2. Automotive Suspension (10 points) when designing an automotive suspension sys
ID: 1716888 • Letter: 2
Question
2. Automotive Suspension (10 points) when designing an automotive suspension system (for simplicity, only discuss one of the four wheels) we can use a spring damper model, as shown in the figure below. The positions of the body mass (xi) and the suspension mass (x2) are both zero at equilibrium, e.g. when the vehicle is at rest in a parking lot or driving smoothly on a flat, horizontal road. The unevenness of the road surface will be transmitted through the tires the wheel axis (modeled here as spring Ka and damper b) and serves as input (w) to the system. to reasonably well isolated from bumps, To keep occupants comfortable and a ride quality (x1) of to choose appropriate of the system to ensure the output the system changes relatively smoothly for a wide range of input (w). In this problem, M 2000 kg, M2 500 kg, spring constant of wheel and tire Ka 00 N/m, damping constant of wheel and tire ba- 20000 N.s/m, spring and damping constants of the suspension system Ki and bi unknown. (a) The first step toward the design is to build a differential equation model from the physical configuration shown in the figure above. Using Newton's second law to the body mass M1 we have M1* -K (x1 -x2) -b1(ij -i2), and to the suspension mass M2 we have M2E2 K1(x1 -x2) b1(x1 -i2) K20x2 w)-b2 w). Notice that gravity does not appear in these equations because it has been taken care of in the equilibrium. Based on these equations, find the differential equation eliminating x2), operator equation, block diagram, system functional, system function, and unit impulse response. You may use MATLAB to help with symbolic computation. (b) If the input w is a unit step function, what will the output x1 be? Use different values of K1 and bi to investigate the effects of these parameters on the dynamic response. (c) Based on the results of (b), choose a set of parameters with good performance. Now the input w will be a window function between time 0 and t 1 s (w(t 1 in this time interval, zero otherwise). Solve forx1(t). (d) For an active suspension system where an actuator is included between M1 and M2 that is able to generate a force F on M1 and -F on M2 to control the motion, assume F kx1. This forms a negative feedback system called proportional controller. Update the system function, specify values of k, and compare the dynamic response of active and passive suspension systems.Explanation / Answer
the question is not from linear signal and systems .pls check it once
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.