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The Optimal ITAE Transfer Function for Step Input

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The Optimal ITAE Transfer Function for Step Input

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31 Jan 2008 (Updated )

Revisit the optimal ITAE transfer function using numerical optimization and digital computer

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The original ITAE (stands for Integral of Time multiplied by Absolute Error) coefficient table was drived by D. Graham and R.C. Lathrop through an analog computer. The table has been widely adopted as a standard design tool in most undergraduate level control engineering text books. However, the optimality of these coefficients has been questioned by several researchers. This code provides a means to re-calculate these coefficient using more advanced numerical optimization techniques in digital computers.

References:
1. D. Graham and R.C. Lathrop, "The Synthesis of Optimum Response: Criteria ans Standard Forms, Part 2", Transactions of the AIEE 72, Nov. 1953, pp. 273-288

2. Y. Cao, "Correcting the minimum ITAE standard forms of zero-displaceemnt-error systems", Journal of Zhejiang University (Natural Science) Vol. 23, N0o.4, pp. 550-559, 1989.

Required Products Optimization Toolbox
MATLAB release MATLAB 7.5 (R2007b)
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Comments and Ratings (3)
06 Oct 2011 Emile Simon

Note that the same results are achieved by using fminsearch instead of fminunc in itaeoptimtf. fminsearch is the Matlab implementation of the Nelder-Mead algorithm (1965), a direct search method not using gradient information. This indicates that DS methods are adequate for time response shaping problems, and i used this for settling time minimization (for which gradients are not available and fminunc will fail at using finite differencing derivative estimations), see files #33022.

05 Apr 2009 V. Poor  
04 Feb 2008 Duane Hanselman

Good work! The function you acknowledge "System Prototype for ITAE Optimum Step Response" #14104 has been updated to use the revised and much improved coefficients.

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