root/branches/maintenance/3.0/Modelica/Blocks/Discrete.mo

Revision 1046, 19.2 kB (checked in by otter, 9 months ago)

Changed thickness and lineThickness annotation by dividing the current value by 4
(the previous value was not according to the Modelica 3.0 specification)
  • Property svn:eol-style set to native
  • Property svn:keywords set to Author Date Id Revision
Line 
1within Modelica.Blocks;
2package Discrete
3  "Library of discrete input/output blocks with fixed sample period"
4
5  extends Modelica.Icons.Library;
6
7  annotation (Documentation(info="<html>
8<p>
9This package contains <b>discrete control blocks</b>
10with <b>fixed sample period</b>.
11Every component of this package is structured in the following way:
12</p>
13<ol>
14<li> A component has <b>continuous real</b> input and output signals.</li>
15<li> The <b>input</b> signals are <b>sampled</b> by the given sample period
16     defined via parameter <b>samplePeriod</b>.
17     The first sample instant is defined by parameter <b>startTime</b>.
18<li> The <b>output</b> signals are computed from the sampled input signals.
19</ol>
20<p>
21A <b>sampled data system</b> may consist of components of package <b>Discrete</b>
22and of every other purely <b>algebraic</b> input/output block, such
23as the components of packages <b>Modelica.Blocks.Math</b>,
24<b>Modelica.Blocks.Nonlinear</b> or <b>Modelica.Blocks.Sources</b>.
25</p>
26
27</HTML>
28", revisions="<html>
29<ul>
30<li><i>October 21, 2002</i>
31       by <a href=\"http://www.robotic.dlr.de/Martin.Otter/\">Martin Otter</a>:<br>
32       New components TriggeredSampler and TriggeredMax added.</li>
33<li><i>June 18, 2000</i>
34       by <a href=\"http://www.robotic.dlr.de/Martin.Otter/\">Martin Otter</a>:<br>
35       Realized based on a corresponding library of Dieter Moormann and
36       Hilding Elmqvist.</li>
37</ul>
38</html>"));
39
40  block Sampler "Ideal sampling of continuous signals"
41    extends Interfaces.DiscreteSISO;
42
43    annotation (
44      Icon(coordinateSystem(preserveAspectRatio=true, extent={{-100,-100},{100,
45              100}}), graphics={
46          Ellipse(
47            extent={{-25,-10},{-45,10}},
48            lineColor={0,0,127},
49            fillColor={255,255,255},
50            fillPattern=FillPattern.Solid),
51          Ellipse(
52            extent={{45,-10},{25,10}},
53            lineColor={0,0,127},
54            fillColor={255,255,255},
55            fillPattern=FillPattern.Solid),
56          Line(points={{-100,0},{-45,0}}, color={0,0,127}),
57          Line(points={{45,0},{100,0}}, color={0,0,127}),
58          Line(points={{-35,0},{30,35}}, color={0,0,127})}),
59      Diagram(coordinateSystem(preserveAspectRatio=true, extent={{-100,-100},{
60              100,100}}), graphics={
61          Ellipse(
62            extent={{-25,-10},{-45,10}},
63            lineColor={0,0,255},
64            fillColor={255,255,255},
65            fillPattern=FillPattern.Solid),
66          Ellipse(
67            extent={{45,-10},{25,10}},
68            lineColor={0,0,255},
69            fillColor={255,255,255},
70            fillPattern=FillPattern.Solid),
71          Line(points={{-100,0},{-45,0}}, color={0,0,255}),
72          Line(points={{45,0},{100,0}}, color={0,0,255}),
73          Line(points={{-35,0},{30,35}}, color={0,0,255})}),
74      Documentation(info="<HTML>
75<p>
76Samples the continues input signal with a sampling rate defined
77via parameter <b>samplePeriod</b>.
78</p>
79</HTML>
80"));
81  equation
82    when {sampleTrigger, initial()} then
83      y = u;
84    end when;
85  end Sampler;
86
87  block ZeroOrderHold "Zero order hold of a sampled-data system"
88    extends Interfaces.DiscreteSISO;
89    output Real ySample(start=0, fixed=true);
90    annotation (
91     
92      Icon(coordinateSystem(
93          preserveAspectRatio=true,
94          extent={{-100,-100},{100,100}},
95          grid={2,2}), graphics={Line(points={{-78,-42},{-52,-42},{-52,0},{-26,
96                0},{-26,24},{-6,24},{-6,64},{18,64},{18,20},{38,20},{38,0},{44,
97                0},{44,0},{62,0}}, color={0,0,127})}),
98      Documentation(info="<HTML>
99<p>
100The output is identical to the sampled input signal at sample
101time instants and holds the output at the value of the last
102sample instant during the sample points.
103</p>
104</HTML>
105"));
106  equation
107    when {sampleTrigger, initial()} then
108      ySample = u;
109    end when;
110    /* Define y=ySample with an infinitesimal delay to break potential
111       algebraic loops if both the continuous and the discrete part have
112       direct feedthrough
113    */
114    y = pre(ySample);
115  end ZeroOrderHold;
116
117  block FirstOrderHold "First order hold of a sampled-data system"
118    extends Interfaces.DiscreteSISO;
119  protected
120    Real ySample;
121    Modelica.SIunits.Time tSample;
122    Real c;
123    annotation (
124     
125      Icon(coordinateSystem(
126          preserveAspectRatio=true,
127          extent={{-100,-100},{100,100}},
128          grid={1,1}), graphics={Line(points={{-79,-41},{-59,-33},{-40,1},{-20,
129                9},{0,63},{21,20},{41,10},{60,20}}, color={0,0,127}), Line(
130              points={{60,19},{81,10}}, color={0,0,255})}),
131      Documentation(info="<HTML>
132<p>
133The output signal is the extrapolation through the
134values of the last two sampled input signals.
135</p>
136</HTML>
137"));
138  equation
139    when sampleTrigger then
140      ySample = u;
141      tSample = time;
142      c = if firstTrigger then 0 else (ySample - pre(ySample))/samplePeriod;
143    end when;
144    /* Use pre(ySample) and pre(c) to break potential algebraic loops by an
145       infinitesimal delay if both the continuous and the discrete part
146       have direct feedthrough.
147    */
148    y = pre(ySample) + pre(c)*(time - tSample);
149  end FirstOrderHold;
150
151  block UnitDelay "Unit Delay Block"
152    parameter Real y_start=0 "Initial value of output signal";
153    extends Interfaces.DiscreteSISO;
154
155    annotation (
156     
157      Documentation(info="<html>
158<p>
159This block describes a unit delay:
160</p>
161<pre>
162          1
163     y = --- * u
164          z
165</pre>
166<p>
167that is, the output signal y is the input signal u of the
168previous sample instant. Before the second sample instant,
169the output y is identical to parameter yStart.
170</p>
171
172</HTML>
173"),   Icon(coordinateSystem(
174          preserveAspectRatio=true,
175          extent={{-100,-100},{100,100}},
176          grid={2,2}), graphics={
177          Line(points={{-30,0},{30,0}}, color={0,0,127}),
178          Text(
179            extent={{-90,10},{90,90}},
180            textString="1",
181            lineColor={0,0,127}),
182          Text(
183            extent={{-90,-10},{90,-90}},
184            textString="z",
185            lineColor={0,0,127})}),
186      Diagram(coordinateSystem(
187          preserveAspectRatio=true,
188          extent={{-100,-100},{100,100}},
189          grid={2,2}), graphics={
190          Rectangle(extent={{-60,60},{60,-60}}, lineColor={0,0,255}),
191          Text(
192            extent={{-160,10},{-140,-10}},
193            textString="u",
194            lineColor={0,0,255}),
195          Text(
196            extent={{115,10},{135,-10}},
197            textString="y",
198            lineColor={0,0,255}),
199          Line(points={{-100,0},{-60,0}}, color={0,0,255}),
200          Line(points={{60,0},{100,0}}, color={0,0,255}),
201          Line(points={{40,0},{-40,0}}, color={0,0,0}),
202          Text(
203            extent={{-55,55},{55,5}},
204            lineColor={0,0,0},
205            textString="1"),
206          Text(
207            extent={{-55,-5},{55,-55}},
208            lineColor={0,0,0},
209            textString="z")}));
210  equation
211    when sampleTrigger then
212      y = pre(u);
213    end when;
214
215  initial equation
216      y = y_start;
217  end UnitDelay;
218
219  block TransferFunction "Discrete Transfer Function block"
220    parameter Real b[:]={1} "Numerator coefficients of transfer function.";
221    parameter Real a[:] "Denominator coefficients of transfer function.";
222    extends Interfaces.DiscreteSISO;
223    output Real x[size(a, 1) - 1](each start=0, each fixed=true)
224      "State of transfer function from controller canonical form";
225  protected
226    parameter Integer nb=size(b, 1) "Size of Numerator of transfer function";
227    parameter Integer na=size(a, 1) "Size of Denominator of transfer function";
228    Real x1;
229    Real xext[size(a, 1)];
230    annotation (
231     
232      Documentation(info="<html>
233<p>The <b>discrete transfer function</b> block defines the
234transfer function between the input signal u and the output
235signal y. The numerator has the order nb-1, the denominator
236has the order na-1.</p>
237<pre>          b(1)*z^(nb-1) + b(2)*z^(nb-2) + ... + b(nb)
238   y(z) = -------------------------------------------- * u(z)
239          a(1)*z^(na-1) + a(2)*z^(na-2) + ... + a(na)
240</pre>
241<p>State variables <b>x</b> are defined according to
242<b>controller canonical</b> form. Initial values of the
243states can be set as start values of <b>x</b>.<p>
244<p>Example:</p>
245<pre>     Blocks.Discrete.TransferFunction g(b = {2,4}, a = {1,3});
246</pre>
247<p>results in the following transfer function:</p>
248<pre>        2*z + 4
249   y = --------- * u
250         z + 3
251</pre>
252
253</HTML>
254", revisions="<html>
255<p><b>Release Notes:</b></p>
256<ul>
257<li><i>November 15, 2000</i>
258    by <a href=\"http://www.dynasim.se\">Hans Olsson</a>:<br>
259    Converted to when-semantics of Modelica 1.4 with special
260    care to avoid unnecessary algebraic loops.</li>
261<li><i>June 18, 2000</i>
262    by <a href=\"http://www.robotic.dlr.de/Martin.Otter/\">Martin Otter</a>:<br>
263    Realized based on a corresponding model of Dieter Moormann
264    and Hilding Elmqvist.</li>
265</ul>
266</html>"),
267      Icon(coordinateSystem(
268          preserveAspectRatio=true,
269          extent={{-100,-100},{100,100}},
270          grid={2,2}), graphics={
271          Line(points={{82,0},{-84,0}}, color={0,0,127}),
272          Text(
273            extent={{-92,92},{86,12}},
274            lineColor={0,0,127},
275            textString="b(z)"),
276          Text(
277            extent={{-90,-12},{90,-90}},
278            lineColor={0,0,127},
279            textString="a(z)")}),
280      Diagram(coordinateSystem(
281          preserveAspectRatio=true,
282          extent={{-100,-100},{100,100}},
283          grid={2,2}), graphics={
284          Rectangle(extent={{-60,60},{60,-60}}, lineColor={0,0,255}),
285          Line(
286            points={{40,0},{-44,0}},
287            color={0,0,0},
288            thickness=0.5),
289          Text(
290            extent={{-54,54},{54,4}},
291            lineColor={0,0,0},
292            textString="b(z)"),
293          Text(
294            extent={{-54,-6},{56,-56}},
295            lineColor={0,0,0},
296            textString="a(z)"),
297          Line(points={{-100,0},{-60,0}}, color={0,0,255}),
298          Line(points={{60,0},{100,0}}, color={0,0,255})}));
299  equation
300    when sampleTrigger then
301      /* State variables x are defined according to
302       controller canonical form. */
303      x1 = (u - a[2:size(a, 1)]*pre(x))/a[1];
304      xext = vector([x1; pre(x)]);
305      x = xext[1:size(x, 1)];
306      y = vector([zeros(na - nb, 1); b])*xext;
307    end when;
308    /* This is a non-sampled equation and above there are two separate
309       when-clauses. This breaks feeback loops without direct terms,
310       since in that case y will be independent of x1 (and only dependent
311       on pre(x)).
312    */
313    /* Corresponding (simpler) version using when-semantics of Modelica 1.3:
314   equation
315     when sampleTrigger then
316      [x; xn] = [x1; pre(x)];
317      [u] = transpose([a])*[x1; pre(x)];
318      [y] = transpose([zeros(na - nb, 1); b])*[x1; pre(x)];
319     end when;
320*/
321  end TransferFunction;
322
323  block StateSpace "Discrete State Space block"
324    parameter Real A[:, size(A, 1)] "Matrix A of state space model";
325    parameter Real B[size(A, 1), :] "Matrix B of state space model";
326    parameter Real C[:, size(A, 1)] "Matrix C of state space model";
327    parameter Real D[size(C, 1), size(B, 2)]=zeros(size(C, 1), size(B, 2))
328      "Matrix D of state space model";
329
330    extends Interfaces.DiscreteMIMO(final nin=size(B, 2), final nout=size(C, 1));
331    output Real x[size(A, 1)] "State vector";
332
333    annotation (
334     
335      Documentation(info="<html>
336<p>
337The <b>discrete state space</b> block defines the relation
338between the input u=inPort.signal and the output
339y=outPort.signal in state space form:
340</p>
341<pre>
342    x = A * pre(x) + B * u
343    y = C * pre(x) + D * u
344</pre>
345<p>
346where pre(x) is the value of the discrete state x at
347the previous sample time instant.
348The input is a vector of length nu, the output is a vector
349of length ny and nx is the number of states. Accordingly
350</p>
351<pre>
352        A has the dimension: A(nx,nx),
353        B has the dimension: B(nx,nu),
354        C has the dimension: C(ny,nx),
355        D has the dimension: D(ny,nu)
356</pre>
357<p>
358Example:
359</p>
360<pre>
361     parameter: A = [0.12, 2;3, 1.5]
362     parameter: B = [2, 7;3, 1]
363     parameter: C = [0.1, 2]
364     parameter: D = zeros(ny,nu)
365
366results in the following equations:
367  [x[1]]   [0.12  2.00] [pre(x[1])]   [2.0  7.0] [u[1]]
368  [    ] = [          ]*[         ] + [        ]*[    ]
369  [x[2]]   [3.00  1.50] [pre(x[2])]   [0.1  2.0] [u[2]]
370                             [pre(x[1])]            [u[1]]
371       y[1]   = [0.1  2.0] * [         ] + [0  0] * [    ]
372                             [pre(x[2])]            [u[2]]
373</pre>
374</HTML>
375"),   Icon(coordinateSystem(
376          preserveAspectRatio=true,
377          extent={{-100,-100},{100,100}},
378          grid={2,2}), graphics={
379          Text(
380            extent={{-90,15},{-15,90}},
381            textString="A",
382            lineColor={0,0,127}),
383          Text(
384            extent={{15,15},{90,90}},
385            textString="B",
386            lineColor={0,0,127}),
387          Text(
388            extent={{-52,28},{54,-20}},
389            textString="z",
390            lineColor={0,0,127}),
391          Text(
392            extent={{-90,-15},{-15,-90}},
393            textString="C",
394            lineColor={0,0,127}),
395          Text(
396            extent={{15,-15},{90,-90}},
397            textString="D",
398            lineColor={0,0,127})}),
399      Diagram(coordinateSystem(
400          preserveAspectRatio=true,
401          extent={{-100,-100},{100,100}},
402          grid={2,2}), graphics={
403          Rectangle(extent={{-60,60},{60,-60}}, lineColor={0,0,255}),
404          Text(
405            extent={{-54,50},{52,-10}},
406            lineColor={0,0,0},
407            fillColor={128,128,128},
408            fillPattern=FillPattern.None,
409            textString="zx=Ax+Bu"),
410          Text(
411            extent={{-56,14},{54,-50}},
412            lineColor={0,0,0},
413            fillColor={192,192,192},
414            fillPattern=FillPattern.Solid,
415            textString="  y=Cx+Du"),
416          Line(points={{-102,0},{-60,0}}, color={0,0,255}),
417          Line(points={{60,0},{100,0}}, color={0,0,255})}));
418  equation
419    when sampleTrigger then
420      x = A*pre(x) + B*u;
421      y = C*pre(x) + D*u;
422    end when;
423  end StateSpace;
424
425  block TriggeredSampler "Triggered sampling of continuous signals"
426    extends Interfaces.DiscreteBlockIcon;
427    parameter Real y_start=0 "initial value of output signal";
428
429    annotation (
430      Icon(coordinateSystem(preserveAspectRatio=true, extent={{-100,-100},{100,
431              100}}), graphics={
432          Ellipse(
433            extent={{-25,-10},{-45,10}},
434            lineColor={0,0,127},
435            fillColor={255,255,255},
436            fillPattern=FillPattern.Solid),
437          Ellipse(
438            extent={{45,-10},{25,10}},
439            lineColor={0,0,127},
440            fillColor={255,255,255},
441            fillPattern=FillPattern.Solid),
442          Line(points={{-100,0},{-45,0}}, color={0,0,127}),
443          Line(points={{45,0},{100,0}}, color={0,0,127}),
444          Line(points={{0,-100},{0,-26}}, color={255,0,255}),
445          Line(points={{-35,0},{28,-48}}, color={0,0,127})}),
446      Diagram(coordinateSystem(preserveAspectRatio=true, extent={{-100,-100},{
447              100,100}}), graphics={
448          Ellipse(
449            extent={{-25,-10},{-45,10}},
450            lineColor={0,0,255},
451            fillColor={255,255,255},
452            fillPattern=FillPattern.Solid),
453          Ellipse(
454            extent={{45,-10},{25,10}},
455            lineColor={0,0,255},
456            fillColor={255,255,255},
457            fillPattern=FillPattern.Solid),
458          Line(points={{-100,0},{-45,0}}, color={0,0,255}),
459          Line(points={{45,0},{100,0}}, color={0,0,255}),
460          Line(points={{-35,0},{28,-48}}, color={0,0,255}),
461          Line(points={{0,-100},{0,-26}}, color={255,0,255})}),
462      Documentation(info="<HTML>
463<p>
464Samples the continuous input signal whenever the trigger input
465signal is rising (i.e., trigger changes from <b>false</b> to
466<b>true</b>) and provides the sampled input signal as output.
467Before the first sampling, the output signal is equal to
468the initial value defined via parameter <b>y0</b>.
469</p>
470</HTML>
471"));
472    Modelica.Blocks.Interfaces.RealInput u "Connector with a Real input signal"
473                                                          annotation (Placement(
474          transformation(extent={{-140,-20},{-100,20}}, rotation=0)));
475    Modelica.Blocks.Interfaces.RealOutput y
476      "Connector with a Real output signal"                annotation (Placement(
477          transformation(extent={{100,-10},{120,10}}, rotation=0)));
478    Modelica.Blocks.Interfaces.BooleanInput trigger annotation (Placement(
479          transformation(
480          origin={0,-118},
481          extent={{-20,-20},{20,20}},
482          rotation=90)));
483  equation
484    when trigger then
485      y = u;
486    end when;
487  initial equation
488    y = y_start;
489  end TriggeredSampler;
490
491  block TriggeredMax
492    "Compute maximum, absolute value of continuous signal at trigger instants"
493
494    extends Interfaces.DiscreteBlockIcon;
495    annotation (
496      Icon(coordinateSystem(preserveAspectRatio=true, extent={{-100,-100},{100,
497              100}}), graphics={
498          Ellipse(
499            extent={{-25,-10},{-45,10}},
500            lineColor={0,0,127},
501            fillColor={255,255,255},
502            fillPattern=FillPattern.Solid),
503          Ellipse(
504            extent={{45,-10},{25,10}},
505            lineColor={0,0,127},
506            fillColor={255,255,255},
507            fillPattern=FillPattern.Solid),
508          Line(points={{-100,0},{-45,0}}, color={0,0,127}),
509          Line(points={{45,0},{100,0}}, color={0,0,127}),
510          Line(points={{0,-100},{0,-26}}, color={255,0,255}),
511          Line(points={{-35,0},{28,-48}}, color={0,0,127}),
512          Text(
513            extent={{-86,82},{82,24}},
514            lineColor={0,0,0},
515            textString="max")}),
516      Diagram(coordinateSystem(preserveAspectRatio=true, extent={{-100,-100},{
517              100,100}}), graphics={
518          Ellipse(
519            extent={{-25,-10},{-45,10}},
520            lineColor={0,0,255},
521            fillColor={255,255,255},
522            fillPattern=FillPattern.Solid),
523          Ellipse(
524            extent={{45,-10},{25,10}},
525            lineColor={0,0,255},
526            fillColor={255,255,255},
527            fillPattern=FillPattern.Solid),
528          Line(points={{-100,0},{-45,0}}, color={0,0,255}),
529          Line(points={{45,0},{100,0}}, color={0,0,255}),
530          Line(points={{-35,0},{28,-48}}, color={0,0,255}),
531          Line(points={{0,-100},{0,-26}}, color={255,0,255})}),
532      Documentation(info="<HTML>
533<p>
534Samples the continuous input signal whenever the trigger input
535signal is rising (i.e., trigger changes from <b>false</b> to
536<b>true</b>). The maximum, absolute value of the input signal
537at the sampling point is provided as output signal.
538</p>
539</HTML>
540"));
541    Modelica.Blocks.Interfaces.RealInput u "Connector with a Real input signal"
542                                           annotation (Placement(transformation(
543            extent={{-140,-20},{-100,20}}, rotation=0)));
544    Modelica.Blocks.Interfaces.RealOutput y
545      "Connector with a Real output signal" annotation (Placement(
546          transformation(extent={{100,-10},{120,10}}, rotation=0)));
547    Modelica.Blocks.Interfaces.BooleanInput trigger annotation (Placement(
548          transformation(
549          origin={0,-118},
550          extent={{-20,-20},{20,20}},
551          rotation=90)));
552  equation
553    when trigger then
554       y = max(pre(y), abs(u));
555    end when;
556  initial equation
557    y = 0;
558  end TriggeredMax;
559end Discrete;
Note: See TracBrowser for help on using the browser.