1. Consider a simple model of the vehicle dynamics, shown in the free-body diagram in Figure 1. bv u m a=i = Figure 1 Th

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1 Consider A Simple Model Of The Vehicle Dynamics Shown In The Free Body Diagram In Figure 1 Bv U M A I Figure 1 Th 1 (51.46 KiB) Viewed 51 times

1. Consider a simple model of the vehicle dynamics, shown in the free-body diagram in Figure 1. bv u m a=i = Figure 1 The mathematical model of the system is given as mv + b = 4 and the output equation is chosen as follows y = v where m is the vehicle mass, b is the damping coefficient, v is the speed of the vehicle and u is the input force i. Find the transfer function that relates v and u. ii. Find the state space equations of the system. iii. Taking u = 500 N, m= 1000 kg, and b = 50 Ns/m, determine the controllability and observability of the system. iv. Design a full state feedback controller so that the settling time is less than 5 second, maximum overshoot is less than 10% and the steady state error is less than 2%. You may use Matlab. Show your simulation results appropriately.