# System Prototype for ITAE Optimum Step Response 1.0

OS : Windows / Linux / Mac OS / BSD / Solaris

Script Licensing : Freeware

Created : Aug 8, 2007

Downloads : 5

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## STEPITAE(Np,Ts,SP) returns a continuous time system ...

stepitae(Np, Ts, SP) returns a continuous time system that minimizes

integral( |( t*|r(t) - y(t)| ) )

where r(t) is the unit step function system input and y(t) is the controlled system output.

In addition, Np is the number of system poles. Np must be between 2 and 8.

Ts is the desired settling time in seconds.

SP is the settling time percentage. For example, if SP = 2, Ts specifies the 2% settling time. SP must be between 0. 1 and 10. If SP is not given, SP = 2 is assumed.

Example: STEPITAE(7, 5, 1) returns a 7-th order ITAE system having a 5 second settling time to within 1% of the final value.

[N, D] = STEPITAE(. . . ) returns the numerator polynomial vector N and

denominator polynomial D of the prototype system.

[Z, P, K] = STEPITAE(. . . ) returns the zeros Z, the poles P, and the gain K of the prototype system.

[A, B, C, D] = STEPITAE(. . . ) returns the state space matrices of the prototype system.

SYS = STEPITAE(. . . ) returns a Control System Toolbox system object SYS containing the prototype system.

Algorithm: Given Np, normalized itae_optimum step response poles are found then scaled to match the desired Ts. If Np is even, all poles are in complex conjugate pairs. If Np is odd, all poles except one are in complex conjugate pairs.

integral( |( t*|r(t) - y(t)| ) )

where r(t) is the unit step function system input and y(t) is the controlled system output.

In addition, Np is the number of system poles. Np must be between 2 and 8.

Ts is the desired settling time in seconds.

SP is the settling time percentage. For example, if SP = 2, Ts specifies the 2% settling time. SP must be between 0. 1 and 10. If SP is not given, SP = 2 is assumed.

Example: STEPITAE(7, 5, 1) returns a 7-th order ITAE system having a 5 second settling time to within 1% of the final value.

[N, D] = STEPITAE(. . . ) returns the numerator polynomial vector N and

denominator polynomial D of the prototype system.

[Z, P, K] = STEPITAE(. . . ) returns the zeros Z, the poles P, and the gain K of the prototype system.

[A, B, C, D] = STEPITAE(. . . ) returns the state space matrices of the prototype system.

SYS = STEPITAE(. . . ) returns a Control System Toolbox system object SYS containing the prototype system.

Algorithm: Given Np, normalized itae_optimum step response poles are found then scaled to match the desired Ts. If Np is even, all poles are in complex conjugate pairs. If Np is odd, all poles except one are in complex conjugate pairs.

**• MATLAB Release: R2006b**

**Demands:****System Prototype for ITAE Optimum Step Response 1.0 scripting tags:**step response, poles, itae optimum, settling, controls systems modeling, stepitae, returns, prototype.

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