An automobile suspension system has three physical state variables, as shown in Figure AP11.5. The state variable feedback structure is shown in the figure, with K₁ = 1 Select K₂ and K₃ so that the roots of the characteristic equation are three real roots lying between s = −3 and s = −6. Also, select K_p so that the steady-state error for a step input is equal to zero.

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FIGURE AP11.5 R(s) Kp 2 s+4 K3 K₂ K₁ X3(s) 1 s+2 X₂(s) 1 s+3 X₁(s) = Y(s)