Performance of Feedback Control Systems

Test Input Signals:

Performance of a Second Order System

Step Input:

Transient response of a second-order system (Eq. 5.9) for a step input.

The transient response of a second-order system (Eq. 5.9) for a step input as a function of ζ and ωnt.

Impulse Input:

Response of a second-order system for an impulse function input.

Step response of a control system (Eq. 5.9).

شاخصهاي كنترل سيستم درجه دو:

Percent overshoot and normalized peak time versusdamping ratio z for a second-order system (Eq. 5.8).

Normalized rise time Tr1 versus ζ for a second-order system.

The step response for ζ = 0.2 for ωn = 1 and ωn = 10.

Effect of the Third Pole on the 2nd-Order System

An s-plane diagram of a third-order system.

Effect of the Zero on the 2nd-Order System

Percent overshoot as a function of ζ and ωn when a second-order transfer function contains a zero.

The response for the second-order transfer function with a zero for four values of the ratio (a/ζωn): A = 5, B = 2, C = 1, and D = 0.5 when ζ =0.45.

ExampIe 4.1 Parameter Selection

Specifications and root locations on the s-plane.

The s-Plane Root Location and the Transient Response

Impulse response for various root locations in the s-plane.(The conjugate root is not shown.)

The Steady-State Error of Feedback Control Systems

H(s) = 1,

Step Input:

N=0

Step Input:

N>0

Step Input:

Ramp Input:

Ramp Input:

K=1

Acceleration Input:

Acceleration Input:

N=2

Triangular wave response.

Control system model with a second-order model of the motor and load.

Response of the system to a unit step input, r(t) 1, t (a) MATLAB script.

Response of the system to a unit step input, r(t) 1, t (b) Response for Ka 30 and 60.

Performance Indices

ISE:

IAE:

ITAE:

ITSE:

Example:

Example:

Step Response

Example: