An approach for controlling a hydrostatic dynamometer for the hardware-in-the-loop (HIL) testing of hybrid vehicles is proposed and experimentally evaluated. The hydrostatic dynamometer, which is capable of absorbing and regenerating power, was specifically designed and built in-house to evaluate the fuel economy and control strategy of a hydraulic hybrid vehicle being developed. Unlike a chassis dynamometer whose inertia is similar to the inertia of the vehicle being tested, the inertia of this hydrostatic dynamometer is only 3% of the actual vehicle. While this makes the system low cost, compact, and flexible for testing vehicles with different weights and drag characteristics, control challenges result. In particular, the dynamometer must apply, in addition to the torques to mimic the wind and road drag, also the torques to mimic the acceleration and deceleration of the missing inertia. To avoid estimating the acceleration and deceleration, which would be a noncausal operation, a virtual vehicle concept is introduced. The virtual vehicle model generates, in response to the applied vehicle torque, a reference speed profile which represents the behavior of the actual vehicle if driven on the road. This reformulates the dynamometer control problem into one of enabling the actual vehicle dynamometer shaft to track the speed of the virtual vehicle, instead of directly applying a desired torque. To track the virtual vehicle speed, a controller with feedforward and feedback components is designed using an experimentally validated dynamic model of the dynamometer. The approach has been successfully tested on a power-split hydraulic hybrid vehicle with acceptable virtual vehicle speed and dynamometer torque tracking performance.

## Introduction

Hardware-in-the-loop (HIL) simulation is an efficient technique to develop and test complex real-time embedded systems. An HIL system reduces testing complexity by using only part of the hardware which needs to be tested, while the remaining hardware is simulated on the computer. The HIL is widely used in the automotive industry to verify the performance of production powertrain controller modules (PCMs) [1].

A prototype hydraulic hybrid passenger vehicle testbed is being developed within the Center for Compact and Efficient Fluid Power (CCEFP) to advance hydraulic hybrid technologies. While simulations can predict fuel economy and performance of the vehicle, experimental validation is still necessary. Outdoor road tests require a test track and results may not be repeatable due to variable environmental conditions such as wind, rain, snow, and road and traffic conditions. A reliable HIL system, such as a dynamometer (or dyno in short), can enable reliable and consistent measurements in the laboratory and not be influenced by environmental factors. Furthermore, a dynamometer allows the comparison, development, and tuning of various control strategies for different vehicle characteristics and driving conditions. To this end, a hydrostatic dynamometer capable of both absorbing and regenerating energy (a necessity for testing hybrid vehicles) has recently been developed in our group [2].

Commercial chassis dynamometers usually have heavy roller drums to simulate the inertia of the vehicle being tested. The rolling mass is designed to be close to the vehicle inertia so that when the vehicle is accelerating/decelerating, most of the inertia effect is automatically taken care of by the rolling mass. The dynamometer needs only compensate for the road/aerodynamic drag which can be calculated directly from the wheel speed. On the other hand, hydrostatic dynamometers which use hydraulic pump/motors to provide the braking or regeneration torque on the vehicle have high power density and low inertias. For example, the inertia of the dynamometer in Ref. [2] is around 3% of the intended vehicle inertia even with the addition of a small flywheel. They are, therefore, more compact, low cost, and flexible and have fast response.

A unique challenge in controlling a low inertia dynamometer is the need to emulate the acceleration/deceleration loads related to the large difference in inertia. One approach is to apply the torque according to the acceleration estimate from a Kalman filter [3]. However, this is an inherently noncausal process since acceleration is a result of the torques applied by the powertrain and the dynamometer. Since the applied dynamometer torque should be a function of the acceleration, any delay in estimation will inevitably lead to inaccurate emulation when acceleration/deceleration is high.

In this paper, we propose a *virtual vehicle control concept* to enable a low inertia dynamometer to accurately emulate the dynamic load on the vehicle. The main idea, illustrated in Fig. 1, is to introduce a virtual vehicle dynamic model with information of the intended vehicle, such as inertia and road, and aerodynamic drag characteristics. For a given *applied* vehicle torque supplied by the powertrain, this model generates, in real‐time, a reference vehicle speed which represents the behavior of the vehicle with the intended vehicle inertia and environmental drag conditions. The control objective for the dynamometer becomes one of exerting the correct torque so that the actual speed of the common vehicle dynamometer shaft follows that of the reference generated by the virtual vehicle model. The need for the noncausal acceleration estimation can thus be avoided. When the actual speed tracks the virtual reference speed, the torque applied by the dynamometer on the vehicle will be exactly the same as if the vehicle is driving on the ground with full effect of the intended vehicle inertia and drag.

A variety of control algorithms can be designed to ensure that the vehicle dynamometer shaft speed tracks the virtual vehicle speed. In this paper, we estimate the applied vehicle torque and use a combination of feedforward control of the required dynamometer torque and feedback stabilization that is based upon affine parameterization and sensitivity shaping. The controller has been implemented on the dynamometer, and the virtual vehicle control concept has been experimentally validated.

In the literature, development and use of hydraulic dynamometers are mainly for testing engine performance [4–11]. One of the earliest reports of using a dynamometer for testing a complete powertrain with simulated load and engine is Ref. [12]. Control studies of hydraulic dynamometers in the literature are few. In Refs. [10] and [11], a transient hydrostatic engine dynamometer is controlled with the desired torque to be applied to the engine being obtained through a simulation of the rest of the vehicle. However, the torque associated with the acceleration and deceleration of the missing inertia was not implemented. More recently, a nonlinear controller is developed for another transient hydrostatic engine dynamometer to track a predetermined engine speed trajectory in Ref. [9]. The control is based on feedback linearization and estimating the engine speed and acceleration using a Kalman filter. In Ref. [13], control approaches and performance limitations for dynamic emulation systems are considered, using the electrohydraulic load emulator for an earthmoving vehicle powertrain system as an example. Their objective is to emulate the output response of the closed-loop system, consisting of the actual hardware and the simulated environment, to a physically applied or simulated exogenous input. In contrast to Refs. [9] and [13], the vehicle dynamometer control objective in this paper is to emulate the behavior of the load (missing inertia and wind/road drag) in response to the applied torque and speed of the powertrain, which themselves are generated in the closed‐loop.

The rest of the paper is organized as follows: Section 2 describes the configuration of the hydrostatic dynamometer. Section 3 explains the virtual vehicle control concept. Section 4 describes the modeling and system identification of the dyno system. Section 5 presents the controller design. Section 6 presents the experimental results. Section 7 contains concluding remarks.

## System Description

The hydrostatic dynamometer system consists of a hydraulic power supply unit, an accumulator, a proportional directional valve, and two swash-plate pump/motors that can go overcenter connected in tandem (Fig. 2). The displacements of the pump/motors are used as the primary control input to control the load on the vehicle. By operating them in pumping or motoring modes, both load absorbing and regenerating events can be emulated. The proportional directional valve is normally fully opened to allow unobstructed fluid flow, but it can also be used as the secondary high bandwidth control in case the pump/motor displacement actuation is deemed too slow. They are not used this way in the current study. During load absorbing events, energy from the vehicle is used to charge the hydraulic accumulator. During regenerating events, energy in the hydraulic accumulator is discharged and returned to the vehicle. The hydraulic power unit is used to ensure that the accumulator maintains a sufficiently high and nearly constant pressure.

The shaft of the dyno pump/motors is mechanically connected to the output shaft of the vehicle transmission, prior to the final drive differential, through a torque cell which provides speed and torque measurements (Fig. 3). The dynamics of the common vehicle dyno shaft are

where *J*_{shaft} is the sum of the inertia of vehicle drive train, *J*_{Trans}, and the inertia of the dyno, *J*_{Dyno}. *T*_{veh} is the applied vehicle torque on the transmission output shaft, *T*_{Dyno} is the applied dyno torque, and *T*_{meas} is the torque cell measurement. Because the vehicle is stationary in dynamometer testing, *J*_{Trans} is only a small fraction of the equivalent inertia of the intended vehicle if it is driven on the road. In our system, which incorporates a small flywheel, *J*_{Shaft} represents $\u22483%$ of the inertia of a typical 1000 kg vehicle.

Only when $JDyno\u226bJTrans$, one can assume that the measured torque is the vehicle applied torque *T*_{veh}. This is true in our case, since the dynamometer has been augmented with a small flywheel so that *J*_{Dyno} = 0.2436 kg/m^{2}, *J*_{Trans} = 0.0064 kg/m^{2}, and *J*_{shaft} = 0.25 kg/m^{2}.

## “Virtual Vehicle” Dynamometer Control Concept

### Virtual Vehicle Dynamics.

where *M*_{veh} is the mass of the vehicle, $Fdrag(v)$ is the road and wind drag, and *F*_{veh} is the applied traction force. Note that *M*_{veh} and $Fdrag(v)$ need not correspond to the actual vehicle but can be defined arbitrarily for testing vehicles with different weights, aerodynamic, and tire/road characteristics.

where the first term corresponds to the difference in inertia, and the second term corresponds to aerodynamic and road drag. Note that direct implementation of Eq. (6) is not strictly possible since the measurement or estimation of the acceleration $\omega \u02d9veh$ is noncausal. Specifically, the acceleration is dependent on the control *T*_{Dyno} applied to it in Eq. (1).

*Example.*To estimate $\omega \u02d9veh$ causally, a delay or a causal “dirty differentiator” such as $[s/(\tau accs+1)]$, where

*τ*

_{acc}is the filter time constant, is often needed. To see its effect, we assume linear dynamics for simplicity and suppose that the virtual (target) vehicle dynamics are

where $v\u02d9\u0302test$ is obtained using the dirty differentiator on *v*_{test} with some measurement noise. In this example, suppose that $Mveh=20Mtest=1000\u2009\u2009kg$, *b*_{veh} = 20 N/(m/s), $\tau acc=1\u2009s$ (to emphasize the effect), and that the vehicle force *F*_{veh} is commanded by a driver simulated to be a proportional-integral (PI) controller tracking a 3 rad/s sinusoidal drive cycle. Figure 4 shows that the virtual (target) vehicle speed *v*(*t*) differs from the test vehicle dyno speed $vtest(t)$. The applied dyno force also differs significantly from the ideal dyno force (i.e., with $v\u02d9test$ obtained (perfectly) from postprocessing). This dynamometer control will (most likely) lead to overly optimistic fuel economy results.

### Control Concept.

The above equation is referred to as the virtual vehicle model, and *ω*_{veh} as the virtual vehicle (shaft) speed.

To avoid the noncausal operation of estimating the acceleration as in Ref. [3] or the dirty differentiator in the example, instead of implementing Eq. (6) directly, the dynamometer will control the actual combined dyno vehicle shaft dynamics (*ω* in Eq. (1)) according to the virtual vehicle speed (*ω*_{veh}) (computed in real‐time based on the measurement or an estimate of the applied vehicle torque *T*_{veh} and the virtual vehicle dynamics in Eq. (9)).

which is exactly the desired dynamometer torque in Eq. (6) that could not be implemented directly.

The advantage of this approach is that the original task of controlling the dyno torque becomes a speed control problem, which respects system causality. Moreover, it allows one to test different vehicles under different road conditions by simply tuning the parameters for the virtual vehicle dynamics (9).

*Example (continued).* In the virtual vehicle control approach, *F*_{dyno} is determined by a controller (here, a PI+feedforward control for simplicity) to coordinate the virtual vehicle *v* and the actual vehicle speed (*v*_{test}). Figure 5 shows that the virtual vehicle speed *v*(*t*) matches the test vehicle speed $vtest(t)$, and the applied dyno force matches the ideal dyno force. Hence, the desired emulation is obtained.

## Modeling and Identification of the Dynamometer Dynamics

where $\Delta P$ is the system pressure which is regulated to be constant at 19.3 MPa (2800 psi), *D*(*t*) is the actual displacement of the pump/motor, *D*_{max} = 56 cc is the maximum displacement of the pump/motor, *a* is the bandwidth of the swash-plate dynamics, *b* is the damping coefficient, $U\u2208[0,1]$ is the normalized displacement command input, and *η* is the pump/motor's mean mechanical efficiency.

where $K=\eta \Delta PDmax/(2\pi )$. The combined inertia of the vehicle drive train and dyno was estimated from computer-aided design models, and engine specifications to be *J*_{shaft} = 0.25 kg/m^{2}.

Combining Eqs. (1) and (12), the open-loop transfer function from the pump/motor command *U*(*s*) to the shaft speed $\omega (s)$ (see Fig. 6) is

*a*,

*b*, and

*K*, system identification experiments have been performed. Because of the small physical damping

*b*, an inner closed‐loop is formed with a small proportional feedback gain of $Kp=0.01$ and with

*T*

_{veh}= 0 to form a closed-loop system (Fig. 6)

System identification is then performed on $Gp(s)$ by applying a series of sinusoidal reference speeds and measuring its gains and phases. The model parameters in Eq. (14) are optimized to match the measured gains and phases. In this way, a second-order closed-loop transfer function was identified to be (Fig. 7)

This corresponds to a swash-plate bandwidth of *a* = 2.539 rad/s, damping coefficient of *b* = 0.3574 rad/s $\xd7Jshaft=0.0893$ N·m/(rad/s), *K* = 81.5 N·m, and mean pump/motor efficiency of $\eta =0.47$, which are reasonable values.

Note that the second-order model and the third-order model have nearly identical magnitudes but differ slightly in phase.

## Virtual Vehicle Speed Tracking Control

In this section, we design a controller that enables the combined dyno/transmission shaft *ω* in Eq. (1) to track the virtual vehicle speed *ω*_{veh} as given in Eq. (9). The control scheme (Fig. 6) consists of a feedforward component and a feedback component. The feedforward controller is intended to supply the major control effort for the drag and missing inertia load. The feedback controller is designed to account for model uncertainty and disturbances.

### Estimation of Vehicle Torque $Tveh(t)$.

*T*

_{meas}is the torque cell measurement,

*T*

_{veh}is the applied vehicle torque which is assumed to be slowly time varying, and

*J*

_{trans}is the inertia of the transmission. Then,

*T*

_{veh}is estimated from a Luenberger observer [14]

where *ω* is the measured common vehicle dyno shaft speed; *L*_{1} and *L*_{2} are the observer gains chosen to set the poles for the observer. By setting the poles to be fast, time variation of $Tveh(t)$ within the observer bandwidth can also be estimated.

### Feedforward Control.

where $T\u0302veh$ is the estimated vehicle applied torque in Eq. (20).

where *λ* is large compared to the desired bandwidth.

### Feedback Control.

The feedback controller is designed directly around the identified closed-loop system with the proportional gain $Gp(s)$ in Eq. (16) (see Fig. 6). The third-order identified model in Eq. (18) is used. The feedback is designed using the affine parameterization of all stabilizing controls to shape the complementary sensitivity function [14].

Thus, *Q*(*s*) can be chosen to shape $To(s)$. The target $To(s)$ is chosen as a third-order low-pass filter (Fig. 8)

*C*(

*s*) is designed to be

Figure 8 shows the achieved complementary sensitivity function with this controller obtained experimentally by tracking sinusoids of different frequencies. It indicates that the target complementary sensitivity is indeed achieved.

## Experimental Results

The dynamometer control is applied to the in-house built hydrostatic dynamometer and tested experimentally using the hydraulic hybrid passenger vehicle (HHPV) in Fig. 9, which is developed in our lab. The vehicle has a diesel engine and a hydraulic input-coupled power-split transmission, hybridized by a pair of hydraulic accumulators for energy storage [15]. The hydraulic hybrid vehicle is controlled by a three-level control scheme described in Refs. [16] and [17] that aims to achieve the driver demanded vehicle torque in an energy-efficient manner. In order to have repeatable testing results, the driver is simulated by a virtual driver controller which is a PI speed controller. The virtual driver controller, the hybrid powertrain controller, and the dynamometer controller operate independently of each other (Fig. 10).

where $CD=0.5$ is the drag coefficient, $Af=1.784\u2009m2$ is the frontal area, $\rho =1.29\u2009kg/m3$ is the air density, $g=9.81\u2009m/s2$ is the acceleration due to gravity, and $fo=0.0095$ and $fs=0.0035$ are the coefficients for rolling resistance. The drag coefficients correspond to the vehicle in Fig. 9. The final drive ratio is $\rho d=3.45$ and wheel radius is $Rw=0.3095\u2009m$. Note that the target vehicle parameters do not need to correspond to a vehicle that has been built.

The Environmental Protection Agency's (EPA) Urban Dynamometer Driving Schedule (UDDS) and Highway Fuel Economy Driving Schedule (HWFET) with some modifications^{3} are used as reference speed profiles to test the efficacy of the dynamometer control scheme. For verifying the performance of the dynamometer control, the HHPV is operated in continuously variable transmission (CVT) mode in which the accumulator pressure is kept nearly constant.

Figures 11 and 12 show the actual vehicle dyno shaft speed *ω* and the virtual vehicle speed *ω*_{veh} for the modified UDDS and HWFET drive cycles, respectively. The errors in tracking the virtual vehicle speed are shown in Fig. 13. Despite the errors being larger during high acceleration/deceleration, the actual speed tracks the virtual vehicle speed reasonably with root-mean-square (RMS) errors of 17 rpm (UDDS) and 11 rpm (HWFET), which are 1.25% and 0.8% of the mean speeds of the cycles. This demonstrates the effectiveness of the dyno speed controller design in Sec. 5.

The real-time vehicle torque estimate $T\u0302veh$ obtained using the observer (20) is verified by comparing it with *T*_{veh} computed offline from Eq. (19) using the measured shaft speed $\omega (t)$ and the torque cell measurement $Tmeas(t)$, where $\omega \u02d9(t)$ is obtained in conjunction with a 2.5 Hz second-order zero-phase low-pass filter. A portion of this comparison is shown in Fig. 14, which shows that they are virtually identical.

*T*

_{Dyno}is estimated based on the torque measurement

*T*

_{meas}and the dynamics of

*J*

_{Dyno}

The desired dyno torque is computed based on Eq. (6). There are two options for the speed profile *ω*_{veh} in Eq. (6): (i) the actual measured speed *ω* or (ii) the virtual vehicle speed *ω*_{veh}. Since the entire profile is known, either profile can be differentiated offline, in conjunction with a zero-phase low-pass filter (fifth-order Butterworth filter with 5 rad/s cutoff) to obtain the acceleration. Figures 15 and 16 show the torque tracking performance for the UDDS and HWFET with respect to the desired torque profiles. Figure 17 shows the torque tracking errors. When the desired torque is computed using the output speed *ω*, the RMS torque errors are 6.1 N·m (UDDS) and 3.9 N·m (HWFET). However, when they are computed using the virtual vehicle speed *ω*_{veh}, the RMS torque errors are only 2.6 N·m (UDDS) and 1.6 N·m (HWFET). From Fig. 15 (bottom), it is seen that the larger error when *ω* is used to compute the desired torque can be attributed to the oscillatory nature of $\omega \u02d9$ rather than *T*_{Dyno} itself. This highlights the inherent difficulty in estimating $\omega \u02d9$ even in postprocessing (and more so in real‐time for feedback) and the advantage of the virtual vehicle control concept.

Figure 18 (top) shows the feedforward and feedback control efforts in terms of the pump/motor displacements. As intended from the controller design, the feedforward component is more dominant in providing the necessary actuation to track the desired virtual vehicle speed. However, the feedback component is also necessary to eliminate tracking error due to model uncertainty and unmodeled disturbances. Figure 18 (bottom) also shows that the dynamometer system pressure $\Delta P$ remains relatively constant within 18.6 ± 2.1 MPa (2700 ± 300 psi), which was an assumption in modeling the pump/motor torque in Eq. (12).

## Conclusion

A hydrostatic dynamometer with its high power density and low inertia has the advantages of being low cost, compact, and flexible. This paper presents a novel virtual vehicle control concept that eliminates the noncausal operation of estimating the acceleration. With this concept, the control system needs only track the real-time generated virtual vehicle speed in order to emulate the programmable drag and acceleration/ deceleration load. A feedback/feedforward controller has been designed for this purpose. The control concept has been experimentally validated. The dynamometer is now being actively utilized in the laboratory for testing and evaluating different hydraulic hybrid vehicle designs and control schemes.

The control performance is acceptable for assessing vehicle fuel economy by controlling the pump/motor displacement alone. System identification results indicate that the bandwidth of the pump/motor is indeed somewhat limited (2.5 rad/s). Future work will consider using the proportional directional control valve in Fig. 2 as an active control element for improving the control.

## Acknowledgment

This material is based upon work performed within the Center for Compact and Efficient Fluid Power (CCEFP) which is supported by the National Science Foundation under Grant No. EEC-0540834.

A preliminary version of this paper was presented at the 2014 ASME Dynamic Systems and Control Conference, San Antonio, TX.

The drive cycle is modified so that the speed does not violate the low-speed limit of the dynamometer hardware configuration.