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Nonlinear.mo

Revision 463, 25.9 kB (checked in by hubertus, 22 months ago)
Created maintenance version from Dynasims version with minimal changes (no checksum, 1 graphics, a few improved documentation places, structurallyIncomplete annotations in Visualizers)

Line
1	package Nonlinear
2	"Discontinuous or non-differentiable algebraic control blocks"
3	import Modelica.Blocks.Interfaces;
4	extends Modelica.Icons.Library;
5
6	annotation(preferedView="info",
7	Coordsys(
8	extent=[0, 0; 207, 132],
9	grid=[1, 1],
10	component=[20, 20]),
11	Window(
12	x=0.05,
13	y=0.1,
14	width=0.21,
15	height=0.23,
16	library=1,
17	autolayout=1),
18	Documentation(info="
19	<HTML>
20	<p>
21	This package contains <b>discontinuous</b> and
22	<b>non-differentiable, algebraic</b> input/output blocks.
23	</p>
24	</HTML>
25	", revisions="<html>
26	<ul>
27	<li><i>October 21, 2002</i>
28	by <a href=\"http://www.robotic.dlr.de/Christian.Schweiger/\">Christian Schweiger</a>:<br>
29	New block VariableLimiter added.
30	<li><i>August 22, 1999</i>
31	by <a href=\"http://www.robotic.dlr.de/Martin.Otter/\">Martin Otter</a>:<br>
32	Realized, based on an existing Dymola library
33	of Dieter Moormann and Hilding Elmqvist.
34	</li>
35	</ul>
36	</html>
37	"));
38	block Limiter "Limit the range of a signal"
39	parameter Real uMax=1 "Upper limits of input signals";
40	parameter Real uMin= -uMax "Lower limits of input signals";
41	parameter Boolean limitsAtInit = true
42	"= false, if limits are ignored during initializiation (i.e., y=u)";
43	extends Interfaces.SISO;
44
45	annotation (
46	Coordsys(
47	extent=[-100, -100; 100, 100],
48	grid=[2, 2],
49	component=[20, 20]),
50	Window(
51	x=0.22,
52	y=0.06,
53	width=0.43,
54	height=0.51),
55	Documentation(info="
56	<HTML>
57	<p>
58	The Limiter block passes its input signal as output signal
59	as long as the input is within the specified upper and lower
60	limits. If this is not the case, the corresponding limits are passed
61	as output.
62	</p>
63	</HTML>
64	"), Icon(
65	Line(points=[0, -90; 0, 68], style(color=8)),
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70	fillColor=8)),
71	Line(points=[-80, -70; -50, -70; 50, 70; 80, 70], style(color=0)),
72	Text(
73	extent=[-150, -150; 150, -110],
74	string="uMax=%uMax",
75	style(color=0)),
76	Text(extent=[-150, 150; 150, 110], string="%name")),
77	Diagram(
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80	fillColor=8)),
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83	fillColor=8)),
84	Line(points=[-50, -40; -30, -40; 30, 40; 50, 40], style(color=0)),
85	Text(
86	extent=[46, -6; 68, -18],
87	string="u",
88	style(color=10)),
89	Text(
90	extent=[-30, 70; -5, 50],
91	string="y",
92	style(color=10)),
93	Text(
94	extent=[-58, -54; -28, -42],
95	string="uMin",
96	style(color=10)),
97	Text(
98	extent=[26, 40; 66, 56],
99	string="uMax",
100	style(color=10))));
101	equation
102	assert(uMax >= uMin, "Limiter: Limits must be consistent. However, uMax (=" + String(uMax) +
103	") < uMin (=" + String(uMin) + ")");
104	if initial() and not limitsAtInit then
105	y = u;
106	assert(u >= uMin - 0.01*abs(uMin) and
107	u <= uMax + 0.01*abs(uMax),
108	"Limiter: During initialization the limits have been ignored.\n"+
109	"However, the result is that the input u is not within the required limits:\n"+
110	" u = " + String(u) + ", uMin = " + String(uMin) + ", uMax = " + String(uMax));
111	else
112	y = smooth(0,if u > uMax then uMax else if u < uMin then uMin else u);
113	end if;
114	end Limiter;
115
116	block VariableLimiter "Limit the range of a signal with variable limits"
117	extends Interfaces.SISO;
118	parameter Boolean limitsAtInit = true
119	"= false, if limits are ignored during initializiation (i.e., y=u)";
120	Interfaces.RealInput limit1
121	"Connector of Real input signal used as maximum of input u"
122	annotation (extent=[-140, 60; -100, 100]);
123	Interfaces.RealInput limit2
124	"Connector of Real input signal used as minimum of input u"
125	annotation (extent=[-140, -100; -100, -
126	60]);
127	protected
128	Real uMax;
129	Real uMin;
130
131	annotation (
132	Documentation(info="<html>
133	<p>
134	The Limiter block passes its input signal as output signal
135	as long as the input is within the upper and lower
136	limits specified by the two additional inputs limit1 and
137	limit2. If this is not the case, the corresponding limit
138	is passed as output.
139	</p>
140	</HTML>
141	"), Icon(
142	Line(points=[0, -90; 0, 68], style(color=8)),
143	Line(points=[-90, 0; 68, 0], style(color=8)),
144	Polygon(points=[90, 0; 68, -8; 68, 8; 90, 0], style(color=8, fillColor=
145	8)),
146	Line(points=[-80, -70; -50, -70; 50, 70; 80, 70], style(color=0)),
147	Text(extent=[-150, 150; 150, 110], string="%name"),
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153	Polygon(points=[0, 90; -8, 68; 8, 68; 0, 90], style(color=8, fillColor=
154	8))),
155	Diagram(
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157	Polygon(points=[0, 60; -5, 50; 5, 50; 0, 60], style(color=8, fillColor=
158	8)),
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160	Polygon(points=[60, 0; 50, -5; 50, 5; 60, 0], style(color=8, fillColor=
161	8)),
162	Line(points=[-50, -40; -30, -40; 30, 40; 50, 40], style(color=0)),
163	Text(
164	extent=[46, -6; 68, -18],
165	string="inPort",
166	style(color=10)),
167	Text(
168	extent=[-30, 70; -5, 50],
169	string="outPort",
170	style(color=10)),
171	Text(
172	extent=[-66, -40; -26, -20],
173	string="uMin",
174	style(color=10)),
175	Text(
176	extent=[30, 20; 70, 40],
177	string="uMax",
178	style(color=10)),
179	Line(points=[-100, 80; 40, 80; 40, 40]),
180	Line(points=[-100, -80; -40, -80; -40, -40]),
181	Polygon(points=[40, 40; 35, 50; 45, 50; 40, 40], style(fillPattern=1)),
182	Polygon(points=[-40, -40; -45, -50; -35, -50; -40, -40], style(
183	fillPattern=1))));
184	equation
185	uMax = max(limit1, limit2);
186	uMin = min(limit1, limit2);
187
188	if initial() and not limitsAtInit then
189	y = u;
190	assert(u >= uMin - 0.01*abs(uMin) and
191	u <= uMax + 0.01*abs(uMax),
192	"VariableLimiter: During initialization the limits have been ignored.\n"+
193	"However, the result is that the input u is not within the required limits:\n"+
194	" u = " + String(u) + ", uMin = " + String(uMin) + ", uMax = " + String(uMax));
195	else
196	y = smooth(0,if u > uMax then uMax else if u < uMin then uMin else u);
197	end if;
198	end VariableLimiter;
199
200	block DeadZone "Provide a region of zero output"
201	parameter Real uMax=1 "Upper limits of dead zones";
202	parameter Real uMin=-uMax "Lower limits of dead zones";
203	parameter Boolean deadZoneAtInit = true
204	"= false, if dead zone is ignored during initializiation (i.e., y=u)";
205	extends Interfaces.SISO;
206
207	annotation (
208	Coordsys(
209	extent=[-100, -100; 100, 100],
210	grid=[1, 1],
211	component=[20, 20]),
212	Window(
213	x=0.39,
214	y=0.18,
215	width=0.56,
216	height=0.6),
217	Documentation(info="
218	<HTML>
219	<p>
220	The DeadZone block defines a region of zero output.
221	</p>
222	<p>
223	If the input is within uMin ... uMax, the output
224	is zero. Outside of this zone, the output is a linear
225	function of the input with a slope of 1.
226	</p>
227	</HTML>
228	"), Icon(
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235	Line(points=[-80, -60; -20, 0; 20, 0; 80, 60], style(color=0)),
236	Text(
237	extent=[-150, -150; 150, -110],
238	string="uMax=%uMax",
239	style(color=9)),
240	Text(extent=[-150, 150; 150, 110], string="%name")),
241	Diagram(
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249	Text(
250	extent=[62, -7; 88, -25],
251	string="u",
252	style(color=10)),
253	Text(
254	extent=[-36, 72; -5, 50],
255	string="y",
256	style(color=10)),
257	Text(
258	extent=[-51, 1; -28, 19],
259	string="uMin",
260	style(color=10)),
261	Text(
262	extent=[27, 21; 52, 5],
263	string="uMax",
264	style(color=10))));
265	equation
266	assert(uMax >= uMin, "DeadZone: Limits must be consistent. However, uMax (=" + String(uMax) +
267	") < uMin (=" + String(uMin) + ")");
268
269	if initial() and not deadZoneAtInit then
270	y = u;
271	else
272	y = smooth(0,if u > uMax then u - uMax else if u < uMin then u - uMin else 0);
273	end if;
274	end DeadZone;
275
276	block FixedDelay "Delay block with fixed DelayTime"
277	extends Modelica.Blocks.Interfaces.SISO;
278	parameter SI.Time delayTime=1
279	"Delay time of output with respect to input signal";
280
281	annotation (
282	Coordsys(
283	extent=[-100, -100; 100, 100],
284	grid=[2, 2],
285	component=[20, 20]),
286	Window(
287	x=0.27,
288	y=0.09,
289	width=0.65,
290	height=0.78),
291	Documentation(info="<html>
292	<p>
293	The Input signal is delayed by a given time instant, or more precisely:
294	</p>
295	<pre>
296	y = u(time - delayTime) for time > time.start + delayTime
297	= u(time.start) for time ≤ time.start + delayTime
298	</pre>
299	</html>
300	"), Icon(
301	Text(
302	extent=[8, -102; 8, -142],
303	string="delayTime=%delayTime",
304	style(color=0)),
305	Line(points=[-92, 0; -80.7, 34.2; -73.5, 53.1; -67.1, 66.4; -61.4, 74.6;
306	-55.8, 79.1; -50.2, 79.8; -44.6, 76.6; -38.9, 69.7; -33.3, 59.4;
307	-26.9, 44.1; -18.83, 21.2; -1.9, -30.8; 5.3, -50.2; 11.7, -64.2;
308	17.3, -73.1; 23, -78.4; 28.6, -80; 34.2, -77.6; 39.9, -71.5;
309	45.5, -61.9; 51.9, -47.2; 60, -24.8; 68, 0], style(color=73)),
310	Line(points=[-62, 0; -50.7, 34.2; -43.5, 53.1; -37.1, 66.4; -31.4, 74.6;
311	-25.8, 79.1; -20.2, 79.8; -14.6, 76.6; -8.9, 69.7; -3.3, 59.4;
312	3.1, 44.1; 11.17, 21.2; 28.1, -30.8; 35.3, -50.2; 41.7, -64.2;
313	47.3, -73.1; 53, -78.4; 58.6, -80; 64.2, -77.6; 69.9, -71.5; 75.5,
314	-61.9; 81.9, -47.2; 90, -24.8; 98, 0], style(color=9))),
315	Diagram(
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317	Line(points=[-80, -80; -88, -80], style(color=8)),
318	Line(points=[-80, -88; -80, 86], style(color=8)),
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328	Line(points=[-80, 0; -68.7, 34.2; -61.5, 53.1; -55.1, 66.4; -49.4, 74.6;
329	-43.8, 79.1; -38.2, 79.8; -32.6, 76.6; -26.9, 69.7; -21.3, 59.4;
330	-14.9, 44.1; -6.83, 21.2; 10.1, -30.8; 17.3, -50.2; 23.7, -64.2;
331	29.3, -73.1; 35, -78.4; 40.6, -80; 46.2, -77.6; 51.9, -71.5;
332	57.5, -61.9; 63.9, -47.2; 72, -24.8; 80, 0], style(color=73)),
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338	-27.8, 79.1; -22.2, 79.8; -16.6, 76.6; -10.9, 69.7; -5.3, 59.4;
339	1.1, 44.1; 9.17, 21.2; 26.1, -30.8; 33.3, -50.2; 39.7, -64.2;
340	45.3, -73.1; 51, -78.4; 56.6, -80; 62.2, -77.6; 67.9, -71.5; 73.5,
341	-61.9; 79.9, -47.2; 88, -24.8; 96, 0], style(color=0)),
342	Text(
343	extent=[67, 22; 96, 6],
344	string="time",
345	style(color=9)),
346	Line(points=[-64, -30; -64, 0], style(color=8)),
347	Text(extent=[-58, -42; -58, -32], string="delayTime"),
348	Line(points=[-94, -26; -80, -26], style(color=8)),
349	Line(points=[-64, -26; -50, -26], style(color=8)),
350	Polygon(points=[-80, -26; -88, -24; -88, -28; -80, -26], style(color=8,
351	fillColor=8)),
352	Polygon(points=[-56, -24; -64, -26; -56, -28; -56, -24], style(color=8,
353	fillColor=8))));
354	equation
355	y = delay(u, delayTime);
356	end FixedDelay;
357
358	block PadeDelay "Pade approximation of delay block with fixed DelayTime "
359	extends Modelica.Blocks.Interfaces.SISO;
360	parameter SI.Time delayTime=1
361	"Delay time of output with respect to input signal";
362	parameter Integer n(min=1) = 1 "Order of pade approximation";
363	parameter Integer m(
364	min=1,
365	max=n) = n "Order of numerator";
366
367	protected
368	Real x1dot "Derivative of first state of TransferFcn";
369	Real xn "Highest order state of TransferFcn";
370	Real a[n + 1];
371	Real b[m + 1];
372
373	public
374	final output Real x[n]
375	"State of transfer function from controller canonical form";
376	annotation (
377	Coordsys(
378	extent=[-100, -100; 100, 100],
379	grid=[2, 2],
380	component=[20, 20]),
381	Window(
382	x=0.27,
383	y=0.09,
384	width=0.65,
385	height=0.78),
386	Documentation(info="<html>
387	<p>
388	The Input signal is delayed by a given time instant, or more precisely:
389	</p>
390	<pre>
391	y = u(time - delayTime) for time > time.start + delayTime
392	= u(time.start) for time ≤ time.start + delayTime
393	</pre>
394	<p>
395	The delay is approximated by a Pade approximation, i.e., by
396	a transfer function
397	</p>
398	<pre>
399	b[1]s^m + b[2]s^[m-1] + ... + b[m+1]
400	y(s) = --------------------------------------------- * u(s)
401	a[1]s^n + a[2]s^[n-1] + ... + a[n+1]
402	</pre>
403	<p>
404	where the coefficients b[:] and a[:] are calculated such that the
405	coefficients of the Taylor expansion of the delay exp(-T*s) around s=0
406	are identical upto order n+m.
407	</p>
408	<p>
409	The main advantage of this approach is that the delay is
410	approximated by a linear differential equation system, which
411	is continuous and continuously differentiable. For example, it
412	is uncritical to linearize a system containing a Pade-approximated
413	delay.
414	</p>
415	<p>
416	The standard text book version uses order \"m=n\", which is
417	also the default setting of this block. The setting
418	\"m=n-1\" may yield a better approximation in certain cases.
419	<p>
420	<p>
421	Literature:<br>
422	Otto Foellinger: Regelungstechnik, 8. Auflage,
423	chapter 11.9, page 412-414, Huethig Verlag Heidelberg, 1994
424	</p>
425	</html>
426	"), Icon(
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428	extent=[8, -102; 8, -142],
429	string="delayTime=%delayTime",
430	style(color=0)),
431	Line(points=[-94, 0; -82.7, 34.2; -75.5, 53.1; -69.1, 66.4; -63.4, 74.6;
432	-57.8, 79.1; -52.2, 79.8; -46.6, 76.6; -40.9, 69.7; -35.3, 59.4;
433	-28.9, 44.1; -20.83, 21.2; -3.9, -30.8; 3.3, -50.2; 9.7, -64.2;
434	15.3, -73.1; 21, -78.4; 26.6, -80; 32.2, -77.6; 37.9, -71.5;
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437	-35.8, 79.1; -30.2, 79.8; -24.6, 76.6; -18.9, 69.7; -13.3, 59.4;
438	-6.9, 44.1; 1.17, 21.2; 18.1, -30.8; 25.3, -50.2; 31.7, -64.2;
439	37.3, -73.1; 43, -78.4; 48.6, -80; 54.2, -77.6; 59.9, -71.5; 65.5,
440	-61.9; 71.9, -47.2; 80, -24.8; 88, 0], style(color=9)),
441	Text(
442	extent=[-10, 100; 100, 38],
443	string="m=%m",
444	style(color=9)),
445	Text(
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447	string="n=%n",
448	style(color=9))),
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