source: mso/eml/controllers/PIDIncr.mso @ 1

Last change on this file since 1 was 1, checked in by Rafael de Pelegrini Soares, 16 years ago

Initial import of the library

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1#*-------------------------------------------------------------------
2* Model of incremental PIDs
3*--------------------------------------------------------------------
4*  - Inputs
5*       - a scaled processs variable
6*       - a scaled bias
7*       - a scaled setpoint
8*
9*  - Outputs
10*   - a scaled output
11*
12*  - Assumptions
13*
14*
15*--------------------------------------------------------------------
16* Author: Tiago Osório
17* $Id: PIDIncr.mso 1 2006-06-20 17:33:53Z rafael $
18*-------------------------------------------------------------------*#
19using "types";
20
21Model MParameters
22
23        VARIABLES
24       
25        alpha      as positive (Brief="Derivative term filter constant", Default=1);
26        beta       as positive (Brief="Proportional term setPoint change filter");
27        bias       as control_signal (Brief="Previous scaled bias", Default=0.5);
28        derivTime  as time_sec (Brief="Derivative time constant");
29        intTime    as time_sec (Brief="Integral time constant");
30        gain       as positive (Brief="Controller gain", Default=0.5);
31        gamma      as positive (Brief="Derivative term SP change filter");
32        tau        as time_sec (Brief="Input filter time constant");
33        tauSet     as time_sec (Brief="Input filter time constant");
34       
35end
36
37Model MOptions 
38
39        VARIABLES       
40       
41        action     as Real     (Brief="Controller action: (-1) Direct,(1) Reverse", Default=-1);
42    autoMan    as Real     (Brief="Controller option: (0) Automatic, (1) Manual", Default=0);   
43        clip       as Real     (Brief="Controller option: (1) output clipped, (0) output unclipped", Default=1);
44
45end
46
47Model MPorts
48
49        VARIABLES
50       
51        input      as control_signal (Brief="Previous scaled input signal", Default=0.5);
52        output    as control_signal (Brief="Scaled output signal", Default=0.5);
53        setPoint   as control_signal (Brief="Scaled setPoint",Default=0.5);
54
55end
56
57Model MInternal_Variables
58       
59        VARIABLES
60
61        dderivTerm    as control_signal (Brief="Derivative term",Unit="1/s", Default=0);
62        dFilt         as control_signal (Brief="Derivative term filtered", Default=0.5,Unit="1/s");
63        error         as control_signal (Brief="Error definition for proportional term",Unit="1/s");
64        errorD        as control_signal (Brief="Error definition for derivative term",Unit="1/s");
65        errorI        as control_signal (Brief="Error definition for integral term");
66        inputFilt     as control_signal (Brief="Filtered input");
67        dintTerm      as control_signal (Brief="Integral term", Default=0,Unit="1/s");
68        doutp         as control_signal (Brief="Sum of proportional, integral and derivative terms",Unit="1/s");
69        outps         as control_signal (Brief="Variable outp scaled between -1 and 1");
70        outp          as control_signal (Brief="Variable outp");
71        dpropTerm     as control_signal (Brief="Proportional term", Default=0,Unit="1/s");
72        setPointFilt  as control_signal (Brief="Filtered setPoint", Default=0);
73
74end
75
76Model PIDIncr_basic
77
78        VARIABLES
79        Parameters         as MParameters;
80        Options            as MOptions;
81        Internal           as MInternal_Variables;
82        Ports              as MPorts;
83       
84        EQUATIONS
85
86        if (Parameters.tau equal 0) then
87                "Input first order filter"
88                (Parameters.tau + 1e-3*"s")*diff(Internal.inputFilt)= Ports.input - Internal.inputFilt;
89        else
90                "Input first order filter"
91                Parameters.tau*diff(Internal.inputFilt)= Ports.input - Internal.inputFilt;     
92        end
93
94        if (Parameters.tauSet equal 0) then
95                "setPoint first order filter"
96                (Parameters.tauSet + 1e-3*"s")*diff(Internal.setPointFilt)= Ports.setPoint - Internal.setPointFilt;
97        else
98                "setPoint first order filter"
99                Parameters.tauSet*diff(Internal.setPointFilt)= Ports.setPoint - Internal.setPointFilt;
100        end
101
102        if Options.autoMan equal 1 then
103                "Error definition for proportional term"
104                Internal.error*"s" = Internal.inputFilt*(Parameters.beta-1.0);
105                "Error definition for derivative term"
106                Internal.errorD*"s"= Internal.inputFilt*(Parameters.gamma-1.0);
107                "Error definition for integral term"           
108                Internal.errorI= 0;
109        else
110                "Error definition for proportional term"                       
111                Internal.error = Parameters.beta*diff(Internal.setPointFilt) - diff(Internal.inputFilt);
112                "Error definition for derivative term"
113                Internal.errorD = Parameters.gamma*diff(Internal.setPointFilt) - diff(Internal.inputFilt);
114                "Error definition for integral term"
115                Internal.errorI = Internal.setPointFilt-Internal.inputFilt;     
116        end
117       
118        "Calculate proportional term"
119        Internal.dpropTerm=Internal.error; 
120       
121        if (Parameters.derivTime equal 0) then
122                "Derivative term filter"       
123                Parameters.alpha*(Parameters.derivTime + 1e-3*"s")*diff(Internal.dFilt) = Internal.errorD - Internal.dFilt;
124        else
125                "Derivative term filter"       
126                Parameters.alpha*(Parameters.derivTime)*diff(Internal.dFilt) = Internal.errorD - Internal.dFilt;
127        end
128
129        "Calculate derivative term"
130        Internal.dderivTerm = Parameters.derivTime*diff(Internal.dFilt);
131       
132    "Unscaled output"
133        diff(Internal.outp)=Internal.doutp;
134
135        "Scale outp"
136        Internal.outps=2*Internal.outp-1;
137
138        if Options.clip equal 1 then
139                if abs(Internal.outps)>1 then
140                        "Calculate clipped output when it´s saturated"
141                        Ports.output=(sign(Internal.outps)*1+1)/2;
142                else
143                        "Calculate clipped output when it´s not saturated"
144                        Ports.output=Internal.outp;
145                end
146        else
147                "Calculate unclipped output"
148                Ports.output=Internal.outp;
149        end
150
151        INITIAL
152        Ports.output = Parameters.bias;
153        diff(Internal.dFilt) = 0*"1/s^2";
154        diff(Internal.inputFilt)=0*"1/s";
155        diff(Internal.setPointFilt)=0*"1/s";
156end
157
158Model PIDIncr_Ideal as PIDIncr_basic
159       
160        EQUATIONS
161       
162        "Calculate integral term"
163        Parameters.intTime*Internal.dintTerm = Internal.errorI;
164       
165        "Sum of proportional, integral and derivative terms"
166        Internal.doutp = Options.action*Parameters.gain*(Internal.dpropTerm + Internal.dintTerm + Internal.dderivTerm);
167
168end
169
170Model PIDIncr_Parallel as PIDIncr_basic
171       
172        EQUATIONS
173       
174        "Calculate integral term"
175        Parameters.intTime*Internal.dintTerm = Internal.errorI;
176       
177        "Sum of proportional, integral and derivative terms"
178        Internal.doutp = Options.action*(Parameters.gain*Internal.dpropTerm + Internal.dintTerm + Internal.dderivTerm);
179
180end
181
182Model PIDIncr_Series as PIDIncr_basic
183       
184        EQUATIONS
185
186        "Calculate integral term"
187        Parameters.intTime*Internal.dintTerm = Internal.errorI;
188       
189        "Sum of proportional, integral and derivative terms"
190        Internal.doutp = Options.action*(Parameters.gain*(Internal.dpropTerm + Internal.dintTerm)*(1*"1/s" + Internal.dderivTerm)*"s");
191       
192end
193
194Model PIDIncr_Ideal_AWBT as PIDIncr_basic
195       
196        EQUATIONS
197       
198        "Calculate integral term with anti-windup and bumpless transfer"
199        Options.action*Parameters.gain*(Parameters.intTime*Internal.dintTerm-Internal.errorI) = Ports.output-Internal.outp;
200
201        "Sum of proportional, integral and derivative terms"
202        Internal.doutp = Options.action*Parameters.gain*(Internal.dpropTerm + Internal.dintTerm + Internal.dderivTerm);
203
204end
205
206Model PIDIncr_Parallel_AWBT as PIDIncr_basic
207       
208        EQUATIONS
209       
210        "Calculate integral term with anti-windup and bumpless transfer"
211        Options.action*Parameters.gain*(Parameters.intTime*Internal.dintTerm-Internal.errorI) = Ports.output-Internal.outp;
212       
213        "Sum of proportional, integral and derivative terms"
214        Internal.doutp = Options.action*(Parameters.gain*Internal.dpropTerm + Internal.dintTerm + Internal.dderivTerm);
215
216end
217
218Model PIDIncr_Series_AWBT as PIDIncr_basic
219       
220        EQUATIONS
221       
222        "Calculate integral term with anti-windup and bumpless transfer"
223        Options.action*Parameters.gain*(Parameters.intTime*Internal.dintTerm-Internal.errorI) = Ports.output-Internal.outp;
224
225        "Sum of proportional, integral and derivative terms"
226        Internal.doutp = Options.action*(Parameters.gain*(Internal.dpropTerm + Internal.dintTerm)*(1*"1/s" + Internal.dderivTerm)*"s");
227
228end
229
230Model PIDIncr_Ideal_AW as PIDIncr_basic
231       
232        VARIABLES
233        AWFactor     as Real     (Brief="Integral term multiplier used in anti-reset windup");
234
235        EQUATIONS
236
237        "Calculate integral term with anti-windup"
238        Parameters.intTime*Internal.dintTerm = AWFactor*Internal.errorI;
239       
240        "Sum of proportional, integral and derivative terms"
241        Internal.doutp = Options.action*Parameters.gain*(Internal.dpropTerm + Internal.dintTerm + Internal.dderivTerm);
242       
243
244        if abs(Internal.outps)>1 and (Options.action*sign(Internal.outps)*Internal.errorI)>0 then
245                "Calculate AWFactor"
246                AWFactor=-tanh(sign(Internal.outps)*Internal.outps*100-102);
247        else
248                "Calculate AWFactor"
249                AWFactor=1;
250        end
251
252end
253
254Model PIDIncr_Parallel_AW as PIDIncr_basic
255       
256        VARIABLES
257        AWFactor     as Real     (Brief="Integral term multiplier used in anti-reset windup");
258
259        EQUATIONS
260
261        "Calculate integral term with anti-windup"
262        Parameters.intTime*Internal.dintTerm = AWFactor*Internal.errorI;
263       
264        "Sum of proportional, integral and derivative terms"
265        Internal.doutp = Options.action*(Parameters.gain*Internal.dpropTerm + Internal.dintTerm + Internal.dderivTerm);
266       
267        if abs(Internal.outps)>1 and (Options.action*sign(Internal.outps)*Internal.errorI)>0 then
268                "Calculate AWFactor"
269                AWFactor=-tanh(sign(Internal.outps)*Internal.outps*100-102);
270        else
271                "Calculate AWFactor"
272                AWFactor=1;
273        end
274
275end
276
277Model PIDIncr_Series_AW as PIDIncr_basic
278       
279        VARIABLES
280        AWFactor     as Real     (Brief="Integral term multiplier used in anti-reset windup");
281
282        EQUATIONS
283
284        "Calculate integral term with anti-windup"
285        Parameters.intTime*Internal.dintTerm = AWFactor*Internal.errorI;
286       
287        "Sum of proportional, integral and derivative terms"
288        Internal.doutp = Options.action*(Parameters.gain*(Internal.dpropTerm + Internal.dintTerm)*(1*"1/s" + Internal.dderivTerm)*"s");
289       
290        if abs(Internal.outps)>1 and (Options.action*sign(Internal.outps)*Internal.errorI)>0 then
291                "Calculate AWFactor"
292                AWFactor=-tanh(sign(Internal.outps)*Internal.outps*100-102);
293        else
294                "Calculate AWFactor"
295                AWFactor=1;
296        end
297
298end
299
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