency. In trajectory planning, a B-spline curve is utilized to smooth the linear toolpath and obtain a curvature-smooth trajectory, which is third-order geometry continuous. Thereby, a time-optimal method for the geometric continuous trajectory is proposed based on linear programming algorithm in the feedrate scheduling and the bounded multi-constraints, including axis velocity, axis acceleration, axis jerk, and feedrate. Moreover, it can be seen that the proposed method is near Bang-bang control. To reduce the computation time of the optimal numerical method, an efficient method with a look-ahead window around the transition B-spline curve is applied. In the interpolation stage, a novel interpolation method about arc-length is proposed to improve computation efficiency. Finally, simulation and experiment are conducted to show superiorities of the proposed method to the already existing approaches. The results show that the cycling time of the proposed method is reduced by more than 7% than G2 method and 20% than G3 method with better contour performance.