IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 8, OCTOBER 2012
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A New Control Architecture for Robust Controllers in Rear Electric Traction Passenger HEVs Rafael Coronel Bueno Sampaio, Student Member, IEEE, André Carmona Hernandes, Member, IEEE, Vinicius do Valle Magalhães Fernandes, Student Member, IEEE, Marcelo Becker, Member, IEEE, and Adriano Almeida Gonçalves Siqueira, Member, IEEE
Abstract—It is well known that control systems are the core of electronic differential systems (EDSs) in electric vehicles (EVs)/hybrid HEVs (HEVs). However, conventional closed-loop control architectures do not completely match the needed ability to reject noises/disturbances, especially regarding the input acceleration signal incoming from the driver’s commands, which makes the EDS (in this case) ineffective. Due to this, in this paper, a novel EDS control architecture is proposed to offer a new approach for the traction system that can be used with a great variety of controllers (e.g., classic, artificial intelligence (AI)-based, and modern/robust theory). In addition to this, a modified proportional–integral derivative (PID) controller, an AI-based neuro-fuzzy controller, and a robust optimal H∞ controller were designed and evaluated to observe and evaluate the versatility of the novel architecture. Kinematic and dynamic models of the vehicle are briefly introduced. Then, simulated and experimental results were presented and discussed. A Hybrid Electric Vehicle in Low Scale (HELVIS)-Sim simulation environment was employed to the preliminary analysis of the proposed EDS architecture. Later, the EDS itself was embedded in a dSpace 1103 highperformance interface board so that real-time control of the rear wheels of the HELVIS platform was successfully achieved. Index Terms—Control architecture, control system, electronic differential system (EDS), hybrid electric vehicle (HEV), hybrid electric vehicle in low scale (HELVIS) mini-HEV.
I. I NTRODUCTION
B
ASED ON the global warming issue and the potential depletion of oil resources worldwide and following our tradition of carrying out research focused on mobile robotics for transportation systems [1], we recently started studies on the substitution of conventional oil-based vehicles by hybrid electric vehicles (HEVs) [2], [3]. Important institutes [4]–[6] and industries all over the world are investigating new technologies in this field and searching for skilled manpower resources, which is still very scarce. Grounded on that idea, we are giving the opportunity for undergraduate and graduated students to be in touch with HEV technologies, becoming one Manuscript received December 9, 2011; revised April 24, 2012; accepted June 11, 2012. Date of publication July 12, 2012; date of current version October 12, 2012. This work was supported in part by the Brazilian Electricity Regulatory Agency, by Companhia Paulista de Força e Luz, and by Fundação para o Incremento da Pesquisa e do Aperfeiçoamento Industrial. The review of this paper was coordinated by Prof. M. Krishnamurthy. The authors are with the University of São Paulo, 13566-590 São Carlos, Brazil (e-mail:
[email protected];
[email protected]; viniciusvmf@ yahoo.com.br;
[email protected];
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TVT.2012.2208486
of the first universities in South America to have a real line of research currently running in this area. The “Electric Wheels Project” is supported by the Brazilian Electricity Regulatory Agency (ANNEL) and the Innovation Center of the State of São Paulo Energy Distributor (CPFL). One of the aims of the group is to bring new technologies to the development of electromechanical wheels to replace conventional wheels in preexisting passenger vehicles, turning them into series HEVs. Concrete results of such research were recently published [7], which has strengthened the group, encouraging the launch of the project, the design of a mini-HEV named Hybrid Electric Vehicle In Low Scale (HELVIS) [8], and the implementation of a parametric vehicular simulator named HELVIS-Sim [9], all of which have significantly expedited researches on HEVs, especially regarding the design and evaluation of two-wheeldrive/rear-wheel-drive (2WD/RWD) electronic differential systems (EDSs) [10], [11] for passenger EVs/HEVs [12]. Furthermore, such tools have proven to be valuable opportunities to encourage researchers and enthusiasts to develop a new generation of cleaner vehicles for the new century [13]. Many works in the literature bring relevant results for the EDS problem. When it comes to numerical analysis, the work in [14] and [15] must be highlighted. Other works proposed either classic and nonrobust controller approaches [16] or very simple plant models [17], [18]. A magnetic flow algorithm was proposed in [19], whereas observers were proposed in [20]. The use of artificial intelligence (AI)-based controllers was described in [21] and [22]. In addition to accurate models of the vehicle and the power train, the core of a well-designed EDS lies in the following: 1) the control system’s ability to quickly and properly apply corrective actions and 2) its robustness against noises/disturbances/uncertainties. Maneuverability and stability are considered as direct functions of these two variables. Thus, the vehicle can ultimately follow Ackerman Geometry and minimize the slip phenomena [7], [23]. This work focuses on the design and both simulated and experimental evaluation of an EDS for a rear electric traction HEV that can be used with a great variety of control systems. In this case, the optimal H∞ robust controller for a HELVIS EDS has shown to be highly effective [12]. However, the robust control theory demands that the control architecture (and, thus, the EDS architecture) be rearranged. Thus, this work also proposes a new control architecture to match the EDS problem for the optimal H∞ controller [24]–[27], which consequently allows the use of other control systems of different proposes. It is expected that such a novel architecture leads to the improvement of the
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Fig. 1. Body diagram of a front-steering rear-traction hybrid electric passenger vehicle. TABLE I TABLE OF THE VARIABLES I NVOLVED IN THE M ODEL
EDS for a wide class of vehicles, including passenger cars. Thus, to show how in-depth and versatile the novel EDS module is in terms of performance and operability, two more distinct control approaches were also tested: One classical modified proportional–integral derivative (PID) controller is outlined [28], [29], as is one neuro-fuzzy control system [30]–[33]. At the end, simulated and experimental results, which are both performed in HELVIS-Sim simulation environment and HELVIS mini-HEV, are presented and analyzed, respectively. II. E LECTRONIC D IFFERENTIAL S YSTEM P ROBLEM S TATEMENT A. Vehicle Dynamic and Kinematic Modeling The EDS formulation is based on a 2-D rigid body dynamic model [7]. Fig. 1 shows the body diagram of a front-steering rear-traction hybrid electric passenger vehicle, and Table I shows all parameters that are involved in such a model.
From the free body diagram of the vehicle, it results in the following dynamic equations that represent the kinematic behavior of the car: l2 cos δ2 μg l2 cos δ1 ˙ + + l1 Vcgx = Vcgy Ωcg − L 2 2 P3 (t) 1 P4 (t) + + bΩcg m Vcgx + bΩcg V cgx − 2 2 CψF sinδ1 Vcgy + l1 Ωcg − δ1 − bΩ m Vcgx + 2cg CψF sin δ2 Vcgy + l1 Ωcg − (1) δ2 − bΩ m Vcgx − 2cg 2Vcgx CψR Vcgy − l2 Ωcg ˙ Vcgy = − Vcgy Ωcg − 2 − b2 Ω m Vcgx 4 cg μgl2 − (sin δ1 + sin δ2 ) 2L Vcgy + l1 Ωcg CψF cos δ1 δ1 − + m Vcgx + 2b Ωcg CψF cos δ2 Vcgy + l1 Ωcg + δ2 − (2) m Vcgx 2b Ωcg μmgbl2 μmgl1 l2 Ω˙ cg = (cos δ2 − cos δ1 ) − (sin δ1 + sin δ2 ) 4LIz 2LIz b P4 (t) P3 (t) + − bΩ 2Iz Vcgx + bΩcg Vcgx − 2cg 2 CψF Vcgy + l1 Ωcg b + δ2 − l1 cos δ2 + sin δ2 bΩ Iz 2 Vcgx − 2cg CψF b Vcgy + l1 Ωcg + δ1 − l1 cos δ1 sin δ1 bΩ Iz 2 Vcgx + 2cg 2Vcgx l2 CψR Vcgy − l2 Ωcg + . (3) 2 − b2 Iz Vcgx 4Ωcg The aforementioned equations are solved from the amount of power individually applied to both rear actuators and therefore, in practice, show how the control action will change the dynamic behavior of the vehicle. Exclusively considering the EDS problem, the desired angular velocities for both rear wheels must to be calculated, and it can be obtained from two of the kinematic parameters, i.e., the velocity of the car Vx and the maneuver radius Rcg , respectively. The first parameter can be extracted from (1), and the second can be calculated from the steering angles, which are related to Ackerman Geometry, whose formalism is described in [23]. Finally, the calculated angular velocities of both rear wheels can be determined by using [7] Vcg 2 b 2 ω3 = Rcg − l2 − (4) Rcg r 2 Vcg 2 b Rcg − l22 + . (5) ω4 = Rcg r 2 One important aspect is that, regardless of the dynamic model ability to predict the vehicle’s accelerations from the
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power that is applied to each wheel (which is very useful to simulation evaluation), it represents only an indirect measurement. In practical terms, the vehicle speed can be easily read from the controller-area-network bus network embedded in the real-scale car. The maneuver radius can be estimated by placing an inertial measurement unit (IMU) close to the center of gravity (CG) of the vehicle. Real-time IMU reading ensures the accuracy of the system, even at small slip situations. This procedure is feasible and has been commonly accomplished in many experiments in the “SENA Project” at Mobile Robotics Laboratory [1]. Such sensor fusion has proven to be useful and has been widely used in many mechatronics applications, including transportation systems. Fig. 2. Body diagram of the design of the neuro-fuzzy controller.
III. C ONTROL S YSTEM D ESIGN AND THE N EW C ONTROL A RCHITECTURE The most important element of the EDS design is the control system that acts over the adjustment of the electric wheel angular speeds. It is essential that the control system quickly provides the actuators with the correct amount of current to produce the least possible error and the least overshoot so that the wheel can roll without sliding. A great variety of control approaches based on different techniques match the EDS problem [14]–[22]. Thus, in this work, three different control approaches have been proposed [7], as follows: 1) classic approach, through the use of the modified PID equations; 2) AI approach, through the use of the neuro-fuzzy controller; 3) robust approach, through the use of the optimal H∞ controller. A. Modified Classic PID Controller The implementation of a modified PID controller considers the rearrangement of the recurrence equations for a discrete PID controller, as described in [28], to improve the quality of the process response. One weighting variable is added to the proportional gain, and filters are implemented into both derivative and integrative terms [29]. It also considers the positional form with backward difference approximation to the integrative term (I) and Tustin approximation to derivative term (D), whose control laws for proportional, integrative, and derivative terms can be represented by P (k) =Kp [βr(k)−y(k)] I(k) =I(k−1)+ D(k) =
Kp T e(k−1) Ti
(6) (7)
2Td −T N 2Kp Td N D(k−1)+ (y(k)−y(k−1)) . 2Td +T N 2Td +T N (8)
respectively. Variable Kp is related to the proportional action, Ti refers to the integral action, and Td is related to the derivative action. Variable r(k) is the reference (desired) value, y(k) is the
process output signal, and e(k) refers to the error. Variable T is the sample time, and N is a scalar such that the realizability of the controller is ensured. (In practice, values in the interval of 3 ≤ N ≤ 20 are commonly used.) Proportional action fine tuning is achieved by inserting a parameter β over the reference signal [28] so that considerable improvement in both steadystate error and transitory response is observed. The reset-windup effect occurs over the integrative action and could be suppressed through the implementation of an antireset-windup filter [28]. Regarding the derivative action, it can also present an unexpected behavior regarding the system’s stability in determined circumstances, e.g., high frequencies. At this point, derivative contribution adds a rising gain to the plant, which is commonly referenced as the quick derivate effect. In this case, an anti-quick derivate filter is implemented to decrease the closed-loop gain. It turns out that, from the derivative part in the PID controller (8), the presence of one pole in the infinity is observed, which implies the indefinite growth of the derivative gain as the frequency raises. That turns the system significantly unstable due to the saturation of the control output. The anti-quick derivate filter aims to add a pole to the derivative equation to improve the controllability of the plant. B. AI-Based Neuro-Fuzzy Controller The design of a neuro-fuzzy controller is based on two distinct and very well-defined stages [30] and is inspired in combining the benefits of the knowledge extraction provided by the fuzzy logic plus the low computational cost offered by the artificial neural networks (ANNs), which yield a very efficient class of controllers. The first stage regards the design of a fuzzy controller, involving fuzzification, inference, and defuzzification, which originates a fuzzy control surface, consisting of two input and one output variables. The second stage consists of the process of training a neural network that can learn how the fuzzy controller behaves. Fig. 2 shows all distinct parts that compose the design of the neuro-fuzzy controller. Phase (A) comprehends the establishment of the rule base, fuzzification, inference, and defuzzification so that the fuzzy control surface is generated (B). The vectors containing all data that define
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Fig. 3. Rules matrix established to the electric wheels control. Fig. 4.
the fuzzy control surface are then sent to the ANN (C). It is expected that the neural network can reproduce the very same fuzzy control surface (D). 1) Fuzzification, Inference, and Defuzzification: Fuzzy logic executes a rule-based controller, instead of a model-based controller. This approach is useful because, even if a reliable model is available, nonlinearities often raise in maneuvers [7]. The controller inputs are the angular speed error E and its derivative dE. The control action defines the output dU . Fuzzification involves the representation and the decision making based on linguistic notations, as for inputs (E, dE) and outputs (dU ). In our work, it is determined through the following variables: 1) NL: negative large; 2) NM: negative medium; 3) NS: negative small; 4) Z: zero; 5) PS: positive small; 6) PM: positive medium; 7) PL: positive large. Gaussian functions were used to represent the membership functions for E, dE, and dU because, when compared with other shapes (trapezoidal and triangular), they presented the best response. The Mandani method was used to the inference process, and a set of 49 rules was established, as shown in Fig. 3. The decision-making procedure was based on those rules. Each combination between each value of E and dE corresponds to a particular control level dU . The MAX-MIN composition and CG method were used in the defuzzification process [33]. Thus, the final result of the design of a fuzzy controller is shown in Fig. 4. 2) Feedforward ANN Training Process: ANNs present a satisfactory performance in terms of low computing cost. In particular, feedforward ANN are indicated in classification problems, where each input vector is associated to an output vector [30]. This affirmation perfectly meets the problem of controlling the electric wheels since there is a corresponding control output dU to each couple error derivative E − dE. Thereby, a four-layered feedforward ANN was designed with (Nc /2) + 3 hidden layers, where Nc is the number of inputs.
Fuzzy control surface as the result of the fuzzy design.
Fig. 5. Obtained fuzzy control surface. (a) Reproduced surface after the training process of the feedforward ANN.
Such configuration presents superior performance, compared with a three-layered feedforward ANN regarding the number of parameters that are necessary for the training process. Regarding the NN inputs and outputs, a pair of inputs (k) (k) x = (x1 , x2 ) was considered, representing error E and its (k) derivative dE. In addition, the output y = y1 , representing the increase/decrease in the control action [32], was also considered. A MATLAB toolbox was used, employing the Levenberg–Marquardt algorithm. It is important to highlight that the training performance was in compliance with mean square error (MSE) criteria. 3) Neuro-Fuzzy Controller: When the ANN training process is well succeeded, both control surfaces must be very similar. (Remember that the fuzzy control surface was reconstructed by the ANN.) Fig. 5(a) shows the fuzzy control surface itself, obtained from the implementation of the fuzzy controller, whereas Fig. 5(b) shows the surface provided by the ANN after the training process. It is clear that the four-layered feedforward neural network has reconstructed the original surface. This indicates that the ANN could successfully learn how to eventually provide the EDS with the proper control actions, as if it is in charge of an essentially fuzzy-based controller. The accuracy of the ANN can be quantified by comparing the then-reconstructed control surface and the original control surface obtained by the fuzzy system. The MSE criteria was used to compute an mean error value of e ≈ 5 · 10−5 .
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Fig. 7. Unsuitable feedback block diagram due to the high ability of noise rejection by the H∞ controller. Fig. 6. Augmented plant of the EDS module, representing the transfer function Tzw .
functions obtained through the γ-iteration algorithm and the robustness criteria are given by
C. Robust Optimal H∞ Controller The synthesis of the optimal H∞ controller was based on [24]–[27], considering the fact that the plant is stabilizable and detectable. Thus, the resulting augmented plant Gap , i.e., the respective block diagram, is shown in Fig. 6. The γ-iteration algorithm was employed, aided by a Matlab toolbox, through which the γ value is reduced until the optimal value of γopt is achieved so that at the end of the procedure, both error and control action weighting functions (We and Wu , respectively) and controller K(s) itself are obtained. Thus, the norm of the closed-loop transfer function Tzw between w and z1,2 must satisfy the following condition: We S We S
