Simultaneous Energy Management and Speed Control in a Hybrid Tractor With Experimental Validation

In recent years, the hybridization process is an emerging trend in heavy-duty vehicles and agricultural machinery. In this work, a parallel hybrid tractor is studied, aiming at developing an energy management strategy (EMS) able to deal with the built-in speed tracking requirements. Indeed, a speed controller is originally present in the tractor, so that the driver directly sends a speed command through the pedal. We propose an EMS based on the equivalent consumption minimization strategy (ECMS), which is properly modified to explicitly include the speed tracking objective. Then, the stability of the closed-loop system needs to be proven and discussed. Finally, the designed EMS is implemented on the tractor control unit and validated through a large experimental campaign on a small track. First, the benefits induced by the explicit consideration of the speed tracking are highlighted, and then the fuel-saving performance is assessed in different conditions, experiencing 14% of fuel saved on average, consistent with the simulation results.

Abstract-In recent years, the hybridization process is an emerging trend in heavy-duty vehicles and agricultural machinery.In this work, a parallel hybrid tractor is studied, aiming at developing an energy management strategy (EMS) able to deal with the built-in speed tracking requirements.Indeed, a speed controller is originally present in the tractor, so that the driver directly sends a speed command through the pedal.We propose an EMS based on the equivalent consumption minimization strategy (ECMS), which is properly modified to explicitly include the speed tracking objective.Then, the stability of the closed-loop system needs to be proven and discussed.Finally, the designed EMS is implemented on the tractor control unit and validated through a large experimental campaign on a small track.First, the benefits induced by the explicit consideration of the speed tracking are highlighted, and then the fuel-saving performance is assessed in different conditions, experiencing 14% of fuel saved on average, consistent with the simulation results.

I. INTRODUCTION
T HE hybridization and electrification process is now touch- ing different classes of vehicles, ranging from light-duty urban cars to heavy-duty vehicles.This last kind of vehicles refers to a wide and heterogeneous set [1], composed of agricultural tractors, street sweepers, forklifts, construction vehicles, and many others.Despite being considered a unique class, actually, they are differently operated according to their specific requirements.Therefore, if the behavior of the traditional urban vehicles is well-represented by standard driving cycles, each heavy-duty vehicle is characterized by particular features.Moreover, a single vehicle has different alternatives in the way it can be used.For example, an agricultural tractor can alternatively operate in a transport scenario, moving people or loads, or in a working scenario, operating different machinery in fields for hours.In addition, heavy-duty vehicles can be equipped with additional loads, which can be either mechanical, connected to the propulsion system through a power take-off (PTO), or hydraulic, connected through a system of pumps that feeds the hydraulic circuit.The authors are with the Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, 20133 Milan, Italy (e-mail: stefano.radrizzani@polimi.it;giulio.panzani@polimi.it;sergio.savaresi@polimi.it).
Digital Object Identifier 10.1109/TCST.2024.3362934 Among the heavy-duty vehicles, agricultural ones are experiencing an increase in terms of electric or hybrid solutions proposed.This trend is motivated, not only by the typical advantages of hybrid electric vehicles (HEV) but also by the possibility of reducing the deposit of pollutants on crops and emissions near workers [2].Moreover, if the activation of the full-electric (FE) mode is feasible, it is also possible to work indoors in greenhouses, without emissions, by removing or turning off the engine.Nevertheless, hybridization and full electrification of tractors raise new challenges.For example, high power request for long operations is a very demanding requirement for the battery design.Indeed, the current commercial solutions are mainly oriented to compact or orchard tractors [3].Considering this specific class of agricultural vehicles, different alternatives have been paved up to now by industrial companies for the electrical and mechanical architecture [1].

A. Main Topic and Related Works
This work focuses on an orchard vineyard tractor prototype, which is a parallel hybrid vehicle: a 27-kW electric motor (EM), fed by a 14-kWh battery, is mounted in parallel to the built-in 52-kW internal combustion engine (ICE) before the manual transmission.This vehicle is non-plug-in; hence, the battery state of charge (SoC) is maintained by the engine itself.This prototype has already been introduced by Radrizzani et al. [4], where a detailed model has been experimentally derived and validated.
In this article, the focus is given to the development of an energy management strategy (EMS) for such a prototype, which asks to deal with the built-in engine speed controller.Indeed, due to the way of driving a tractor for long and repetitive operations, many agricultural engines are already equipped with a speed controller [4], [5], [6].
The scientific literature on tractor hybridization is anticipated by the one related to the hybridization of more traditional vehicles (most frequently passenger cars).The recent interest in high-tech agricultural applications and the technological advances, e.g., in battery technology, make the former a topic of particular interest; the latter, in fact, has nowadays reached a much more consolidated background and maturity.This explains why there are not yet many contributions on the specific topic of tractor hybridization.Focusing on the energy management strategies, the literature path for standard HEVs started with the equivalent consumption minimization strategy (ECMS) [7] which represents the basic optimizationbased EMS.Despite its simplicity, ECMS immediately showed high fuel-saving performance when compared with the global optimal solution computed a posteriori with the dynamic programming (DP).Then, thanks to the analysis and application of Pontragyin's minimum principle (PMP), the high performance of the ECMS has been mathematically proven [8], [9].After that, different sub-branches appeared in the literature, like the application of more advanced techniques as the model predictive control (MPC) [10], [11], [12], which revealed to be an interesting tool particularly for multiobjective problems to also deal with engine turn-on phases [13], battery thermal [14] or aging dynamics [15].In addition, adaptive strategies based on additional information, such as driving patterns [16], [17], have been formulated along with and the joint mechanical/electrical design and energy management [18].Among the multiobjective problems, a popular one is the integrated speed control and energy management, which is an area of interest for the tractor application as well.In the traditional parallel HEVs, this problem can be subdivided in a hierarchical way, where a high-level controller, to track the reference speed, computes the total traction or braking power, which is split between the different power sources by the lower level EMS.For example, in [19], an external MPC-based adaptive cruise controller (ACC) is combined with an ECMSbased energy management.Another example is given in [20] where a hierarchical control law is developed using an external cooperative adaptive cruise control and an internal heuristic approach.An even more recent framework is proposed in [21] which is characterized by a neural network, to drive at the target speed and a genetic algorithm is exploited to tune the ECMS-based lower level.None of the discussed works can be directly used on the considered tractor, because of the built-in speed controller.Its presence, in fact, causes two main issues.First, the ICE itself is already responsible for speed tracking, making it impossible to address the fuel-saving and the speed tracking objectives as two decoupled problems.Second, the total torque/power cannot be directly split between the EM and the engine, because in the latter it is autonomously regulated by the built-in controller.
Focusing instead on hybrid tractors, the literature is a step back, when compared with standard vehicles.Indeed, even feasibility studies are very recent as [22], or [23] and [24] which analyze different hybrid architectures with on-shaft or in-wheel EMs.The energy management problem for tractors, e.g., [25], [26], [27], is in a very early stage with respect to the advanced techniques developed for standard vehicles.Finally, in [28] a specific strategy for agricultural operations is proposed.Speed tracking is explicitly considered by [29] but without the presence of a built-in speed controller, which is instead considered by the MPC-based approach proposed in the previous paper [4].Hence, this strategy is the only one that we can use to compare with the ECMS-based approach proposed in this article.

B. Main Contributions and Outline
Given the presence of the built-in controller in the engine, the conventional methods cannot be directly applied to this kind of vehicles.Hence, in this article, we address how to properly modify the conventional ECMS, which is well-established in conventional vehicles, to be used when an integrated speed controller is in the engine.To face this question, we first show that at least at steady-state, i.e., for constant speed and load torque, the solution of the conventional ECMS can be used.Then, it is shown that a load torque estimator is necessary (in the ECMS the reference torque is provided by the driver's command) and one based on engine and EM torque measurements is proposed.The core of this article shows and validates a proper tuning of the ECMS, through its efficiency-based equivalent formulation [30] along with a stability analysis tool to guarantee a stable closed-loop system for any possible operating point.To make the closed-loop system stable, analyses revealed that the speed tracking error must be directly included in the EMS when the engine operates at its saturation.It follows that in such a scenario an integrated energy management and speed control is necessary.Initially, the proposed solution is validated in the simulation environment and compared with the global optimal solution computed offline and the MPC proposed in [4].Given the promising results, the solution is implemented on the tractor control unit, to experimentally test its performance, in terms of speed tracking and fuel-saving.In this way, results based on realistic driving-cycles are obtained for such a vehicle, including when it is carrying an additional trailer.The experimental campaign showed that the speed reference is well-tracked with a significant fuel-saving, which is equal to 14% on average on the considered driving cycles.
To summarize, the main contributions of this article are given by the following points: 1) the formulation of a simultaneous energy management and speed control strategy, able to deal with agricultural speed-controlled engines; 2) the estimation of the ECMS equivalence factor according to the efficiency-based approach recently formulated in [30], whose experimental implementation is novel; 3) the definition of a procedure to verify the stability of the closed-loop system when the energy management and the speed control are integrated into a unique controller; and 4) the experimental evaluation of the fuel-saving performance on the real tractor on transport maneuvers.Agricultural maneuvers are not considered in this work, because it is a specific scenario, where ad hoc strategies [28] can be developed, due to the peculiar features of the driving cycles: long duration and repeatability.
The remainder of this article is organized as follows.In Section II, an overview of the tractor is provided along with its mathematical model.In Section III, the general integrated energy management and speed control problem is discussed.Then, the ECMS-based approach is designed in Section IV together with the stability analysis.Section V shows the tuning of the EMS parameters and the necessary steps to implement it on the tractor.Finally, in Sections VI and VII, the simulation and experimental results are presented.

II. VEHICLE OVERVIEW AND MODELING
The vehicle considered in this work is represented in Fig. 1.The powertrain is composed of a 52-kW ICE and a 27-kW EM mounted in parallel before manual transmission, constituted by Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.four ratios for each set of gears (slow S, medium M, fast F).Each motor is governed by its control unit, the engine one (ECU) includes a built-in rotational speed controller, while the EM one (MCU) regulates the inverter to track a torque reference.Both are in communication with the vehicle control unit (VCU), responsible for the entire control of the vehicle, including the EMS.
Concerning the external loads, two sources are present: the hydraulic system, necessary to drive hydraulic auxiliaries, and the PTO used to transmit drive power to the machinery.It must be pointed out that the vehicle has also internal sources of losses.In fact, a fan is always kept in rotation for cooling purposes, while the transmission is an oil-bath one, and therefore, a significant amount of power is internally dissipated to splash the oil [31].
Another important element is the controllable clutch, which can decouple the engine and the transmission.In this way, the vehicle can also operate in the FE mode, i.e., the EM is the only machine responsible for traction.Considering the current version of the prototype, when the FE is active, the engine is set at the minimum speed to feed the hydraulic system, while keeping the fan in rotation.
A complete vehicle simulator for this vehicle is discussed in [4] and it models: the engine and EM as efficiency maps; the battery as a static equivalent circuit model with SoCvarying open-circuit voltage; the losses of fan used to cool the engine; the transmission losses; the coasting-down losses; and finally the engine controller represented by a PI controller.In the version of the prototype analyzed in this current work, the hydraulic system is not driven by a dedicated EM-pump system.
While the complete model in [4] is used as a simulation environment, the vehicle model is here simplified to derive and analyze a proper energy management The first equation is the result of a torque balance at the main shaft: is the rotational speed of the engine and EM shaft, T ice and T em are the engine and EM torques, respectively, and ξ is a Boolean variable that represents the clutch status, equal to 1 when closed.T in can be considered as an unknown disturbance, representing the counteracted torque to keep the vehicle at constant speed, and therefore, it is the sum of different contributions: the coasting-down torque T cd [32], scaled by the transmission gear ratio τ gb and the final drive one τ 0 , the transmission losses T gb , and the torque requested by the auxiliary loads (fan T fan , pump T pump and PTO T pto ) Finally, J eq is the equivalent inertia where J ice and J em are the engine and motor inertia, respectively, M and M add are the vehicle mass and the additional mass added with trailers in transport scenarios, respectively, and finally, R w is the wheel radius.The second and third equations in (1) compute the consumption rate of the two energy sources, expressed in terms of fuel mass rate ṁ f , also named w f , and the battery SoC.Fuel consumption is computed by scaling the fuel power P f by the fuel power density H f , and SoC by dividing the battery power P b with the battery energy capacity Q b .Fuel and battery power are linked with the mechanical power provided to the vehicle through their respective efficiency maps where η ice and η em are the respective efficiencies [33], shown in Figs. 2 and 3 as nonlinear functions of speed and torque.
The last two equations in (1) are associated with the built-in engine speed controller, aiming at tracking the speed reference ref , requested by the driver: K p and K i are the proportional and integral gain, respectively, and x ice is the state associated with the integral error.Despite the complexity of engine controller [34], [35], an equivalent PI represents well the vehicle behavior from a control-oriented point of view [4].
In conclusion, in this model, the inputs controlled by the driver are the speed reference ref and the gear ratio τ gb .The EM torque T em and the clutch status are electronically controlled by the VCU.The outputs of the model are the vehicle speed, the engine torque, and the consumption, which

TABLE I VEHICLE PARAMETERS
are all measured by the ECU or the MCU.Finally, T in and M add act as unknown disturbances in the system.The main model parameters are reported in Table I, where gear-box values are the fast (F) set, used in the following.

III. PROBLEM FORMULATION
In this article, we propose an ECMS-based EMS for a parallel hybrid tractor.It necessarily differs from the well-known implementation of the ECMS because of the presence of the built-in speed controller that equips the ICE.Indeed, differently from conventional cars, tractor engine control units natively implement an engine speed tracker; accordingly, when the driver acts on the throttle pedal and demands a speed reference and not an engine torque.
In the traditional parallel hybrid vehicles, the combined energy management and cruise control is typically addressed by hierarchical control schemes, e.g., [19], [20], [21], where an external controller computes the total torque necessary to track the desired speed and an internal loop-i.e., the actual EMS-splits the requested torque between the engine and the EM so to minimize the fuel consumption.As previously recalled, an important difference between tractors and traditional vehicles is the speed-controlled ICE.With such a configuration, the delivered engine torque cannot be directly manipulated by the EMS, unless the ICE control architecture is completely revised.Sometimes, for industrial constraints, this is not even possible.Therefore, the family of hierarchical control schemes turns out to be unsuitable for tractors with a built-in speed controller.First, the torque cannot be freely split between the engine and the EM, because the engine receives a speed reference.Second, being the ICE already responsible for speed tracking at a lower level, the external loop of the hierarchical strategy results redundant.It follows that the conventional ECMS cannot be neither applied as it is, but proper modifications are required.In our work, we address this challenge and propose a modification of the traditional ECMS for a parallel hybrid vehicle that manipulates only the EM torque and does not (at least directly) interfere with the ICE control architecture; on the contrary, the EM co-operates with the ICE to fulfill the speed reference tracking goal without loss in performance and stability.The schematic representation of the proposed architecture is depicted in Fig. 4.
The proposed ECMS cannot be directly compared with a standard ECMS due to the discussed constraints.For this reason, in this article, we assess the effectiveness of the proposed modified ECMS solution by comparing its performance against a global optimal solution computed a posteriori and a real-time solution based on MPC that we described in the paper [4].

IV. ECMS-BASED ENERGY MANAGEMENT
In this section, after a brief overview of the traditional ECMS, we discuss how it is extended, to co-operate with the built-in engine speed controller to regulate the speed.

A. ECMS Background
ECMS is a well-known EMS for hybrid vehicles, which became popular due to its simple implementation, while having a high fuel-saving performance [36].Indeed, it simplifies the global fuel-saving minimization problem, turning it into a static optimization at any time instant.In particular, it minimizes an equivalent fuel consumption w eq min w eq (t) = P eq (t) where P eq is the equivalent power consumption The equivalent power is the sum of the fuel power consumption and the battery power, weighted by the equivalence factor λ, which makes the two power sources comparable, in terms of energy consumption.It must be recalled that while the fuel power is always positive, the electrical power of the battery could also assume negative values; this happens when the battery is recharging.Therefore, λ takes into account the complete efficiency chain necessary to recharge the battery, through the engine and external suppliers in plug-in vehicles and through the engine only in non-plug-in vehicles.Hence, the value of the parameter λ is influenced both by the past and future behaviors of the vehicle, so its value can only be estimated for real-time applications.Indeed, different strategies have been developed to estimate it using various inputs, such as the driving style [37] or the past driving information [38].Recently, to provide a physically based estimation of the equivalence factor, the ECMS has been turned into an efficiency maximization problem [30].
One of the advantages of this approach is the possibility of precomputing offline the solution and storing it into maps [39] and then retrieving them on-line using the current operating point.Considering classical schemes for the energy management and speed control problem for parallel hybrid vehicles, the operating point can be defined by the desired speed ref and the torque T ref requested by the external speed controller, then The second equation in (7) highlights the possibility of splitting the total torque between the engine and the EM in parallel hybrid vehicles.However, due to the reduction in the EMS to a local optimization at any time instant, the terminal charge-sustaining constraint cannot be explicitly considered.To cope with this issue, many works, e.g., [40], [41], [42], propose an indirect solution, which changes the physical meaning of λ and uses it as a weight on the battery power, making the battery discharge more or less convenient depending on the current SoC value.
In our scenario, we remark that the gear ratio on our tractor is not an available control variable and it is directly commanded by the driver, through the manual vehicle transmission.As a natural consequence, its optimization cannot be included in the ECMS problem.However, the optimal ECMS maps are indirectly affected by the gear ratio, because they are fed by the speed and load torque defined at the engine shaft.This means that when the driver changes gear ratio, the estimated engine operating point will suddenly move to a new location into the speed-torque map, affecting the torque values that our strategy commands to the EM.Moreover, we also remark that during a gear shift, when the driver pushes the clutch pedal, the EM torque is set to zero so to maintain the expected neutral behavior of the vehicle.Hence, the proposed EMS logic does not optimize consumption during gear changes.Anyhow, this is not a significant limitation; indeed, differently from conventional cars, tractors are typically driven using a (suitable, according to the needs) constant gear ratio.On one side, on-field works typically require to set a specific and constant vehicle speed throughout the entire mission.On the other side, even when addressing transport operations, the maximum vehicle speed is limited by regulation; hereby, using the utmost available gears, the entire vehicle speed span can be covered.For the mentioned reasons, the real-time optimization of the gear ratio has not been addressed.

B. ECMS Extension for Speed-Controlled Engines
As already discussed, considering the vehicle architecture, the torque split cannot be directly controlled; however, it is interesting to study whether it can be at least indirectly influenced at steady-state.Therefore, considering a fixed operating point ( ¯ ref , T in ), the model in (1) reduces to It follows that the equilibria of the system are It means that in any operating point, thanks to the presence of the controller integrator: 1) the engine speed is tracked and 2) the static load torque T in can be split between the engine and the EM one, by manipulating the EM torque.This analysis is crucial because it shows us that the torque split framework is valid-at steady-state-in any operating point ( ¯ ref , T in ) and so the traditional ECMS solution can be computed and applied if and only if 1) T in is known and 2) any operating point ( ¯ ref , T in ) is stable and controllable.It is interesting to highlight that these two assumptions arise considering the control scheme in Fig. 4. Indeed, in a traditional control scheme, load speed and torque are available from the driver speed reference and the outcome of the external speed controller, respectively.Then, the stability is assessed just by having a stable speed controller.In this case, the proof is trivial, just looking at the dynamical equations of the closedloop system.For example, considering an external PI as a speed controller and recalling (7), the closed-loop system in the traditional hierarchical schemes becomes Therefore, the way the EM torque is regulated does not affect the vehicle dynamics, because the engine torque is always equal to the reaming part, necessary to apply the total reference torque on the system.Below, the load torque estimation problem is discussed along with the stability analysis of the closed-loop system, in the proposed framework.
1) Load Torque Estimation: By definition, the load torque is the load to be counteracted by the engine and the EM to drive the vehicle.Looking at the first equation of (1), T ice and T em counteract at any time instant a load torque T l that is the sum of inertial J eq ˙ and additional loads T in It follows that there are at least two strategies to provide a load torque estimate T : 1) use the first branch of ( 12): T l = J eq ˙ + T in and 2) use the second one: The first approach is strongly model-based, and therefore, it is not robust to model uncertainty.Nevertheless, it could provide an advantage in terms of stability when it is used in a feedforward fashion avoiding the creation of feedback loops.
To make the solution independent of the model, the second approach is more promising because it uses the sum of the engine and EM torques as an estimate.It should be remarked that a low-pass filter is required to avoid algebraic loops (given that the EM torque is the outcome of the EMS) and to reduce measurement noise where k T is the time constant of the first-order low-pass filter.However, in this second approach the estimator is fed by measurements and a stability analysis becomes necessary.
2) Closed-Loop System Analysis: The stability of the nonlinear closed-loop system is assessed by applying the linearization theorem [43].First, for any operating point that is an equilibrium for ( 16) the linearized system is computed where Then, it must be verified whether the stability criterion for linear systems Re(eig(A lin )) < 0 (20) is guaranteed in any operating point.Moreover, it is necessary to check that the reference speed can be correctly tracked, meaning that the output controllability from ref to must be verified.Therefore, the following condition must be satisfied [44]: where n is the size of A lin , B lin,1 is the first column of B lin , and C lin,1 = [1 0 0] extracts the first state only as output.
It is important to highlight now that the engine is subject to internal saturations, as reported in Fig. 2. Considering that T ice = T max ice , saturations are directly accounted for in the vehicle model (16) and therefore in the stability/controllability analysis so, the corresponding linearized system matrices are Looking at the expression of B sat lin when engine is saturated in (23), it immediately emerges that its first column B sat lin,1 is composed only of zeros.It follows that the controllability constraints ( 21) cannot be satisfied, and therefore, ECMS solution cannot be applied.
A potential solution lies in the explicit consideration of the tracking error ref − in the optimal torque computation Indeed, in this case the B lin matrix becomes and so in saturation condition, its first column is potentially nonnull or even full Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
It is interesting to note that the explicit consideration of the tracking error in F ′ not only helps in the satisfaction of the controllability criterion but also introduces a new degree of freedom to assess the stability of the closed-loop system, given that also the system matrix A lin is affected.Indeed, the partial derivative with respect to the measured speed changes because the error is a function of the measure itself.
The exact way the tracking error is considered in the EM torque computation is discussed in Section V, when the ECMS-based solution is properly tuned for the considered tractor.

V. TUNING AND IMPLEMENTATION
In this section, the specific tuning of the ECMS for the considered prototype is discussed, along with the results of the stability analysis.Then, the additional aspects necessary to implement the control strategy are introduced.

A. Tuning of the ECMS-Based Solution
In this work, to compute the ECMS and provide an estimate for the equivalence factor λ, we applied the procedure presented in [30].Hence, the ECMS problem is equivalently formulated to a maximization problem aiming at optimizing the total vehicle efficiency where η r and η d are the efficiency during recharge phases and discharge phases, respectively.Given that η r does not depend on λ, it can be used to give a prior estimation of the efficiency chain in the equivalence factor, as shown in [30]: 1) maximize η r ; 2) compute the resulting average efficiency during recharge phase ηr ; and 3) maximize η setting λ = 1/ ηr .Also in this case, the solution can be stored into a map function of the current operating point, while λ becomes a fixed value.The solution applied on the considered tractor returned that ηr = 0.33 and the map is shown in Fig. 5. Analyzing Fig. 5, the main trends can be summed up into the following considerations: discharge is preferred at low loads in the FE mode and at loads higher than the maximum engine efficiency curve; recharge is preferred at loads lower than the maximum efficiency curve.
The second step of the tuning requires the introduction of a weight γ on the battery power In this way, the battery power is made more (γ < 1) or less (γ > 1) convenient.The effect of this parameter on the solution maps is shown in Fig. 6, where it is visible that the optimal torque distribution in the admissible working points can vary from a condition of complete discharge up to a complete recharge, increasing or decreasing as a function of the value of γ with respect to the nominal solution.It follows that γ can be used to deal with the additional requirements, i.e., charge-sustaining and speed tracking.
The design of the weight γ to guarantee the maintenance of the battery SoC can be taken from the ECMS literature.Indeed, different approaches have been proposed: it can be a simple static function of SoC [40] or it can be manipulated by proportional [42] or PI controller, whose reference is the desired SoC target [41].
In this case, we propose a static function linear in SoC, to prefer charge at lower SoC, making the battery usage more costly, increasing γ , and vice versa.Then, to avoid violating hard constraints, γ suddenly changes when the limits are reached to immediately prefer charge and discharge, depending on which bound is touched.The resulting shape is mathematically written as where SoC ref = 50% and γ 0 = γ 0,high , when upper-bound is reached γ 0,low , when lower-bound is reached.
Concerning the tracking requirement, an additional term proportional to the tracking error, err = ref − , has been included in the weight γ , so that it becomes (31) or equivalently written γ (SoC, err ) = γ err,0 (SoC) − K err err (32) where Moreover, the gain K err has been scheduled to guarantee that in the presence of a minimum or maximum tracking error considered acceptable, the system becomes always reactive providing a complete recharge or discharge, respectively, independently of the current value γ err,0 (SoC).The resulting expression of γ is shown in Fig. 7. Fig. 6.Optimal EM torque that optimizes (28) for different values of γ .In red areas, the EM provides a positive torque, while a negative one in the blue ones.In the region between the engine maximum torque (gray) and the total torque (black), the EM torque is always positive to satisfy the load request.

B. FE Mode Management
To be implemented on the real tractor, the FE mode activation or deactivation requires specific management.In particular, the outcome of the EMS is directly used in hybrid mode, while it generates the activation or deactivation request for the FE mode.Then, to turn-off the engine in practice, the following steps are necessary: 1) the development of an EM speed controller, to track the speed reference, to actually work in closed-loop (as in Fig. 8); 2) the development of a high-level control logic to avoid chattering in FE mode activation.In fact, looking at Figs. 5 and 6, it is clear that a sharp transition occurs when the optimal solution changes from FE to recharge; 3) the development of a low-level control logic for the engine engagement/disengagement, controlling the clutch.1) EM Speed Controller: The EM speed controller is a PI controller tuned to have the same tracking performance as the built-in engine speed controller, to make the driver perceive the same response behavior.
2) High-Level Control Logic: To avoid chattering, if the operating point is close to the transition line, a control logic is necessary.The implemented solution consists of a time-based hysteresis, whose threshold reduces as long as the EM torque is closer to its positive saturation, to avoid loss of tracking performance in the FE mode with the ICE turned off.It follows that the map in Fig. 5 is used to detect the FE zone, while in the hybrid mode the applied torque is the solution of the problem (28) with FE disabled, as depicted in Fig. 9, adding the following constraint: The solution to the modified problem is shown in Fig. 9.
3) Low-Level Control Logic: The low-level control logic manages the transition from the hybrid to FE mode and vice versa.In the hybrid mode, the engine speed controller tracks the reference speed, while the EM applies the optimal torque.When an FE activation is requested by the high-level control logic, the booster speed controller is woken-up moving the booster torque to the current estimated load torque.At this point, the clutch is opened and the EM speed controller is activated, while the engine is turned off.On the contrary, when the hybrid mode is requested by the high-level controller, the engine is turned on and brought to the reference speed.Once the engine reaches the reference speed, the clutch is closed and the EM torque returns to be chosen by the optimal map.
The effect of FE activation and deactivation is pointed out with the test in Fig. 10 in a worst case (full recharge in the hybrid mode).The experimental results show how the speed reference is tracked both in the hybrid and FE modes, without any particular effect on the vehicle longitudinal speed.

C. Stability/Controllability Analysis Results
As anticipated in Section IV, during the design of the efficiency-based EMS, a stability/controllability analysis is necessary.Therefore, before implementing the EMS on the tractor control unit, the stability and controllability need to be verified.
Due to the previous design of the FE mode management strategy, during FE phases, the closed-loop system is stable if and only if the speed controller is stable, given that the system assumes the same structure as in (11).On the other hand, in the hybrid mode, the closed-loop is stable if the optimal control maps in Fig. 9 provide stable and controllable equilibria for any operating point and for any value of γ , satisfying (20) and (21).Concerning the load torque low-pass filter, its time constant k T has been fixed to 1 s.Now, the outcome of this check is discussed in detail for the nominal case with γ = 1, comparing the results in Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Fig. 9. Optimal EM torque that optimizes (28) for different values of γ , avoiding the FE solution, thanks to the constraint in (34).As in Fig. 6, in red areas, the EM provides a positive torque, while a negative one in the blue ones.In the region between the engine maximum torque (gray) and the total torque (black), the EM torque is always positive to satisfy the load request.Fig. 10.Transition from the hybrid to FE mode and vice versa.In FE, the engine idles at minimum speed.Fig. 11, where K err = 0, with the one in Fig. 12, where K err = 6.67e −3 1/r/min.It is visible that a not null K err : 1) not only enlarges the stable and controllable area but also increases the damping of the closed-loop system and 2) produces critical points only on the maximum load torque curve, i.e., when both the engine and the EM need to be saturated to satisfy the load constraint.

VI. SIMULATION RESULTS
Before an experimental evaluation of the proposed approach, its performance is evaluated in a simulation environment, where the considered speed profile, taken from [4], is representative of a transport driving-cycle for this tractor.The results of the simulation are shown in Fig. 13, which provides a first validation for the proposed solution.Indeed, it is visible that 1) fuel can be saved with the proposed EMS; 2) the charge-sustaining can be guaranteed; and 3) the chosen value ηr = 0.33 is very close to the real efficiency computed during recharge phases on this driving cycle.Moreover, the almost constant trend of the measured efficiency reduces the  necessity of an online adaptation, different from the experience in the case study on traditional vehicles shown in [30].
The results are quantified in Table II: summarizing, the ECMS-based is able to reach fuel-saving performance close to the MPC-based one proposed in [4], used as a benchmark.Moreover, a very low tracking RMSE is obtained-lower than MPC-given that the ECMS-based strategy can run at 100 Hz Fig. 13.Simulation results on the considered driving cycle (top).Fuel and SoC evolutions are compared between the hybrid and the ICE-only tractor.In the last plot, the real recharge efficiency is compared with the a priori estimator.on the VCU, which is higher than the maximum feasible one with the MPC.

VII. EXPERIMENTAL RESULTS
The experimental campaign aims to quantify the performance of the proposed EMS.First, we evaluate the speed tracking performance, to check that the driver can have a good driving experience, and then we compute the fuel-saving on real driving cycle.

A. Speed Tracking
The fulfillment of the speed tracking requirement is experimentally verified with two different tests, comparing the built-in ICE speed controller behavior with the vehicle operating in the hybrid mode.To prove the solution effectiveness, the strategy of γ as a function of the speed tracking error err is shown, compared also with the nominal solution with γ = 1.
In Fig. 14, the tractor reacts to a step variation in the driver speed request, while moving on a flat ground.The results show  that activating γ = γ ( err ), the step performance is similar to the one obtained with the built-in controller, while with γ = 1 the speed target is reached 0.7 s later.It is worth to be mentioning that the value of the rise time due to a step variation in the speed reference is motivated by the low power of orchard tractor engines and the high vehicle mass.
In Fig. 15, the tractor moves at constant speed on an updown hill, without pushing the brake pedal.The built-in speed controller is not able to perfectly track the reference, due to engine saturation.Indeed, the tractor moves slower in the up-hill phase and faster in the down-hill one.On the other hand, in the hybrid mode with γ = 1, the optimal map requests a negative torque (in the current operating point), and therefore, performance becomes better when descending, but remains unchanged when climbing.Finally, this test highlights Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.how the regulation of γ as a function of the error makes the tractor track the reference in both the phases of the hill.In fact, not only the engine is responsible for speed tracking but also the EM torque depends on the tracking error itself.

B. Fuel-Saving
As anticipated, we are considering the tractor operating in transport profiles.Nevertheless, this scenario is very wide, due to the many possible usages of a tractor.Therefore, we set up a large experimental campaign to explore different situations, on a small track.Fig. 16 shows the considered tests on the speed-torque plane, sorted for increasing load.We would like to highlight that the proposed experimental validation covers a wide range of transport maneuvers, with and without the trailer; on the two extremes of Fig. 16, one can see a very low demanding test and a very demanding one which spans almost the entire engine operating region.We do believe that-having in mind the objective of validating the effectiveness of the modified ECMS strategy-the proposed experimental campaign and the related quantitative results are meaningful.The first three tests are without any additional trailer and the gear increases in each one.Due to the transport scenario, the driver uses only the fast set of gears (1F, 2F, 3F).In the last two tests, the tractor moves with a trailer of 3600 kg.Similar to before, the gear increases in the two tests.
To evaluate fuel-saving performance, defined as the percentage of fuel saved with respect to the ICE-only case, the same profile is repeated twice, one time in the ICE-only mode and then in the hybrid mode (with the possibility to use also the FE mode).In the hybrid mode, the average value γ changes at each lap, to manipulate the SoC so that it returns to the initial value.In this way, it is possible to evaluate performance considering a charge-sustaining scenario, without having any additional battery energy stored or discharged.Moreover, to have meaningful results, the vehicle must follow the same driving cycle, in terms of speed and torque, in both the modes.For this purpose, in the high load tests, the 52-kW engine is mapped with higher power (72 kW) to have a valid benchmark.Furthermore, as the driver is a human, for each test, we need to check that the test is valid by computing the average difference between the test in the ICE-only and hybrid modes (reported in Table III).To have a graphical interpretation and confirm the similarity of the driving cycle in the two cases, the time evolution of speed and load torque in the worst scenario (3F with trailer) is shown in Fig. 17.It is also visible that the SoC actually returns to the initial value, when the percentage of fuel saved is computed.
Generally in HEVs, we recall that fuel-saving performance is strictly dependent on the considered mission profile [45].The fuel-saving performance for each test is summarized in Table III and graphically depicted in Fig. 18.On average, in the considered tests, a saving of 14% has been experienced.In particular, in the two tests with the trailer, a similar saving of 14.3% and 13.6% is visible; while in profiles without the trailer the percentage of saving reduces with the gear increasing: in particular, 19% in 1F, 12.8% in 2F, while in 3F, no fuel-saving has been achieved.This last case is motivated by the fact that this profile makes the engine operate in a high-efficiency zone of the engine, and therefore, changing the operating point with the EM does not represent an advantage.

VIII. CONCLUSION
In this article, the energy management problem for a hybrid tractor has been addressed.With respect to the traditional vehicles, the EMS has been designed to operate with the built-in engine speed controller to save fuel without deteriorating the speed tracking performance of the ICE-only traditional tractor.In particular, an ECMS-based EMS has been proposed and properly extended to work in such a scenario.Moreover, the ECMS has been implemented in an efficiency framework, to provide an easier estimation of the equivalence factor.Not only simulations but also experimental tests confirmed the proposed approach.Possible next steps are a wide experimental campaign to validate the approach on different driving cycles, driving styles, and driving conditions, and the application of more advanced energy management strategies coming from the literature on standard vehicles.

Fig. 2 .
Fig. 2. ICE efficiency map.Engine speed limits are highlighted in dashed lines and maximum torque one limited in continuous line.

Fig. 3 .
Fig. 3. EM efficiency.Torque limits are highlighted in continuous line, and in dashed line the speed limits of the engine are reported to show the speed range possible in hybrid mode.The EM presents different limits in traction and recharge to satisfy the battery ones.

Fig. 4 .
Fig. 4. Proposed control scheme for the simultaneous energy management and speed control in tractors with speed-controlled engines.

Fig. 7 .
Fig. 7. Design of the weight γ as a function of the tracking error.

Fig.
Fig. Equivalent control scheme in FE mode.

Fig. 16 .
Fig.16.Experimental campaign for fuel-saving analysis: it consists of tests carried out with and without an additional trailer, increasing the gear in the fast (F) set.Tests are reported on the speed-torque plane.

Fig. 17 .
Fig.17.Example (3F with trailer) of test consistency in the ICE-only and hybrid modes.The first plots show that at the end of the test, SoC returns to its initial value and fuel consumption.The last two plots compare the measured speed and load torque.

TABLE II SIMULATION
RESULTS.SPEED TRACKING, FUEL CONSUMPTION, AND SAVING ARE SHOWN FOR EACH CONTROL STRATEGY

TABLE III EXPERIMENTAL
RESULTS.SPEED AND TORQUE CHECKS SHOW THE RMSE BETWEEN THE TEST IN HYBRID MODE AND ICE-ONLY MODE.FUEL SAVED IS COMPUTED WHEN THE FINAL SOC IS ZERO.THE DURATION OF THE TEST IS ALSO SHOWN Fig. 18.Fuel-saving performance computed in each test.