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

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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.
1. Consider a simple model of the vehicle dynamics, shown in the free-body diagram in Figure 1. bv u т v=i a= v= Figure 1 The mathematical model of the system is given as mv+bv=u and the output equation is chosen as follows y=y where m is the vehicle mass, b is the damping coefficient, v is the speed of the vehicle and u is the input force