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 ENGR 3350 control systems
ENGR 3350 control systems
Design a controller for an electric vehicle using PID / PI controllers
Electric motors are widely used in industries, such as traction motors installed in electric vehicles. In this project an electric vehicle, being propelled by a DC motor, is considered. The model of this electric vehicle is shown in the block diagram of Figure 1:
Figure 1: Block diagram of the electric vehicle powertrain
The driver applies the input R_{v}(s) to the vehicle by pushing the gas pedal. The block G_{sc}(s) represents the electric powertrain controller. The numerical values of all the parameters involved are tabulated below:
Parameter


Value

Parameter


Value

Wheel radius

r

0.25

Armature gain constant

R_{a}

1

Vehicle mass

M_{tot}

950

Armature time constant

T_{a}

5

Total inertia moment

Jtot

8.6

Actuator gain constant

K_{A}

10

Friction torque gain

K_{f}

0.1

Actuator time constant

T_{A}

5

Armature gain

K_{t}

2

Back emf gain

K_{b}

0.1

Efficiency

ηtot

0.9




In order to design a fast and reliable control system for the attitude control, the following tasks should be performed:
 Find the closedloop transfer function without the controller, i.e., G_{sc}(s) =1.
 Perform the stability analysis of the closedloop system by using the RouthHurwitz stability criterion. In order to achieve a stable system, what would be the relation between the current sensitivity gain, K_{cs} and the speed sensitivity gain K_{ss }?
 For the value of K_{cs} = 0.087, determine the gain K_{ss} such that the system has a steadystate error of 2% for the unitstep input.
 Plot the root locus of the two systems and discuss about the stability of the system from the plots. Also, for the case of marginal stability determine the system gain.
 Plot the unitstep response of the system and find the attributes of the response.
 Plot the Bode diagram of the system and find the Phase Margin (PM), Gain Margin (GM) and the Band Width (BW). Determine their corresponding frequencies.
 According to Figure 1, find the transfer function G(s) of the plant:
Figure 2: The cascade controller G_{sc}(s)
 Select an appropriate controller for G_{sc}(s) as either PI or PID, and then design the controller to obtain M_{p} < 3% and t_{s }< 35 seconds for the unitstep input. Explain your design procedure fully and justify your chosen controller type.
 Find the closedloop transfer function of the compensated system. Determine the type of the system and calculate the steadystate error to an appropriate input.
 Plot the root locus of the compensated system. Discus the stability of the system.
 Plot the unitstep response of the compensated system. Find the attributes of the unitstep response and compare them with the uncompensated system.
 Plot the Bode diagram of the compensated system and determine the PM, GM and BW. Compare with the uncompensated system frequency response attributes.