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[project @ 2004-09-22 02:50:35 by jwe]
author jwe
date Wed, 22 Sep 2004 02:50:36 +0000
parents b8105302cfe8
children 4c8a2e4e0717
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5015:6d481b6e349e 5016:bdbee5282954
18 18
19 ## -*- texinfo -*- 19 ## -*- texinfo -*-
20 ## @deftypefn {Function File} {} buildssic (@var{clst}, @var{ulst}, @var{olst}, @var{ilst}, @var{s1}, @var{s2}, @var{s3}, @var{s4}, @var{s5}, @var{s6}, @var{s7}, @var{s8}) 20 ## @deftypefn {Function File} {} buildssic (@var{clst}, @var{ulst}, @var{olst}, @var{ilst}, @var{s1}, @var{s2}, @var{s3}, @var{s4}, @var{s5}, @var{s6}, @var{s7}, @var{s8})
21 ## 21 ##
22 ## Form an arbitrary complex (open or closed loop) system in 22 ## Form an arbitrary complex (open or closed loop) system in
23 ## state-space form from several systems. "@code{buildssic}" can 23 ## state-space form from several systems. @command{buildssic} can
24 ## easily (despite it's cryptic syntax) integrate transfer functions 24 ## easily (despite its cryptic syntax) integrate transfer functions
25 ## from a complex block diagram into a single system with one call. 25 ## from a complex block diagram into a single system with one call.
26 ## This function is especially useful for building open loop 26 ## This function is especially useful for building open loop
27 ## interconnections for H_infinity and H2 designs or for closing 27 ## interconnections for
28 ## loops with these controllers. 28 ## @iftex
29 ## 29 ## @tex
30 ## Although this function is general purpose, the use of "@code{sysgroup}" 30 ## $ { \cal H }_\infty $ and $ { \cal H }_2 $
31 ## "@code{sysmult}", "@code{sysconnect}" and the like is recommended for 31 ## @end tex
32 ## @end iftex
33 ## @ifinfo
34 ## H-infinity and H-2
35 ## @end ifinfo
36 ## designs or for closing loops with these controllers.
37 ##
38 ## Although this function is general purpose, the use of @command{sysgroup}
39 ## @command{sysmult}, @command{sysconnect} and the like is recommended for
32 ## standard operations since they can handle mixed discrete and continuous 40 ## standard operations since they can handle mixed discrete and continuous
33 ## systems and also the names of inputs, outputs, and states. 41 ## systems and also the names of inputs, outputs, and states.
34 ## 42 ##
35 ## The parameters consist of 4 lists that describe the connections 43 ## The parameters consist of 4 lists that describe the connections
36 ## outputs and inputs and up to 8 systems s1-s8. 44 ## outputs and inputs and up to 8 systems @var{s1}--@var{s8}.
37 ## Format of the lists: 45 ## Format of the lists:
38 ## @table @var 46 ## @table @var
39 ## @item clst 47 ## @item clst
40 ## connection list, describes the input signal of 48 ## connection list, describes the input signal of
41 ## each system. The maximum number of rows of Clst is 49 ## each system. The maximum number of rows of Clst is
42 ## equal to the sum of all inputs of s1-s8. 50 ## equal to the sum of all inputs of s1-s8.
43 ## 51 ##
44 ## Example: 52 ## Example:
45 ## @code{[1 2 -1; 2 1 0]} ==> new input 1 is old inpout 1 53 ## @code{[1 2 -1; 2 1 0]} means that: new input 1 is old input 1
46 ## + output 2 - output 1, new input 2 is old input 2 54 ## + output 2 - output 1, and new input 2 is old input 2
47 ## + output 1. The order of rows is arbitrary. 55 ## + output 1. The order of rows is arbitrary.
48 ## 56 ##
49 ## @item ulst 57 ## @item ulst
50 ## if not empty the old inputs in vector Ulst will 58 ## if not empty the old inputs in vector @var{ulst} will
51 ## be appended to the outputs. You need this if you 59 ## be appended to the outputs. You need this if you
52 ## want to "pull out" the input of a system. Elements 60 ## want to ``pull out'' the input of a system. Elements
53 ## are input numbers of s1-s8. 61 ## are input numbers of @var{s1}--@var{s8}.
54 ## 62 ##
55 ## @item olst 63 ## @item olst
56 ## output list, specifiy the outputs of the resulting 64 ## output list, specifiy the outputs of the resulting
57 ## systems. Elements are output numbers of s1-s8. 65 ## systems. Elements are output numbers of @var{s1}--@var{s8}.
58 ## The numbers are alowed to be negative and may 66 ## The numbers are allowed to be negative and may
59 ## appear in any order. An empty matrix means 67 ## appear in any order. An empty matrix means
60 ## all outputs. 68 ## all outputs.
61 ## 69 ##
62 ## @item ilst 70 ## @item ilst
63 ## input list, specifiy the inputs of the resulting 71 ## input list, specifiy the inputs of the resulting
64 ## systems. Elements are input numbers of s1-s8. 72 ## systems. Elements are input numbers of @var{s1}--@var{s8}.
65 ## The numbers are alowed to be negative and may 73 ## The numbers are allowed to be negative and may
66 ## appear in any order. An empty matrix means 74 ## appear in any order. An empty matrix means
67 ## all inputs. 75 ## all inputs.
68 ## @end table 76 ## @end table
69 ## 77 ##
70 ## Example: Very simple closed loop system. 78 ## Example: Very simple closed loop system.
80 ## | | 88 ## | |
81 ## +----------------------------+ 89 ## +----------------------------+
82 ## @end group 90 ## @end group
83 ## @end example 91 ## @end example
84 ## 92 ##
85 ## The closed loop system GW can be optained by 93 ## The closed loop system @var{GW} can be optained by
86 ## @example 94 ## @example
87 ## GW = buildssic([1 2; 2 -1], 2, [1 2 3], 2, G, K); 95 ## GW = buildssic([1 2; 2 -1], 2, [1 2 3], 2, G, K);
88 ## @end example 96 ## @end example
89 ## @table @var 97 ## @table @var
90 ## @item clst 98 ## @item clst
91 ## (1. row) connect input 1 (G) with output 2 (K). 99 ## 1st row: connect input 1 (@var{G}) with output 2 (@var{K}).
92 ## (2. row) connect input 2 (K) with neg. output 1 (G). 100 ##
101 ## 2nd row: connect input 2 (@var{K}) with negative output 1 (@var{G}).
93 ## @item ulst 102 ## @item ulst
94 ## append input of (2) K to the number of outputs. 103 ## Append input of 2 (@var{K}) to the number of outputs.
95 ## @item olst 104 ## @item olst
96 ## Outputs are output of 1 (G), 2 (K) and appended output 3 (from Ulst). 105 ## Outputs are output of 1 (@var{G}), 2 (@var{K}) and
106 ## appended output 3 (from @var{ulst}).
97 ## @item ilst 107 ## @item ilst
98 ## the only input is 2 (K). 108 ## The only input is 2 (@var{K}).
99 ## @end table 109 ## @end table
100 ## 110 ##
101 ## Here is a real example: 111 ## Here is a real example:
102 ## @example 112 ## @example
103 ## @group 113 ## @group
104 ## +----+ 114 ## +----+
105 ## -------------------->| W1 |---> v1 115 ## -------------------->| W1 |---> v1
106 ## z | +----+ 116 ## z | +----+
107 ## ----|-------------+ || GW || => min. 117 ## ----|-------------+
108 ## | | vz infty 118 ## | |
109 ## | +---+ v +----+ 119 ## | +---+ v +----+
110 ## *--->| G |--->O--*-->| W2 |---> v2 120 ## *--->| G |--->O--*-->| W2 |---> v2
111 ## | +---+ | +----+ 121 ## | +---+ | +----+
112 ## | | 122 ## | |
113 ## | v 123 ## | v
114 ## u y 124 ## u y
115 ## @end group 125 ## @end group
116 ## @end example 126 ## @end example
117 ## 127 ## @iftex
118 ## The closed loop system GW from [z; u]' to [v1; v2; y]' can be 128 ## @tex
119 ## obtained by (all SISO systems): 129 ## $$ { \rm min } \Vert GW_{vz} \Vert _\infty $$
130 ## @end tex
131 ## @end iftex
132 ## @ifinfo
133 ## @example
134 ## min || GW ||
135 ## vz infty
136 ## @end example
137 ## @end ifinfo
138 ##
139 ## The closed loop system @var{GW}
140 ## @iftex
141 ## @tex
142 ## from $ [z, u]^T $ to $ [v_1, v_2, y]^T $
143 ## @end tex
144 ## @end iftex
145 ## @ifinfo
146 ## from [z, u]' to [v1, v2, y]'
147 ## @end ifinfo
148 ## can be obtained by (all @acronym{SISO} systems):
120 ## @example 149 ## @example
121 ## GW = buildssic([1, 4; 2, 4; 3, 1], 3, [2, 3, 5], 150 ## GW = buildssic([1, 4; 2, 4; 3, 1], 3, [2, 3, 5],
122 ## [3, 4], G, W1, W2, One); 151 ## [3, 4], G, W1, W2, One);
123 ## @end example 152 ## @end example
124 ## where "One" is a unity gain (auxillary) function with order 0. 153 ## where ``One'' is a unity gain (auxillary) function with order 0.
125 ## (e.g. @code{One = ugain(1);}) 154 ## (e.g. @code{One = ugain(1);})
126 ## @end deftypefn 155 ## @end deftypefn
127 156
128 ## Author: Kai P. Mueller <mueller@ifr.ing.tu-bs.de> 157 ## Author: Kai P. Mueller <mueller@ifr.ing.tu-bs.de>
129 ## Created: April 1998 158 ## Created: April 1998