Figure 2

Feedback analysis. (A) Block diagram representation of the feedback in Eqs. 1–3. X(s), Y(s) and Z(s) are the Laplace transforms of x(t), y(t), and z(t). G _Y (s) and G _Z (s) are the transfer functions. E(s) is the Laplace transform of the error e(t) between the input and output. D(s) represents the disturbance. (B) Time responses (unit step response) for a second-order system with different damping ratios (p _z = p _y = 0.01 min^-1). (C) As the damping ratio (ζ) increases from 0 to near 1 the %OS decreases from 100% to near 0%. (D) Block diagram representation of the discrete-time feedback model. X(z), Y(z), and Z(z) are the z-transforms of x(i), y(i), and z(i). G _Y (z) and G _Z (z) are the transfer functions. E(z) is the transform of the error e(i) between the input and output. D(z) represents the disturbance.