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* Poznan University of Technology.
Bogdan FABIAŃSKI*
Bartłomiej WICHER*
CONTROL SYSTEM IN ELECTRIC TRICYCLE FOCUSED ON HIGH DYNAMICS OF PEDALS LOAD
TORQUE RESPONSE
In the article two different control system structures of electric driven tricycle are presented. The very specific feature of the vehicle is that it works with "pedaling by wire". It means, that there is no mechanical coupling between pedals and any of driven wheels. This structure gives an advantage of achieving wide range of the correlation between the pedals load torque and speed and the driven wheels electromagnetic torque and speed. The challenge is to provide a natural pedaling feels for the rider. Two different approaches for control system signal flow are compared for natural pedaling feel for cyclist. The system architecture bases on CAN network distributed control that links three independent wheel drives, dedicated HMI panel, generator inverter and centralized supervisory board. The modelling methods are presented in the paper with an appropriate analytical base. Simulation results of presented control structures follows experimental ones taken from the electric tricycle..
KEYWORDS: electric vehicle, tricycle, distributed control system, pedaling by wire system, CAN network, electric drive, BLDC motor, power inverter, STM32F4 MCU
1.INTRODUCTION 1.1. State of the research
In the article there are presented two different approaches to design control system structures of electric driven tricycle. Those structures are mutually exclusive, bases on different control idea called speed/current oriented. First idea bases on the assumption that resistive torque on the pedals is in the relation to the motor drives currents which are generated by external speed loop (stabilize pedals and vehicle speeds). The second – current oriented idea of CS – bases on the assumption that pedal resistive torque is regulated directly by speed loop and drives currents relates to that. That omits some latencies introduced by CAN and motor electromagnetic conversions in pedals torque generating.
The very specific feature of the system is that it works with "pedaling by wire". That means, that there is no mechanical coupling of pedals with any of drive wheels. That structure gives such an advantage that the correlation of pedals torque and speed to the driven wheels relatives are fully controlled by electronics thus are not limited by mechanical construction (eg. gear). It means that one can implement fully electronic equivalent of mechanical gear and gives additional freedom degree with shaping of the energy balance between the energy taken form the cyclist and the batteries. Usage of such a vehicle is expanded comparing to the conventional pedaling system from the stationary one, recreational one through the sports. Also, the number of the electronic gears is only a parameter, so automatic gear can be programmed focused on the human muscle maximal efficiency point of work. The challenge, however, is to provide a natural pedaling feels for the rider. This links with adequate (high) dynamics in the system, and the shaping of the load profile in the angular distribution for the pedals assuming that this profile is not constant.
The three wheel vehicle control system has been previously investigated [1, 2, 3, 4]. In [3] and [4] – mechanical and electrical construction of the first prototype of the vehicle has been presented. The [2] presents in details a kinematic and dynamic model of the second prototype of the vehicle. The model implementation in Matlab/Simulink environment and simulations for several scenarios (path, speed, acceleration/deceleration) are presented. In [1]
selected (four) control structures are investigated in the real conditions – while driving the vehicle. Based on the states variables registrations, specified quality rates are calculated in order to select the best structure to be finally implemented. Except that, the problem of human driver load (resistive torque on pedals) is investigated. Due to the lack of the mechanical coupling between pedals and wheels control system must emulate the cyclist load in proper way (feelings of driving the tricycle should be similar to riding an ordinary bicycle).
This is done by dependence the load toque of the cyclist on the motor load but there is also a problem of low moment of inertia of the support system therefore constant load torque is inadequate (causes big, unnatural fluctuations of pedals angular velocity) – this issue has been investigated in [5] for stationary bike. At the moment – the proper cyclist load torque generation that guarantee natural driver feelings is the biggest challenge. The presented article measured with the problem of improving the pedals torque dynamic response.
1.2. System architecture
The internal vehicle network consists of two sub networks: power (Fig. 1a) and control (Fig. 1b). The power network is controlled by Central Power Module (CPM) – where Solid State Relays (SSR) for each power line are used and one electromechanical for main power battery terminal (automotive 150 [A] rated
relay). The control network is based on two Control Area Networks (CAN) complemented by 24 V auxiliary power supply line and distributed via Ethernet CAT5 cable. The main node (common for those two networks) is called Central Control Module which is physically independent from CPM. The CCM implements master control and safety algorithms, whereas each motor inverter control module implements local control algorithms (eg. current or speed controller) for each wheel.
Fig. 1. Power distribution (a) and CAN network structure of vehicle modules (b)
1.3. Power inverters
The power inverter is specially designed for the vehicle. It has several unique features guarantee by physical construction. Its construction source in fault tolerance, high power density, utilization of new semiconductor elements to make sure of power transistors work in save voltage–current–temperature range.
Power bridge and controller of inverter are separate projects and power bridge can be driven by any STM32 evaluation board supplied with ST motor control connector. Controller is based on STM32F4 MCU with utilization of several different interfaces such as double CAN 2.0, Bluetooth smart energy, Ethernet.
Software is based on FreeRTOS, LwIP Ethernet stack and dedicated to power bridge structure control algorithms. System construction guarantee galvanic separation of all power, Ethernet, CAN, Hall sensors from MCU.
2.SYSTEMMODELING 2.1. Control object equations
The mechanical equations of the mathematical vehicle model are presented below. Selected state variables are: vehicle position in the orthogonal 2D axles (x, y – dealt with the movement on the plane), vehicle orientation related to the x axle Θ, steering angle of the vehicle Ψ, and angular positions of all three drives φL φR φF (1). Dynamics of the tricycle is modeled by simple equation of forces balance connected with overall mass (2). More details is shown in [2].
cos 0
sin 0
1tan 0
0 1
1 1 tan 0
2
1 1 tan 0
2
1 0
cos
LIN
L L R F R
F
x
y l
b v
r l
b
r l
r
(1)
F L R cos
FT LIN D
F L R
LIN
T T T
k v F
r r r
a m
(2)
2.2. Reference control structure
The best control structure, according to quality rates described in [1] consists of main speed controller implemented in CCU and slave current controllers implemented in BLDC drives (BLDCD) – Figure 2 and 3.
Fig. 2. Present control structure – overall view
Fig. 3. Primary control structure – cyclist load torque control structure in details
The structure ensures that each drive of the vehicle generates identical torque – this is an electrical equivalent to the mechanical differential system. The cyclist load torque depends on the sum of the actual drive currents with additional corrects from free wheel algorithm [5]. Introduced coefficients (kω, kt) are related to the electronic gear.
2.3. Proposed control structures
As mentioned in the introduction, the reference structure from Figures 2 and 3 can be called speed oriented (motor torque follows pedals speed), therefore the new structure shown in Figure 4 can be called current (torque) oriented (motor torque follows pedals load torque). It bases on the assumption that pedal load torque is regulated directly by speed control loop and the electric drives currents are proportional to the generator load. This ensures smaller delays between generator load torque and drives electromagnetic torque. Invariably coefficients (kω, kt) are related to the electronic gear.
Fig. 4. Modified control structure – version I – cyclist load torque control structure in details
In the Figure 5, some modifications of current oriented control structure are introduced to maximize torque response on pedals speed change when the vehicle starts. The cyclist load torque has been divided into two components: the first dependent on the speed error and the second one dependent on the actual vehicle speed. The k*T0 component is dominant at very low speed – its impact is rapidly reduced when vehicle speed increases (at 0.1 nominal value of additional component is negligible). The (1–k)*TCONTR component dominates the load while driving with middle and high speed, ensuring proper dynamic load pedals torque response for the speed error.
Fig. 5. Modified control structure – version II – cyclist load torque control structure in details
3.RESEARCH 3.1. Methodology
Simulations and experimental test focus on the two aspects: vehicle speed regulation process (effectiveness and stability of this control loop is confirmation of the new control structure correctness) and load torque generation dynamics (assumed that new system when omitted motor electromagnetic path of pedals torque generation gives higher dynamics – less torque response latency on pedal while pedaling speed increases).
After implementing structures from Figure 4 and 5 in simulation environment, some test runs are made on the laboratory stand. In the Figure 6 a mechanical part of the dedicated braking stand with two BLDC motors rigidly coupled by steel construction is presented. The motors are the same as installed on the vehicle (with the power of 1 kW each). Selected, reduced to one or two motors, control structures may be tested on that stand. Mechanical construction guarantees the possibility of carry a very high torques.
In the Figure 7 an electric part of the laboratory stand with BLDC power inverter (on the table) is presented. The stand is supplied by low–power laboratory DC adjustable supply (up to 180 W) or directly by batteries. The utilized oscilloscope (Tektronix DPO3014) is equipped with A622 current probes and P5205 isolated voltage probe what greatly simplifies the verification of the drive operation.
What is important, for test purposes an HTTP server accessible via Ethernet (featured interface in power inverter) has been created. That makes the drive service (changing work state, on–line parameters set) easy through any PC computer (by web browser).
After the simulations and laboratory tests confirm that proposed control structure works in a stable way, it is implemented in target vehicle from Figure 8. Before final tests on track, drive is tested with raised wheels (wooden platform presented in the Figure 8). Such an interface can be used in the object parameter identification and PI controllers tuning. Complex tuning process methodology for CAN based vehicle distributed control system with analytical base is introduced in [6], similar task is presented also in [6].
Fig. 6. Mechanical part of the laboratory stand – BLDC type motors set
Fig. 7. Electronic part of the laboratory stand
Static and dynamic states are investigated. Static states measurements are made at stable pedaling speed while dynamic is tested on vehicle rapid acceleration. Such a benches are made in the reference structure from Figures: 2 and 3 which is compared with new control structure from Figure 4 and 5.
Experimental measurements (from the vehicle) are made by saving on–line data on the SD card placed in Central Control Module (see Figure 2) – which has access to all the system variables (available as internal states or grabbed by CANopen interface). The data vectors acquired with sample time around 20 [ms]
are processed off–line on the PC software.
All the presented in the subsection 3.2 visual data (waveforms) are prepared through Matlab and LaTeX environment by author's script that converts Matlab
figures to LaTeX PSTrics which is then compiled to PDF format. Thanks to this methodology, all the waveforms comes from either simulation and experiment have the same, clear and well formatted presentation form what makes the data analysis easier.
Fig. 8. The vehicle on the test stand
3.2. Simulation results
In Figures 9 and 10 simulation results are presented. The Figure 9 compares two structures: reference (speed oriented) – the one on the left, and torque oriented – on the right from macro point of view. It is assumed that the current control loop dynamics is as high it can be omitted while analysing the waveforms. The simulation is carried out in order to show the reaction of the system to step extortion. It can be seen that both structures stabilize the vehicle velocity. The biggest difference between the structures is the amount of latency in current response of the generator inverter. In the reference structure – the generator current appears after the pedals start to rotate while in the new modified structure – constant value is present even without pedalling. It greatly improves the load feedback for the driver and makes the pedalling more like bike riding. In the Figure 10, the dynamic part of the generator inverter current set point is shown in micro scale. It can be clearly seen that the reference structure introduces delay between the motor current and generator set point currents, whereas in the proposed new structure the motor current follows the generator current. This minimizes the annoying lags of load torque while driving.
Fig. 9. Time domain waveforms: upper – generator (dark) and vehicle wheel radial speed (bright) [rad/s], lower – generator set point (dark) and vehicle mean drives current (bright) [A].
Left waveforms refer to reference structure of the vehicle control system, right refer to second modified structure
Fig. 10. Time domain waveforms: generator current set point (dark) and vehicle mean drives current (bright) [A]. Left waveforms refer to reference structure of the vehicle control system,
right refer to second modified structure
3.3. Experimental results
In Figures 11, 12 and 13 experimental results are presented. The figures two structures are compared: the reference (speed oriented) – figures on the left, and torque oriented – figures on the right, from macro (wide time scale) point of view. It can be seen that the both structures stabilize the vehicle velocity (as it was assumed and confirmed by simulation). The main difference between these structures is that the new structure provides slightly better dynamic response of the load torque and may produce a wider range of the load torque due to no impact of the ripples of motor current.
4.SUMMARY
A new control structure (called current–oriented), of the tricycle driven by the pedaling by wire system, was presented in the article. Simulation and experimental results confirmed that the proposed structure behaved predictably and exhibits stable operation based on the analysis of the steady–state speed operation thus, correctness of the proposed solution was positive verified.
Fig. 11. Time domain waveforms for primary structure: upper – generator set point (dark) and vehicle wheel radial speed (bright) [rad/s], lower – generator (dark) and vehicle mean drives
current (bright) [A]. Left waveforms refer to start of the vehicle, right refer driving with constant speed
Fig. 12. Time domain waveforms for I modified structure: upper – generator set point (dark) and vehicle wheel radial speed (bright) [rad/s], lower – generator (dark) and vehicle mean drives
current (bright) [A]. Left waveforms refer to start of the vehicle, right refer driving with constant speed
It must be noticed that the waveforms of selected state variables obtained from the real system were more complex in analysis than those coming from simulation.
The complexity stems from several factors: the impact of the external environment in which the vehicle is moving, the presence of interference in the measuring channels and – above all – the presence of the human driver, the behavior of which is difficult to model (eg. there is a complex interaction between the desire constant pedaling speed and generated load torque on pedals).
Fig. 13. Time domain waveforms for II modified structure: upper – generator set point (dark) and vehicle wheel radial speed (bright) [rad/s], lower – generator (dark) and vehicle mean drives
current (bright) [A]. Left waveforms refer to start of the vehicle, right refer driving with constant speed
Analysis of the connected experimental and simulation results confirmed that the proposed, new control structure reduces the torque generation latency in pedals as theoretically assumed. Proposed modification of the new structure (with kT0 component) gave better driver feelings.
The observations during the research gave some new ideas of further system developing. First of all – generator inverter based on the typical boost topology with only one power transistor have an important disadvantage – it cannot generate current flow from zero voltage (pedals not moving), what brings much bigger latency of pedals load torque generation than changes in control structures. Pedals boost inverter will be replaced by the typical 3–phase bridge inverter what gives much more control options eg. possibility of generating torque even from zero induced voltage [8] (omitting energy efficiency of such a solution). Another solution is to split controllers for generator and motor drives as they are objects with different parameters.
In the field of data acquisition, which bases nowadays on CAN and SD card with limited write throughput (using of FAT32 format require a lot MCU core power) and with only offline analyze possibility, using Ethernet interface must be considered. Ethernet network will greatly improve data throughput, moreover, combined with Wi–Fi interface, it makes it possible to stream data
online what makes experimental research more effective and more precise (bigger sample frequency). Embedded into the power inverter controller Bluetooth 4 interface connected with smartphone will replace nowadays HMI based on evaluation board with LCD. There solutions of adding MEMS sensors as an control system signal feedback source, as its relatively cheap technology, easy to utilize as an vehicle acceleration, vibration detector or in more advanced system of track stabilization. MEMS technology is used in vehicles also as an HMI interface element [7].
Currently, the most important research goal, besides obtain as high dynamics response as possible is to get angular distribution of pedal load torque to allow for a smooth pedals move by cyclist in a position near horizontal one. It is a challenge, at a high loads system behaves unnaturally what results in high pedals speed fluctuation. It will be consider to parametrize radial torque distribution by two parameters: one defining the elliptic shape and another one defining orientation of such a distribution. System needs to be auto tunable on–line to adopt to differs vehicle work point and different cyclist. Auto tuning criterion will be to minimize periodic ripple of pedals speed.
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(Received: 26. 02. 2016, revised: 3. 03. 2016)
