A simplified model of the steering of a four-wheel drive

Chapter 7, Problem 56

(choose chapter or problem)

A simplified model of the steering of a four-wheel drive vehicle is shown in Figure P7.26.

In this block diagram, the output r is the vehicle's yaw rate, while \(\delta_f\) and \(\delta_r\) are the steering angles of the front and rear tires, respectively. In this model,

\(r^*(s)\) = \(\frac{\frac{s}{300}+0.8}{\frac{s}{10}+1}\), \(G_f(s)\) = \(\frac{h_1 s+h_2}{s^2+a_1 s+a_2}\)

\(G_r(s)\) = \(\frac{h_3 s+b_1}{s^2+a_1 s+a_2}\)

and K(s) is a controller to be designed. (Yin, 2007).

a. Assuming a step input for \(\delta_f\), find the minimum system type of the controller K(s) necessary so that in steady-state the error, as defined by the signal e in Figure P7.26, is zero if at all possible.

b. Assuming a step input for \(\delta_f\), find the system type of the controller K(s) necessary so that in steady state the error as defined by \(\delta_f(\infty)-r(\infty)\) is zero if at all possible.