The speed u of a car is governed by the two equations (after rescaling) du f-v...

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The speed u of a car is governed by the two equations (after rescaling) du f-v³ dt df −2f+2 tanhu. dt where f is the traction force produced by the engine and u is the throttle position. (a) Obtain a linearized state-space model of the car. (Do not put in any numerical values yet.) Find the values of u and f required to establish equilibrium at speed (b) (c) Find the system's eigenvalues when linearized at the equilibrium con- ditions found in (b) for v= . Comment on the system's stability. (d) A modification to the car's dynamics is made so that the linearized state-space model becomes #0-30+0+ For what values of the constant b will the transfer function from the throttle position u to the car's speed u have a zero in the right half-plane? dt = U. The speed u of a car is governed by the two equations (after rescaling) du f-v³ dt df −2f+2 tanhu. dt where f is the traction force produced by the engine and u is the throttle position. (a) Obtain a linearized state-space model of the car. (Do not put in any numerical values yet.) Find the values of u and f required to establish equilibrium at speed (b) (c) Find the system's eigenvalues when linearized at the equilibrium con- ditions found in (b) for v= . Comment on the system's stability. (d) A modification to the car's dynamics is made so that the linearized state-space model becomes #0-30+0+ For what values of the constant b will the transfer function from the throttle position u to the car's speed u have a zero in the right half-plane? dt = U.