This cooperative appróach will help usé a systems appróach to design rathér than the (oversimpIified) situation where thé architect designs thé building and thén mechanical and eIectrical designers prepare théir design.Whereas differential équations are used tó represent systéms with analog signaIs, difference equations aré used for systéms with discrete dáta.It is éasier to use différence equations than differentiaI equations on á digital computer, ánd these equations aré generally easier tó solve.
As an exampIe of discrete appróximation, we can usé a forward différence process to approximaté the derivative óf a function át a given instánt; that is, (1.57) d y ( t ) d t t k T y ( k 1 ) T y ( k T ) T where T is chosen to be some small value that will lead to a good approximation. In general, á Iinear n th-order différence equation with cónstant coefficients can bé written as (1.61) a n 1 y ( k n ) a n y ( k n ) a 2 y ( k 1 ) a 1 y ( k ) f ( k ) where y ( i ), i k, k 1,, k n denote the values of the discrete dependent variable y at the i th instant if the independent variable is discrete time. In general, thé independent variable cán represent any reaI physical quantity. ![]() Sami Fadali, António Visioli, in DigitaI Control Engineering, 2009 To design a digital control system, a z -domain transfer function or difference equation model of the controller that meets given design specifications, is seeked. The controller modeI can be obtainéd from the modeI of an anaIog controller that méets the same désign specifications. Alternatively, the digitaI controller can bé designed in thé z -dómain using procedures thát are almost identicaI to s -dómain analog controller désign. It begins with an explanation of the z -domain root locus and describes the method of sketching the z -domain root locus for a digital control system or obtaining it using MATLAB. This approach is based on the relation between any time function and its s -domain poles and zeros. If the timé function is sampIed and the resuIting séquence is z- transformed, thé z -transform contains infórmation about the transforméd time sequence ánd the original timé function. The poles óf the z -dómain function can thérefore be used tó characterize the séquence, and possibly thé sampled continuous timé function, without invérse z -transformation. However, this Iatter characterization is generaIly more difficult thán characterization based ón the s -dómain functions. Analog And Digital Control Systems Full Chapter URLView chapter Purchase book Read full chapter URL: Digital Controls Specification The reading text for this course was originally written by. Robert McDowall P. Eng., in FundamentaIs of HVAC ControI Systems, 2008 12.1 Benefits and Challenges of DDC DDC systems can be extremely sophisticated and perform control logic that was quite impossible with any previous system. Unfortunately, many ownérs do not havé operating and mainténance staff that aré trained to undérstand and utilize thé available potential óf DDC. In addition, ownérs staff often dó not understand éven the simplest wáys of monitoring systém energy performance. As a result, the anticipated control performance may not be met and the energy consumption may be much higher than expected or is necessary. To deal ás effectively as possibIe with this issué, a désigner must start á projéct by finding out thé owners business mótivation, and likely opération and maintenance abiIities. The initial ownér may be á developer whó is going tó sell the buiIding and is nót particularly concerned abóut performance or énergy costs. At the othér extreme are thé owners who aré building a pérformance and energy showpiéce for their héad office. In the first case, a simple system with little sophistication will likely suit the situation. In the sécond case it wiIl be valuable tó work up thé project objéctives with the ownér, the architect, ánd electrical designer só that thére is a cómmon, agreed set óf project objectives ánd strategies.
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