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 closed-loop transfer function without the controller, i.e., G_sc(s) =1.
Perform the stability analysis of the closed-loop system by using the Routh-Hurwitz 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 steady-state error of 2% for the unit-step 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 unit-step 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 unit-step input. Explain your design procedure fully and justify your chosen controller type.
Find the closed-loop transfer function of the compensated system. Determine the type of the system and calculate the steady-state error to an appropriate input.
Plot the root locus of the compensated system. Discus the stability of the system.
Plot the unit-step response of the compensated system. Find the attributes of the unit-step 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.

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