Question

3.2 Pre-Lab Assignment When deriving the governing equations for an electromechanical system, it is often beneficial to examine the electrical and mechanical components independently. Looking at only the electrical components of the QUBE-Servo DC motor (as shown in Figure 3.2): R v00 C e, (00 Figure 3.2: Electrical curcuit of the QUBE-Servo DC motor Q1. Write the differential equation in the form of Kirchoff's voltage law) in the Laplace domain for the electrical circuit (do not use parameter values given in Table 3.1). In this particular motor, the inductance is much less than the resistance; therefore, the inductance can be neglected. Rewrite this equation for the case when the motor inductance can be neglected. Now take a look only at the mechanical components of the system (as shown in Figure 3.3). Figure 3.3: Mechanical components of the QUBE-Servo DC motor and load Assume this is a frictionless system, the differential equation in the Laplace domain for the rotational mechanical system is given by: [(J. +JA+J.)s+D]2(5)=T(s) Noting that these two systems are coupled together, mainly the relationships between e, and a as well as T and i: Q3. Combined the two differential equations derived for the electrical and mechanical systems independently, such that the result is a single differential equation in the Laplace domain relating input voltage to output angular velocity. Using the differential equation of the electromechanical system, solve for the transfer function relating input voltage to output angular velocity. Q5. Using the parameter values provided in Table 3.1 and assuming that the viscous damping of the motor is negligible ( D ), use MATLAB to simulate the response of the electromechanical system when a 3 V step input is applied. 04.

Answer 1

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