Lab 1: Dynamic and Steady-State Responses of a Simplified Electric Vehicle

Introduction The objective of this lab is for you to get familiar with the basic dynamics of motion as well as the steady-state characteristics of a simplified electric vehicle.

Consider an electric vehicle, with the parameters listed in Table 1, whose tractive motor has the torquespeed and power-speed characteristics shown in Fig. 1. The torque speed characteristic can be mathematically formulated as 𝑇𝑚

= �( (𝑥 𝑥𝜃𝑚 𝜃𝑚𝑃 𝑃𝑚𝑎𝑥 𝑚𝑎𝑥) )/ /𝜔 𝜔𝑚 𝐵 𝜔𝐵 ≤ 𝜔𝜔 𝑚𝑚≤≤ 3𝜔 𝜔𝐵 𝐵 where 𝑇 𝑚 is the machine's developed (or internal, or electromagnetic) torque, 𝑃𝑚𝑎𝑥is the maximum tractive power that the motor is capable of delivering (i.e., corresponding to the rated flux, rated armature current, and rated speed), 𝜔𝐵 is the rated speed of the motor, and 𝜔𝑚 is the shaft speed of

the motor. Thus, 𝑃𝑚𝑎𝑥/𝜔𝐵 is the maximum tractive torque that the motor can produce. Variable 𝑥𝜃𝑚is a control variable that can be varied continuously from −1 to 1, to control the machine's torque (in the constant-torque region) or power (in the constant-power region); it can be thought of as the ratio of the armature current to the rated armature current, or as the throttle in a conventional vehicle.

Fig. 1. Torque-speed and power-speed characteristics of an electric motor. Page 2 of 3 Table 1. Parameters of electric vehicle.

Parameter Value Remark 𝐶 0 0.025 𝐶

1 1.6 × 10−6 𝑠2/𝑚2

𝐴𝑓 1.8 𝑚2 𝐶 𝑑 0.35 𝛿 1.0 𝑀 1200 𝑘𝑔 𝑟𝑑 0.31 𝑚 𝐺𝑅 6.3 : 1 Overall gear ratio, 𝜔𝑚/𝜔

𝑃 𝑚𝑎𝑥 50 𝑘𝑊 𝜔

𝐵 261.8 𝑟𝑎𝑑/𝑠 𝛼 0 Grade angle in degrees 𝜌 1.225 𝑘𝑔/𝑚3

𝑔 9.81 𝑚/𝑠2 Pre-Lab (each student must present P1 through P3 on paper, and email P4) P1. For 𝑥𝜃𝑚 = 1, that is for full throttle, manually calculate the 0-to-100 𝑘𝑚/ℎ acceleration time

and the steady-state speed of the vehicle on a level road. P2. Manually calculate the values of 𝑥𝜃𝑚for the vehicle to maintain a steady-state speed of 100 𝑘𝑚/ℎ on a level road. P3. Manually calculate the amount of energy retrieved by the motor if the vehicle is brought to stop

from 100 𝑘𝑚/ℎ, by changing 𝑥𝜃𝑚 from its value in P2 to 𝑥𝜃𝑚 = −0.3. P4. Build a simulink model for the vehicle, as well as an associated Matlab code for initializing the parameter and for plotting the waveforms. The Simulink model must enable the user to

dynamically change (control) 𝑥𝜃𝑚, for example, by means a signal source. The parameters of Table 1 shall be imported by the Simulink model upon the execution of the Matlab code. In addition, the Matlab code shall call and run the Simulink model of the vehicle and produce the waveforms. The model shall produce (and plot, when applicable) the following outputs

P4a. Waveform of the tractive force of the vehicle in 𝑘𝑁, versus time P4b. Waveform of the resistive force of the vehicle in 𝑘𝑁, versus time P4c. Waveform of the tractive power of the vehicle in 𝑘𝑊, versus time

P4d. Waveform of the resistive power of the vehicle in 𝑘𝑊, versus time

P4e. Waveform of the speed of the vehicle in 𝑘𝑚/ℎ, versus time P4f. The 0-to-100 𝑘𝑚/ℎ acceleration time in 𝑠 P4g. The energy delivered by the motor, in 𝑘𝑊ℎ, over a time interval Δ𝑡, spanning any

desired two instants within the simulation runtime. Note that a negative number for the delivered energy means that energy has flowed back to the motor and, therefore, to the batteries.

Page 3 of 3 Lab Work E1. Using your model, simulate the vehicle for the following scenario and produce the outputs listed

in P4: E1a. Start from stand-still with 𝑥𝜃𝑚 = 1, until the vehicle speed reaches a speed of 100 𝑘𝑚/ℎ at instant 𝑡1, which you shall record.

E1b. At 𝑡 1, step 𝑥𝜃𝑚 from 1 to the value that corresponds to a speed of 100 𝑘𝑚/ℎ. Note

that you calculated this value of 𝑥𝜃𝑚 in P2. E1c. At instant 𝑡

2, which is sufficiently larger than 𝑡1, to ensure that the vehicle has reached

a steady state, step 𝑥𝜃𝑚 from its values in E1b to 𝑥𝜃𝑚 = −0.3, and wait until the speed (which immediately starts to drop from 100 𝑘𝑚/ℎ) reaches zero at instant 𝑡3. Record 𝑡

3 and measure the energy delivered by the motor over the interval 𝑡3 − 𝑡2. Lab Report

Each group shall submit a lab report. The report shall include the pre-labs of both partners (i.e., manual calculations, Simulink diagram(s), and a print-out of the Matlab code, for each partner), the waveforms

and any numerical results required by the Lab Work and generated by the model, and your comments, interpretation of results, and conclusions. Deliver a typed report no larger than 15 single-sided lettersize pages, including the cover page