• University of Illinois, Urbana Champaign

• SE 320

SE320 | Pre-Lab 5 | Justin Habana (Jhabana) | 11-18-20 1. From Lab 3 and Lab 4, we found the following transfer function for a DC motor: ? ?? = ?? ??? + ? Using integration in the Laplace domain, derive the transfer function for motor position from the velocity transfer function above. ? = ∫ ω ⅆt → 1 ? Ω ? → Θ = 1 ? Ω sΘ Ea = Km τms+1  Θ ?? = ?? ?(???+1) 2. Place the position transfer function in a unity feedback loop with proportional gain controller. See Figure 1. Calculate the closed loop transfer function of this system. Hint: it should simplify into the form of an ideal second order system. Substitute in the values for ???? and ???? from the step response in Lab 4. Then choose Kp (using Equation 1 and Equation 2) to satisfy the following designs with their constraints. If not possible, explain why: Design 1: i. Peak overshoot < 10 % (Use Eq.1 below or text Fig.4.16) ii. Settling time < 800 ms Design 2: i. Peak o