70 kg x(t) f(t) 30 kg + i(t) 7 SOFOS mele R eee FIGURE 1: LINEAR SOLENOID Task 1: Derive a transfer function for X(s)/E₂(s). Task 2: Calculate the rise time and settling time of your system. Task 3: Do you think the system response is reasonable, or should the system be changed? Clearly state any assumptions that you have made in the above tasks. TUTORIAL 5-TIME RESPONSE Objective • Integrate material from all previous lectures into a practical problem. Sarah Salsa is opening a new attraction at her theme park. One of the features of this new attraction is a trick floor panel that throws people off balance by moving vertically with somebody standing on it. The floor panel itself weighs 30 kg, and it is expected to operate with a typical 70 kg load (average human) standing on it. It is operated by a large solenoid that produces a linear force to accelerate the floor and the theme park patron. Sarah's idea is that the panel will be constrained to the surrounding floor with a spring system. The panel will fall when the patron stands on it, compressing the spring and settling to a stationary initial position. The solenoid will then be activated, lifting the mass of the panel and the patron. The workplace health and safety consultant has advised that the patron must rise to a final position 100 mm above his or her initial position, where initial position is defined as the position after the patron has stood on the panel, but before the solenoid has been activated. The patron should reach a maximum height of 120 mm above the initial position in his or her transient response. The solenoid will be driven from a 100V source that can supply up to 10 A. The below figure presents a typical diagram of an electromagnetic actuator (more realistic than this week's worked tutorial because it includes back EMF voltage). The electromagnetic actuator contains a solenoid which produces a magnetic force proportional to the current in the coil, i.e., f = K₁i. The solenoid has a resistor R and an inductor L. The solenoid's back EMF voltage is proportional to velocity & of mass M, i.e., V₁ = K₁x. The spring K = 1 N/m is used to balance forces acting on the mass M (the sum of the customer and the floor plate). Assume that the solenoid rod has negligible weight. The force constant for their solenoids is 10 Newtons/Amp for every 1000 turns, ie. a 10000 turn solenoid will produce 100 N/A. Similarly, the back EMF constant for their solenoids is 10 Volt- Seconds/Metre for every 1000 turns, ie. a 10000 turn solenoid will produce 100 Volt- Seconds/Metre. The solenoids also have a resistance of 1 for every 1000 turns, and inductance of 1 mH for every 1000 turns. Assume solenoid has R-10 2. Assume D=1 Ns/M.