# System Prototype for Step Response Matching 1.0

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

Script Licensing : Freeware

Created : Aug 8, 2007

Downloads : 3

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## STEPSHAPE(Np,OS,Ts,SP) returns a continuous time ...

stepshape(Np, OS, Ts, SP) returns a continuous time system that meets the given unit step response specifications.

Np is the number of system poles. Np must be between 2 and 15.

OS is the percent overshoot. OS must be between 0 and 20.

Ts is the 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: STEPSHAPE(7, 5, 1) returns a 7-th order system having 5% overshoot and a 1 second settling time to within 2% of the final value.

Example: STEPSHAPE(3, 0, 2, 1) returns a 3-rd order system having 0% overshoot and a two second settling time to within 1% of the final value.

[N, D] = STEPSHAPE(. . . ) returns the numerator polynomial vector N and denominator polynomial D of the prototype system.

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

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

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

Algorithm: Given Np, normalized Butterworth and Bessel low pass filter poles are computed. Linear interpolation/extrapolation from these sets of poles is used to find a set of poles that have the desired OS. These poles are then scaled to provide 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.

Np is the number of system poles. Np must be between 2 and 15.

OS is the percent overshoot. OS must be between 0 and 20.

Ts is the 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: STEPSHAPE(7, 5, 1) returns a 7-th order system having 5% overshoot and a 1 second settling time to within 2% of the final value.

Example: STEPSHAPE(3, 0, 2, 1) returns a 3-rd order system having 0% overshoot and a two second settling time to within 1% of the final value.

[N, D] = STEPSHAPE(. . . ) returns the numerator polynomial vector N and denominator polynomial D of the prototype system.

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

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

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

Algorithm: Given Np, normalized Butterworth and Bessel low pass filter poles are computed. Linear interpolation/extrapolation from these sets of poles is used to find a set of poles that have the desired OS. These poles are then scaled to provide 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: R2006a**

**Demands:****System Prototype for Step Response Matching 1.0 scripting tags:**settling, system, prototype, response matching, controls systems modeling, system prototype, stepshape, poles, returns.

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