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ELEC 9732 Assignment 3

Q1 (25) Input-Output NCF.

Consider the system

˙x1 = −αx1 − βx2u + γ

˙x2 = −ax2 + bx1u

y = x2

which describes a field-controlled DC motor.

x1 is the armature current; x2 is the speed; u is the field current taken to be the control input.

The parameters are positive constants.

(i) Calculate the relative degree of the system.

(ii) Find a non-linearity cancelling feedback control law.

(iii) Find the internal or zero dynamics and investi-gate its stability. To do this take v(t) = −gy(t).

Show that stable zero dynamics is possible with 0 < g < a.

Then show that |x1(t)| is bounded and in partic-ular that |x1(t)| ≤ max(|x1(0)|, α/γ).

Q2 (25) State NCF.

Consider the system

˙x1 = −x1 + x2

˙x2 = x1 − x1x3 − x2 + u

˙x3 = x1 − x1x2 + 2x3

(i) Show the system allows NCF.

(ii) Find the most general form of h(x).

(iii) Design a nonlinearity cancelling feedback control law.