This This document document is an open-sourc open-sourcee project. Introd trodu uctio tion Intr Introdu oduct ctio ion n 52 8 Not Notes es and ref refere erence ncessĬopyright c 2008-2009 - Michael Baudin This file must be used under the terms of the Creative Commons AttributionShareAlike 3.0 Unported License: 51 7.3 Com Computi putings ngs the the coeffici coefficien ents ts in Sci Scilab lab. 49 7.2 Automa Automaticall tically y computi computings ngs the coefficien coefficients ts. ħ Auto Automati maticall cally y computing computing the the coefficien coefficients tsħ.1 The coeffici coefficien ents ts of finite finite differen difference ce formu formulas las. Perfor Pe rformanc mancee of fini finite te diffe differenc rences es. Vary arying ing order order to chec check k accurac accuracy y. Taki aking ng into into accoun accountt bounds on parame parameters ters. Computing Computi ng deriv derivativ atives es with with more accuracy accuracy. Nested Nes ted deriv derivativ atives es with with Scila Scilab b . Computi Com puting ng higher higher degree degree deriv derivati ative vess. Derivativ Deriv atives es of a vectorial vectorial functio function n with Scilab. Derivativ Deriv atives es of a multiv multivariate ariate function function in Scilab Scilab. Numerical Numeri cal deriv derivativ atives es of multiv multivariate ariate function functionss. Multivari Multiv ariate ate func function tionss. Ĥ Fini Finite te difference differencess of multiv multivaria ariate te functions functions A collection collection of finite difference formulas formulas. Accuracy Accurac y of finite difference formulas formulas. A three three points points formula formula for for the second second deriv derivati ative ve. Somee finite differen Som difference ce formula formulass for the first derivati derivative ve. Centere Cen tered d form formula ula wit with h 4 poin points ts. Centere Cen tered d form formula ula wit with h 2 poin points ts.
Numerical Numeri cal experimen experiments ts with with the robust robust forwa forward rd formula formula. Floating Floati ng point point implemen implementation tation of the forwa forward rd formula formula. 64 Vari arious ous resu results lts for sin sin(2 (2 ). 2 Fin Finite ite diff differen erences ces. 2.1.1 Tayl aylor’s or’s form formula ula for univ univariate ariate functio functions ns 2.1.2 2.1. Ģ A surp surpri risi sing ng res resul ultt In the the thir third d part, part, we pres presen entt the the derivative function function, its featur features es and its performances. We presen presentt severa severall formula formulass and their their associa associated ted optima optimall steps. In the second part, we analyse the method to use the optimal step to compute derivatives with finite differences on floating point system systems. In the first part, we present a result which is surprising when we are not familiar with floating point numbers. resulting in a maximum overshoot value of 3.6% and a peaktime value of 3.Numerical Derivatives in Scilab Micha¨el el Baudin May 2009 Abstract This document document present present the use of numerical numerical derivativ derivatives es in Scilab. The system performance characteristics produced in the tuning process are 3.994 seconds of settling time at 2.36 seconds research time. From the system simulation results, the best parameter is obtained through the Zieglar Nichols PID tuning process based on the results of the transient response analysis, namely when the proportional gain value (K p) is 50. The second method is automatic tuning which is done through mathematical calculations to obtain PID control constants, namely Zieglar Nichols PID tuning with the oscillation method. The value adjustment of system control parameters is carried out with several variations, namely K p control variation, K p variation to constant K d, K d variation to constant K p, K p variation to K i, constant K d, variation of K i to K p, constant K d and variation of K d to K p, K i constant.
#Scilab derivative trial#
The method used is the trial and error method by setting and varying the values of the control constants K p, K i, and K d to produce the desired system response. In this research, P, PD, and PID control simulations with the transfer function of the mass-damper spring as a plant using Xcos Scilab. This control has controlling parameters, namely K p, K i, and K d which will have a control effect on the overall system response. PID (Proportional Integral Derivative) control is a popular control in the industry and aims to improve the performance of a system. P control, PD, PID, PID tuning, Xcos Scilab, Zieglar-Nichols Abstract
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