This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Sample and hold systems Sample and Hold Systems The continuoustime plant, P ( s ), is preceeding by a zeroorder hold and followed by a sampler. P ( s ) ZOH C ( z ) a64 a64 T a14a13 a15a12 + a117 a27 a27 a27 a27 a27 a27 a54 r ( k ) u ( k ) u ( t ) y ( t ) y ( k ) Performance and stability is specified in terms of the digital domain signals, r ( k ), y ( k ), u ( k ), etc. Analog/Digital (A/D) board: sampler. Digital/Analog (D/A) board: zeroorder hold. Other options are possible but the above are by far the most common. Roy Smith: ECE 147b 5 : 2 Modeling sampled systems Modeling P ( z ) P ( s ) C ( s ) C ( z ) P ( z ) Approximation of C ( s ) with C ( z ) Model P ( s ), and sample/hold as P ( z ) Continuoustime design Discretetime design Develop a model of the discretetime behavior of the plant. Allows digital designs to be performed directly. Evaluating the stability of the discretetime system ( C ( z ) and P ( z ) in feedback). Roy Smith: ECE 147b 5 : 1 Sample and hold systems Zeroorder hold equivalence This is a reasonable model of a typical digital to analog (D/A) converter. At the sampletime, t = kT , the discrete input, u ( k ), is put on the output, u ( t ). This value is held constant for the entire sample period. So, u ( t ) = u ( k ) , for kT t &lt; kT + T. T 2T 3T 4T 5T 6T21 1 2 3 4 Time: t u ( k ) u ( t ) Roy Smith: ECE 147b 5 : 4 Sample and hold systems Sample and Hold Systems Model the system from the ZOH block to the sampler: P ( s ) ZOH a64 a64 T a27 a27 a27 a27 u ( k ) u ( t ) y ( t ) y ( k ) P ( s ) is an LTI system = the system from u ( k ) to y ( k ) is LSI. It has an equivalent Ztransform, P ( z ). P ( z ) a102 a102 u ( k ) y ( k ) Zeroorder hold equivalence: The closedloop combination of P ( z ) and C ( z ) exactly models P ( s ) in closedloop at the sample times....
View Full
Document
 Spring '07
 RODWELL

Click to edit the document details