Semi-active Magnetorheological Damper Research Articles

Methodology to minimize the dynamic response of tall buildings under wind load controlled through semi-active magneto-rheological dampers

This paper proposes a methodology to evaluate and optimize the dynamic response of tall buildings under wind loading, controlled through semi-active Magneto-Rheological dampers (MR dampers). For this, a tall building, modeled as a 2D frame, is taken as case study and three structural control configurations are proposed. The original structural configuration of the building is the first configuration analyzed, called Uncontrolled Original (C1). In the second configuration, called Uncontrolled Optimized (C2), the fundamental frequency of the building is optimized via PSO algorithm as a function of its mass. Then, in the third configuration, Controlled Optimized (C3), a set of MR dampers with behavior formulated via the modified Bouc-Wen rheological model and controlled through the Linear Quadratic Regulator associated with the Clipped Optimal control strategy (LQR-CO) is applied to the structure. Finally, the dynamic response of the three scenarios under wind action is analyzed and compared to performance criteria established in the literature. The results demonstrate that the C3 configuration is the only one able of satisfying all the established performance criteria, proving that the proposed methodology y that combines structural optimization with MR dampers is a powerful tool for vibration control.

Semi-Active Groundhook Control of Offshore Tension Leg Platforms Using Tuned Mass Damper With Optimized Parameters and Magneto-Rheological Damper Under Multiple Hazards

Abstract The purpose of the current study is to recommend an offshore tension leg platform (TLP) semi-active control system to lessen vibrations caused by various risks, such as the wind load and regular and irregular waves. State-of-the-art indicates that there has not been much study on semi-active management of offshore TLPs exposed to numerous hazards while taking into account system nonlinearities and employing a control method that is resilient to uncertainty. An augmented velocity–displacement-based groundhook (AVDB-GH) semi-active control scheme using magneto-rheological (MR) dampers, which is an improvement over the displacement-based groundhook (DB-GH) control algorithm, is proposed. The proposed controller uses a semi-active tuned mass damper (SATMD) consisting of a passive tuned mass damper (TMD) and two semi-active MR dampers as the control devices. Constrained nonlinear optimization is used to determine the SATMD's optimized parameters in order to produce the best control performance. A significant reduction in surge response of TLP is observed both in the time domain and the frequency domain. Compared to the SATMD using the usual DB-GH algorithm, the suggested control strategy more successfully decreases the key response variables—deck displacement, power spectral density, and acceleration. The effectiveness of the controller is better for regular waves than for irregular waves and wind forces. Because the performance of the controller is unaffected by changes in the mass and stiffness of the TLP, the controller can be regarded as robust.

The riding comfort improvement by the paralleled semi-active magnetorheological damper and passive inertance suspension from the power perspective

Extensive research demonstrates that a semi-active damper in combination with inerter-based suspension could improve the ride comfort and road-holding performance of vehicles. However, the inherent dynamics of a semi-active damper is always neglected. The underlying mechanism of the controller with inerter in different frequency ranges is not well understood. Accordingly, this paper investigated the quarter-car suspension consisting of the paralleled nonlinear hysteretic semi-active magnetorheological (MR) damper and a passive inerter. To study the influence of different strategies, the clipped optimum controlled- (COC) and the mixed skyhook power-driven damper (SKYPDD) controlled- MR damper with the inerter are both adopted and denoted as COCI and SKYPDI, respectively. The optimal inertance is selected to minimize the sprung acceleration. Since there lacks quantitative method to analyze the working mechanism of semi-active controllers, an innovative power-based criterion was proposed in this paper. The trajectory of the control force and the sprung mass velocity determines the equivalent damping ratio added to the sprung mass and the input power it receives from the unsprung mass. The sprung mass vibration is reduced by decreasing the input power or increasing the damping ratio. Under harmonic excitation, the additional inertance decreases the power input to the sprung mass in the low-frequency range and isolates the sprung mass from the forced vibration at the unsprung resonance. Under the broadband stochastic excitation, SKYPDI and COCI can effectively decrease the input power spectrum and increase the damping ratio spectrum in the dominant sprung mass resonance. A parametric study on varying stiffness ratio demonstrates the semi-active strategy takes effects mainly in the high-stiffness-ratio range where the additional inertance more evidently enhances the damping ratio, especially for COCI. In summary, this paper proposes the power-based criterion for analyzing the working mechanism of semi-active strategies in ride comfort improvement.

Ride comfort analysis of vehicle seat suspension systems: A co-simulation study

In this study, the vehicle seat suspension system installed with a semi-active magnetorheological (MR) damper is excited by the power spectral density (PSD) and its vibration control performance is evaluated using finite element analysis (FEA). The control system receives the velocity of the sprung and unsprung mass from the seat mounting locations and calculates the desired controllable damping forces available from MR damper. The effectiveness of the control systems is demonstrated by adopting ride quality evaluation method. To predict a better ride comfort and ride quality, co-simulation methodology is utilized considering the dynamic behavior of the real-world seat system. In this case, the multi-body dynamics and control system are coupled by solving the mechanical equations and the control logic. Then, the computed damping force is exchanged between the dynamics and controller in an iterative manner by passing state variables. The simulation results achieved from co-simulation methodology associated with the controller are analyzed by comparing with ISO 2631-1. The co-simulation results studied using vibration dose value (VDV), crest factor (CF) and seat effective amplitude transmissibility (SEAT) in terms of percentage improvement were found to be 44.33%, 26.66% and 17.65% respectively which were better than that for the passive suspension for a random rough road profile. Modified skyhook controller delivers superior performance for vibration suppression of the vehicle seat suspension as compared to other control policies. The application of co-simulation methodology can reduce time and cost for the development of a semi-active seat suspension system.

Multimode vibration control of stay cables using pseudo negative stiffness MR damping system

At present the vibration control of stay cable suffers from low damping effectiveness in single mode vibration caused by the limitation of damper installation position as well as the poor modal compatibility, that is, a rapid degradation performance when the actual mode deviates from the designed optimal mode. In this paper, one practical semi-active magnetorheological (MR) damper based control solution is proposed to address the problems faced in multi-modal vibration control of stay cables. The semi-active pseudo negative stiffness (PNS) control strategy takes full account of the MR damper’s mechanical characteristics and the demands of the stay cable vibration control. Compared with the linear equivalent model, the proposed time-varying model exhibits more details of the damping force and the nonlinear response of the damped stay cable, which shows its essential role in the optimal design of MR-PNS scheme. Then the optimal design method of MR-PNS multi-modal vibration control for stay cable is summarized by taking the first three modes vibration control of the J20 cable in Nanjing Baguazhou Yangtze River Bridge as simulation examples. The simulations of cross-modal, multi-modal and wind-induced vibration cases are conducted respectively, while the results show that the optimal designed multi-modal MR-PNS scheme can simultaneously exceed the passive maximum modal damping ratio within first three modes. The advantages of the proposed MR-PNS method in high damping efficiency and modal compatibility could be verified by comparing with the passive multi-modal damping solution.

Seismic Response Analysis of Vertically Irregular RC Building with MR Dampers

Seismic hazard mitigation has become one of the emerging problems in structural engineering therefore; many researchers have been studied on seismic performance of reinforced concrete structures having vertically regular and irregular. It is noted that vertically irregular structures are more prone to hazards due to earthquake. The recent emerging trend is to use active, passive, semi-active controls that aid in keeping the responses of structures in permissible. The most dynamically varied semi-active damper is a Magneto-Rheological (MR) damper which is used in this study to control the seismic responses. In the present study, four different models with and without MR dampers of which three models are vertically irregular in height are subjected to four realistic ground motions. The governing equation of motion for various building models is solved numerically by Newmark’s step-by-step integration method. The dynamic behaviour of semiactive MR damper has been predicted by modified Bouc-Wen model. This study employed the Lyapunov direct approach as a control algorithm for stability analysis and design of MR controller. The responses of various building models are simulated through MATLABâcomputing software. The study observed that considerable reduction in seismic responses of models with MR dampers is obtained as compared to respective building models without control. It is also observed that responses of building models are influenced by the vertical irregularities in mass and stiffness of building models.

Wind and Seismic Response Control of Dynamically Similar Adjacent Buildings Connected Using Magneto-Rheological Dampers

Wind and/or earthquake-imposed loadings on two dynamically similar adjacent buildings cause vigorous shaking that can be mitigated using energy dissipating devices. Here, the vibration response control in such adjacent structures interconnected with semi-active magneto-rheological (MR) dampers is studied, which could also be used as a retrofitting measure in existing structures apart from employing them in new constructions. The semi-active nature of the MR damper is modeled using the popular Lyapunov control algorithm owing to its least computational efforts among the other considered control algorithms. The semi-active performance of the MR damper is compared with its two passive states, e.g., passive-off and passive-on, in which voltage applied to the damper is kept constant throughout the occurrence of a hazard, to establish its effectiveness even during the probable electric power failure during the wind or seismic hazards. The performance of the MR damper, in terms of structural response reduction, is compared with other popular energy dissipating devices, such as viscous and friction dampers. Four damper arrangements have been considered to arrive at the most effective configuration for interconnecting the two adjoining structures. Structural responses are recorded in terms of storey displacement, storey acceleration, and storey shear forces. Coupling the two adjacent dynamically similar buildings results in over a 50% reduction in the structural vibration against both wind and earthquake hazards, and this is achieved by not necessarily connecting all the floors of the structures with dampers. The comparative analysis indicates that the semi-active MR damper is more effective for response control than the other passive dampers.

A semi-active control method for magnetorheological dampers to suppress the milling vibration of thin-walled workpieces

Thin-walled workpieces are widely used in the aerospace field, and milling is the main processing method of such components. However, thin-walled workpieces are prone to vibrate during milling because of their weak stiffness, and the vibrations significantly affect the processing quality. Therefore, it is important to develop a novel milling vibration suppression method for thin-walled parts. The present work focused on the milling vibration control of a thin-walled workpiece using a semi-active magnetorheological (MR) damper. The forward dynamic model and inverse control model of the MR damper were first established, and its actuating position on the workpiece was then determined by modal analysis. The dynamic model of the MR damper at this position was built based on the proposed dynamic parameter acquisition method and used in the following semi-active control algorithm design. The effectiveness of this algorithm was verified by MATLAB/Simulink simulations. Finally, six groups of milling experiments were carried out using the non-damper, the rigid rod, the damper applied with 1-, 2-, and 3-A currents, and the semi-active control damper to validate the practical effect of the proposed algorithm. It was found that the designed semi-active control MR damper outperformed the constant-current control dampers or the rigid rod. In comparison to the non-damper experiment, the root mean square (RMS) values of milling forces in x- and y-directions decreased by 45.12% and 48.58%, respectively, and surface roughness decreased by 40.22%.

An LPV-Based Online Reconfigurable Adaptive Semi-Active Suspension Control with MR Damper

This study introduces an online reconfigurable road-adaptive semi-active suspension controller that reaches the performance objectives with satisfying the dissipativity constraint. The concept of the model is based on a nonlinear static model of the semi-active Magnetorheological (MR) damper with considering the bi-viscous and hysteretic behaviors of the damper. The input saturation problem has been solved by using the proposed method in the literature that allows the integration of the saturation actuator in the initial system to create a Linear Parameter Varying (LPV) system. The control input meets the saturation constraint; therewith, the dissipativity constraint is fulfilled. The online reconfiguration and adaptivity problem is solved by using an external scheduling variable that allows the trade-off between driving comfort and road holding/stability. The control design is based on the LPV framework. The proposed adaptive semi-active suspension controller is compared to passive suspension and Bingham model with Simulink simulation, and then the adaptivity of the controller is validated with the TruckSim environment. The results show that the proposed LPV controller has better performance results than the controlled Bingham and passive semi-active suspension model.

Observer-based anti-windup robust PID controller for performance enhancement of damped outrigger structure

This study presents an observer-based anti-windup robust proportional–integral–derivative controller with state estimator method for damped outrigger structure using magneto-rheological damper to mitigate the seismic response. In this approach, full-order Kalman observer is designed for estimating the states of the damped outrigger system from the feedback of the system output with optimum observer gain. However, due to the computational complexity, the integral windup is observed in the loop; therefore, integral anti-windup is introduced for the internal stability in the loop to produce the desired output. The semi-active magneto-rheological damper is integrated with the proposed system, to produce the required force by the system that ranges between the maximum and minimum values as regulated by the voltages produced by the controller in action for every instant of the seismic energy. The proposed strategy is designed in MATLAB and Simulink to find the adequacy of the damped outrigger system in terms of mitigating the following seismic responses like displacement, velocity, and acceleration. The dynamic analysis of the damped outrigger structure with the proposed control strategy shows enhanced performance in reducing the response of the structure as observed in peak response values. The evaluation criteria show a significant reduction in the vibration of the structure.

A semi-active control algorithm for nonlinear structures based on uniform distribution of deformation theory

Semi-active control is a promising method for vibration control of civil structures. Magneto-rheological (MR) damper is one of the most common and practical devices among other semi-active control devices. The command voltage is the only controllable property of an MR damper. There are several algorithms for determining the MR damper command voltage such as active control-based algorithms. On active-based algorithms, an initial reference control force is achieved based on a reference active control algorithm, then this force converts to applied voltage. Uniform Distribution of Deformations (UDD) theory is a concept which intends to use the maximum capacity of elemental and structural ductility. When deformations are uniform throughout the entire structure, damages are mostly uniform and the maximum of damage is reduced. This point can be used for designing a new active-based semi-active algorithm. The innovative Uniform Deformation Control (UDC) is an active-based control algorithm. Reference active control forces are achieved using a massless Virtual Added frame with Pinned connections (VAP). This virtual frame makes deformation of the structure more uniform. The axial forces of the VAP beams are the reference active control forces. Afterward, based on these forces, the command voltages of semi-active MR damper are determined. The VAP characteristics are optimized using Charged System Search (CSS) optimization method for making the structural deformations more uniform. Therefore, this new innovative proposed algorithm focuses on reducing damages contrary to common algorithms which focus on reducing responses. The contribution of the present paper is to introduce the new damage-based algorithm. Then, this algorithm will be investigated in comparison with two other common algorithms. The effectiveness of the new proposed algorithm is proved via nonlinear numerical investigations on an office building. The new algorithm can reduce displacements and accelerations with relatively low control forces while making deformations more uniform.

Semi-Active System of Vehicle Vibration Damping

This article discusses the vibration of a vehicle equipped with four semi-active dampers. The friction forces generated in these dampers have crucial influence on the intensity of the vehicle vibration. To estimate the effect of the vehicle vibration damping, a criterial function depending on the values of these forces has been selected. Solving the problem has the purpose of determining four values of the forces at which the criteria function reaches the minimum at any moment. On the basis of the above, signals for the devices controlling the operation of the semi-active dampers are determined. In this work, the analysis of the discussed problem was conducted in regard to the method for determining the optimal force values. Moreover, the results of the simulation of the vibration of the vehicle equipped with semi-active magneto-rheological dampers are presented. In addition, the analysis of the influence of the form of the criterial function on the vehicle vibration damping efficiency is proposed. Based on the tests carried out on the vehicle with MR dampers, the comfort index improved by 51.6%, compared to the classic suspension.

High-performance semiactive secondary suspension of high-speed trains using negative stiffness and magnetorheological dampers

With increasing transportation speed, the excessive vibrations of high-speed trains (HSTs) have become a critical issue to be solved. This study presents an innovative semiactive suspension system consisting of a magnetorheological (MR) damper in parallel with a magnetic negative stiffness (NS) element. The proposed semiactive dampers, called MRNS dampers, are integrated into the secondary suspension of an HST to improve riding comfort. The MRNS design can effectively enhance the vibration mitigation performance of semiactive MR dampers and compensate for the performance gap between traditional semiactive MR dampers and active controllers (e.g. linear quadratic regulator (LQR)). The effects of the NS coefficient and control force weight coefficient are presented, and the optimal selections of these parameters are discussed with respect to the control performance and force tracking errors of the MRNS controller. Results indicate that the MRNS damper can satisfactorily emulate LQR force trajectories. Hence, the semiactive MRNS controller can achieve vibration suppression performance comparable to that of an active LQR controller.

A New Switching Adaptive Fuzzy Controller with an Application to Vibration Control of a Vehicle Seat Suspension Subjected to Disturbances

This paper proposes a new switching adaptive fuzzy controller and applies it to vibration control of a vehicle seat suspension equipped with a semi-active magnetorheological (MR) damper. The proposed control system consists of three functioned filters: (1) Filter 1: a model of interval type 2 fuzzy to compensate disturbances; (2) Filter 2: a ‘switching term’ to evaluate the magnitude of disturbance; and (3) Filter 3: a group of adaptation laws to enhance the robustness of control input. These filters play a role of powerful shields to improve control performance and guarantee the stability of the applied system subjected to external disturbances. After embedding a PID (proportional-integral-derivative) model into Riccati-like equation, main control parameters are updated based on the adaptation laws. The proposed controller is then synthesized in two different cases: high disturbance and small disturbance. For the high disturbance, a special type of sliding surface function, which relates to an exponential function and its t-norm, is used to increase the energy of control system. For the small disturbance, the energy from the modified t-norm of the sliding surface is neglected to reduce the energy consumption with maintaining the desired performance. To demonstrate the effectiveness of the proposed controller, a vehicle seat suspension installed with controllable MR damper is adopted to reflect the robustness against external disturbances corresponding to road excitations. It is validated from computer simulation that the proposed controller can provide better vibration control performance than other existing robust controllers showing excellent control stability with well-reduced displacement and velocity at the position of the seat.

Semi-active control of a nonlinear quarter-car model of hyperloop capsule vehicle with Skyhook and Mixed Skyhook-Acceleration Driven Damper controller

A suspension system is one of the integral parts of a hyperloop capsule train, which is used to isolate the car-body from bogie vibration to provide a safer and comfortable service. A semi-active suspension system is one of the best candidates for its advantageous features. The performance of a semi-active suspension system relies greatly on the control strategy applied. In this article, Skyhook (SH) and mixed Skyhook-Acceleration Driven Damper (SH-ADD) controlling algorithms are adopted for a nonlinear quarter-car model of a capsule with semi-active magnetorheological damper. The nonlinear vertical dynamic response and performance of the proposed control algorithms are evaluated under MATLAB Simulink environment and hardware-in-loop-system (HILS) environment. The SH controlled semi-active suspension system performance is found to be better at the first resonance frequency and worse at the second resonance frequency than the passive MR damper, but the mixed SH-ADD controlled semi-active suspension system performs better than the passive at all frequency domains. Taking the root-mean-square (RMS) value of sprung mass vertical displacement as an evaluation criterion, the response is reduced by 58.49% with mixed SH-ADD controller and by 54.49% with the SH controller compared to the passive MR damper suspension.

A Full-Scale Experimental Investigation on Ride Comfort and Rolling Motion of High-Speed Train Equipped With MR Dampers

Achieving higher operation speeds safely and comfortably is yet a significant challenge in the railway industry. The rail irregularities and wheel-rail interactions in a train running at high speeds may result in large-amplitude vibration in the train’s car body and affect passengers by reducing ride comfort. The train suspension systems have a crucial role in reducing the vibration and improving ride comfort to an acceptable level. In this context, an exclusive semi-active magneto-rheological (MR) damper with a favorable dynamic range was designed and fabricated. The MR dampers were installed in a high-speed train’s secondary lateral suspension system in replacement of original passive hydraulic dampers, with intent to mitigate vibration of the car body and keep the ride comfort in a proper level at low and high running speeds. A unique full-scale experimental investigation on the high-speed train equipped with MR dampers was carried out to evaluate the MR damper functionality in a real operating situation. The full-scale roller experiments were conducted in a vast range of speeds from 80 to 350 km/hr. At each speed, different currents were applied to the MR dampers. The car body dynamic responses were collected to evaluate the ride quality of the train. Ride comfort indices under various train operating conditions are calculated through Sperling and UIC513 rules. This study reveals that the designed MR dampers effectively reduce the car body’s rolling motion. According to Sperling ride comfort index, the car body vibration was “clearly noticeable” at some running speeds when adopting the MR dampers, but it was not unpleasant. Besides, a “very good comfort” was achieved according to the UIC513 criterion. Also, no train instability was whatsoever observed at high speeds. This experimental investigation bears out the capability of the devised MR damper to achieve desirable ride comfort under high running speeds.

Step-control and vibration characteristics of a hybrid vehicle suspension system considering energy consumption

This paper proposes a hybrid suspension system, consisting of a linear electric motor (LM) and a semi-active mono-tubed magnetorheological damper (MRFD), to improve vehicle dynamics with lower power demand. For determining the damping force directly and concisely, a modified bi-viscosity magnetorheological fluid (MRF) model that explicitly includes the current parameter is developed. The fabricated LM and MRFD are calibrated and tested for validation of the implemented mathematical models. The simulation results show that the modified bi-viscosity model is able to calculate the experimental MRFD external forces very well. Thereafter, the hybrid suspension system is integrated into a 2-DOF (degree-of-freedom) quarter-vehicle dynamic model for simulation analysis, considering bump and pothole road profiles and the wheel bounce movements. Moreover, the two step-control methods, namely SC1 and SC2, are modelled for enhancing vibration mitigation and reducing power demand. The MRFD current influences on the root mean square (RMS) of the vehicle body vibration amplitudes are studied. Results reveal that the optimal MRFD current is ranged from 1 to 2.2A considering the SC1 method. Finally, the energy efficiency of the step-control methods is proved to be much higher than the PID method especially at low vehicle speed and in large road heave situations.

Load balancing and neural dynamic model to optimize replicator dynamics controllers for vibration reduction of highway bridge structures

Earthquakes cause irreparable damages to the built environment, which has led bridge engineers to develop structural control systems to mitigate damage and improve vibration reduction in real-time. Among control systems, base isolation is one of the most commonly used passive control strategies for seismic protection of civil structures. Yet, it lacks real-time adaptability, has lower energy dissipation, and poor performance during near-fault earthquakes. To overcome these limitations, a hybrid control system comprised of semi-active magneto-rheological (MR) dampers and passive base isolation bearings is installed at the deck and piers for vibration reduction of highway bridge structures. This paper, inspired by evolutionary game theory and artificial intelligence, proposes data-driven replicator dynamic control algorithms to distribute the command voltage to the current driver of the semi-active MR dampers. It incorporates a load balancing strategy to reallocate additional resources. To achieve a high-performance design of the game-theory-inspired controllers, a patented neural dynamic model is used to optimize the control parameters. The evaluation of the proposed methodology uses a benchmark control problem based on the 91/5 highway bridge in Southern California subjected to near-field earthquake accelerograms. The performance of five different proposed controllers is compared with conventional Lyapunov and fuzzy logic control algorithms using 21 performance criteria. Results show the load balancing capability of the proposed control algorithms to mitigate the vibrations experienced by the bridge structure and further increase the durability of semi-active devices. The novelty of the methodology impacts how game-theory controllers make control decisions among multiple devices in engineering problems.

Response of Piping System with Semi-active Magnetorheological Damper under Tri-directional Seismic Excitation

ABSTRACT Seismic loads on piping system due to earthquakes can cause excessive vibrations, which can lead to serious instability resulting in damage or complete failure of piping system. Vibrations in the piping system can be reduced using passive control, active control, semiactive control and hybrid control. In this paper, semi-active magnetorheological (MR) dampers have been studied to mitigate seismic response and vibration control in piping system used in the process industries, fossil and fissile fuel power plant. The performance of MR dampers using various control algorithms is explored. A study is also conducted on the performance of control due to variation in the command voltage of MR dampers. The effectiveness of the MR dampers in terms of the reduction in responses, namely, displacements, accelerations and base shear of the piping system are compared with uncontrolled and passive controlled responses. This study is carried out under four artificial earthquake motions with increasing amplitudes in all the three directions of motion. The analytical results demonstrate that the MR dampers under particular optimum parameters are very effective and practically implementable for the seismic response mitigation, vibration control and seismic requalification of piping system.

Life‐cycle cost optimization of semiactive magnetorheological dampers for the seismic control of steel frames

SummaryThis paper aims to achieve minimum life‐cycle cost, by applying a seismic design optimization of the steel frames with semiactive magnetorheological (MR) dampers. The total life‐cycle cost, which includes the initial constructional and expected damage costs, is an adequate goal to satisfy both employer and users. For optimal performance of the dampers, two fuzzy control systems are suggested, each having two different inputs. Results of numerical analysis for an 11‐story steel structure show that using MR dampers decreases the interstory drift ratios to a permissible limit. It also reduces life‐cycle cost when the design is optimum and when the dampers are evenly distributed by 23% and 14%, respectively. In the case where the objective function was to minimize the total life‐cycle cost, the expected injury and fatality, as the most crucial financial parameters, had the highest decrease rate. There was also a 17% drop in comparison to the state that the dampers are evenly distributed. The fuzzy control with drift and velocity as inputs had better performance in minimizing the total life‐cycle cost than the other fuzzy control, which used acceleration instead of velocity.