Overview
Comment:Revised to work with LQ on alnalogue circuit example with integration
Downloads: Tarball | ZIP archive | SQL archive
Timelines: family | ancestors | descendants | both | origin/master | trunk
Files: files | file ages | folders
SHA3-256: 19c0c38ddef0f75491646728bf880b82b6333b32d46b7f7e3ca37d723954b08d
User & Date: gawthrop@users.sourceforge.net on 2003-10-21 09:30:24
Other Links: branch diff | manifest | tags
Context
2003-10-21
09:55:02
Make time horizon tau part of p_c struct check-in: fb3311a46f user: gawthrop@users.sourceforge.net tags: origin/master, trunk
09:30:24
Revised to work with LQ on alnalogue circuit example with integration check-in: 19c0c38dde user: gawthrop@users.sourceforge.net tags: origin/master, trunk
2003-10-20
17:10:31
Link ancestry of version-0-1 to it's source branch check-in: c318408021 user: gawthrop@users.sourceforge.net tags: origin/master, trunk
Changes
Hide Diffs Unified Diffs Ignore Whitespace Patch

Modified mttroot/mtt/lib/control/PPP/ppp_lin_quad.m from [2ba9cc3698] to [b791777adb]. 

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23

function [k_x,k_w,K_x,K_w,Us0,J_uu,J_ux,J_uw,J_xx,J_xw,J_ww,A_u] = \
      ppp_lin_quad (A,B,C,D,tau,Q,R,augment)

  ## usage:[k_x,k_w,K_x,K_w,Us0,J_uu,J_ux,J_uw,J_xx,J_xw,J_ww,A_u] =
  ## ppp_lin_quad (A,B,C,D,tau,Q,R)
  ##
  ## 

  ## Steady-state Linear Quadratic solution
  ## using Algebraic Riccati equation (ARE)
  [P,A_u,A_w] = ppp_are (A,B,C,D,Q,R);

  ## Augment with a constant term
  if augment
    A_u = ppp_aug(0,A_u);
  endif
  
  ## PPP solution
  [k_x,k_w,K_x,K_w,Us0,J_uu,J_ux,J_uw,J_xx,J_xw,J_ww] = \
      ppp_lin(A,B,C,D,A_u,A_w,tau,Q,R,P);


endfunction


|










<
<
<
<
<







1
2
3
4
5
6
7
8
9
10
11
12





13
14
15
16
17
18

function [k_x,k_w,K_x,K_w,Us0,J_uu,J_ux,J_uw,J_xx,J_xw,J_ww,A_u] = \
      ppp_lin_quad (A,B,C,D,tau,Q,R)

  ## usage:[k_x,k_w,K_x,K_w,Us0,J_uu,J_ux,J_uw,J_xx,J_xw,J_ww,A_u] =
  ## ppp_lin_quad (A,B,C,D,tau,Q,R)
  ##
  ## 

  ## Steady-state Linear Quadratic solution
  ## using Algebraic Riccati equation (ARE)
  [P,A_u,A_w] = ppp_are (A,B,C,D,Q,R);






  ## PPP solution
  [k_x,k_w,K_x,K_w,Us0,J_uu,J_ux,J_uw,J_xx,J_xw,J_ww] = \
      ppp_lin(A,B,C,D,A_u,A_w,tau,Q,R,P);


endfunction

Modified mttroot/mtt/lib/control/PPP/ppp_lin_run.m from [96369350d9] to [fdb48937ab].

︙︙
52
53
54
55
56
57
58
59
60
61
62
63
64
65

















66
67
68
69
70
71
72
73
74
75
76
77
78
79
80

  endif

  if !struct_contains(p_c,"delta_ol")
    p_c.delta_ol = 0.5;	# OL sample interval
  endif
  
  if !struct_contains(p_c,"T")
    p_c.T = 2.5;			# Last time point.
  endif

  if !struct_contains(p_c,"augment")
    p_c.augment = 1;		# Augment basis funs with contand
  endif
  

















  if !struct_contains(p_c,"Method")
    p_c.Method = "original";
  endif

  if struct_contains(p_c,"Method")
    if strcmp(p_c.Method,"lq") 
      p_c.Q = eye(n_y);
      p_c.R = (0.25^2)*eye(n_u);
      p_c.n_U = n_x;
    elseif strcmp(p_c.Method,"original");
      if !struct_contains(p_c,"A_w")
	p_c.A_w = 0;
      endif
      if !struct_contains(p_c,"A_u")
	p_c.n_U = n_x;








|



|


>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>

|



|

|








52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97

  endif

  if !struct_contains(p_c,"delta_ol")
    p_c.delta_ol = 0.5;	# OL sample interval
  endif
  
  if !struct_contains(p_c,"T")
    p_c.T = 10;			# Last time point.
  endif

  if !struct_contains(p_c,"augment")
    p_c.augment = 0;		# Augment basis funs with constant
  endif
  
  if !struct_contains(p_c,"integrate")
    p_c.integrate = 0;		# Augment basis funs with constant
  endif
  
  if !struct_contains(p_c,"Tau_u")
    p_c.Tau_u = [];
    p_c.Min_u = [];
    p_c.Max_u = [];
  endif

  if !struct_contains(p_c,"Tau_y")
    p_c.Tau_y = [];
    p_c.Min_y = [];
    p_c.Max_y = [];
  endif


  if !struct_contains(p_c,"Method")
    p_c.Method = "lq";
  endif

  if struct_contains(p_c,"Method")
    if strcmp(p_c.Method,"lq")
      p_c.Q = eye(n_y);
      p_c.R = (0.1^2)*eye(n_u);
      p_c.n_U = n_x;
    elseif strcmp(p_c.Method,"original");
      if !struct_contains(p_c,"A_w")
	p_c.A_w = 0;
      endif
      if !struct_contains(p_c,"A_u")
	p_c.n_U = n_x;
︙︙
115
116
117
118
119
120
121
122
123
124
125
126

127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147




148
149
150
151
152
153
154

  if ControlType==0		# Step input
    I = 1;			# 1 large sample
    p_c.delta_ol = p_c.T	# I
    K_w = zeros(p_c.n_U,n_y);
    K_w(1,1) = 1;
    K_w(2,1) = -1;
    K_x = zeros(p_c.n_U,n_x);
    U = K_w*w;			# Initial control U
  else
    I = ceil(p_c.T/p_c.delta_ol) # Number of large samples
    if strcmp(p_c.Method, "original")
      tau = [10:0.1:11]*(2/a_u);	# Time horizons

      [k_x,k_w,K_x,K_w] = ppp_lin(A,B,C,D,p_c.A_u,p_c.A_w,tau); # Design
    elseif strcmp(p_c.Method, "lq") # LQ design
      tau = [0:0.1:2.0]*1; # Time horizons
      [k_x,k_w,K_x,K_w,Us0,J_uu,J_ux,J_uw,J_xx,J_xw,J_ww,A_u] \
	  = ppp_lin_quad (A,B,C,D,tau,p_c.Q,p_c.R,p_c.augment);
      p_c.A_u = A_u;
    else
      error(sprintf("Control method %s not recognised", p_c.Method));
    endif

    ##Sanity check A_u
    [p_c.n_U,M_u] = size(p_c.A_u);
    if (p_c.n_U!=M_u)
      error("A_u must be square");
    endif
    U = K_w*w;			# Initial control U

    ## Checks
    [ol_zeros, ol_poles] = sys2zp(sys)
    cl_poles = eig(A - B*k_x)
  endif





  ## Short sample interval
  dt = p_c.delta_ol/p_c.N;

  ## Observer design
  G = eye(n_x);		# State noise gain 
  sigma_x = eye(n_x);		# State noise variance








<




>
|

|

|










<





>
>
>
>








132
133
134
135
136
137
138

139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158

159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174

  if ControlType==0		# Step input
    I = 1;			# 1 large sample
    p_c.delta_ol = p_c.T	# I
    K_w = zeros(p_c.n_U,n_y);
    K_w(1,1) = 1;
    K_w(2,1) = -1;
    K_x = zeros(p_c.n_U,n_x);

  else
    I = ceil(p_c.T/p_c.delta_ol) # Number of large samples
    if strcmp(p_c.Method, "original")
      tau = [10:0.1:11]*(2/a_u);	# Time horizons
      [k_x,k_w,K_x,K_w,Us0,J_uu,J_ux,J_uw,J_xx,J_xw,J_ww] =\
	  ppp_lin(A,B,C,D,p_c.A_u,p_c.A_w,tau); # Design
    elseif strcmp(p_c.Method, "lq") # LQ design
      tau = [0:0.1:2]; # Time horizons
      [k_x,k_w,K_x,K_w,Us0,J_uu,J_ux,J_uw,J_xx,J_xw,J_ww,A_u] \
	  = ppp_lin_quad (A,B,C,D,tau,p_c.Q,p_c.R);
      p_c.A_u = A_u;
    else
      error(sprintf("Control method %s not recognised", p_c.Method));
    endif

    ##Sanity check A_u
    [p_c.n_U,M_u] = size(p_c.A_u);
    if (p_c.n_U!=M_u)
      error("A_u must be square");
    endif


    ## Checks
    [ol_zeros, ol_poles] = sys2zp(sys)
    cl_poles = eig(A - B*k_x)
  endif

  ## Initial control U
  U = zeros(p_c.n_U,1);	


  ## Short sample interval
  dt = p_c.delta_ol/p_c.N;

  ## Observer design
  G = eye(n_x);		# State noise gain 
  sigma_x = eye(n_x);		# State noise variance
︙︙
176
177
178
179
180
181
182
183
184
185







186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207

  endif
  
  ## Display the poles
  obs_poles

  ## Write the include file for the real-time function
  ## Use double length to allow for overuns
  disp("Writing Ustar.h");
  overrun = 2;
  ppp_ustar2h(ppp_ustar (p_c.A_u, n_u, [0:dt:overrun*p_c.delta_ol], 0,0)); 









  ## Control loop
  y = [];
  u = [];
  t = [];
  y_e = [];
  t_e = [];
  e_e = [];
  tick = time;
  i=0;
  for j=1:10
    for k=1:I
      tim=time;			# Timing
      i++
      if Simulate		# Exact simulation 
	t_sim = [1:p_c.N]*dt;	# Simulation time points
	[yi,ui,xsi] = ppp_ystar(A,B,C,D,x,p_c.A_u,U,t_sim); # Simulate
	x = xsi(:,p_c.N);	# Current state (for next time)
	ti  = [(i-1)*p_c.N:i*p_c.N-1]*dt; 
	y_i = yi(1);	# Current output
	t_i = ti(1);








<

|
>
>
>
>
>
>
>











|


|








196
197
198
199
200
201
202

203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233

  endif
  
  ## Display the poles
  obs_poles

  ## Write the include file for the real-time function
  ## Use double length to allow for overuns

  overrun = 2;
  Ustar = ppp_ustar (p_c.A_u, n_u, [0:dt:overrun*p_c.delta_ol], 0,0);
  if p_c.integrate		# Integrate Ustar
    disp("Integrating Ustar");
    Ustar = cumsum(Ustar)*dt;
  endif
  
  disp("Writing Ustar.h");
  ppp_ustar2h(Ustar); 


  ## Control loop
  y = [];
  u = [];
  t = [];
  y_e = [];
  t_e = [];
  e_e = [];
  tick = time;
  i=0;
  for j=1:4
    for k=1:I
      tim=time;			# Timing
      i++;
      if Simulate		# Exact simulation 
	t_sim = [1:p_c.N]*dt;	# Simulation time points
	[yi,ui,xsi] = ppp_ystar(A,B,C,D,x,p_c.A_u,U,t_sim); # Simulate
	x = xsi(:,p_c.N);	# Current state (for next time)
	ti  = [(i-1)*p_c.N:i*p_c.N-1]*dt; 
	y_i = yi(1);	# Current output
	t_i = ti(1);
︙︙
221
222
223
224
225
226
227

228

















229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249


250
251
252
253
254
255
256
257
258
259
260

	  Ui = A_ud'*Ui;
	  y_e = [y_e; y_new'];
	  e_e = [e_e; e_est'];
	endfor
      endif
      
      ##Control

      U = K_w*w - K_x*x_est;


















      ## Save data
      if Simulate
	t = [t;ti'];
	y = [y;yi'];
	u = [u;ui'];
      else
	t = [t;t_i];
	y = [y;y_i'];
	u = [u;u_i'];
      endif
      

      if strcmp(p_o.method, "intermittent")
	y_e = [y_e; y_new'];
	e_e = [e_e; e_est'];
	t_e = [t_e; t_i];
      endif

      delta_comp = time-tim;
      usleep(floor(1e6*(p_c.delta_ol-delta_comp-0.01)));


    endfor			# Main loop
    w = -w;
  endfor 			# Outer loop

  if !Simulate
    ppp_put_get(0*U); 		# Reset to zero
  endif

  
  if strcmp(p_o.method, "continuous")
    t_e = t;








>
|
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>


















|
|
|
>
>



<








247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298

299
300
301
302
303
304
305

	  Ui = A_ud'*Ui;
	  y_e = [y_e; y_new'];
	  e_e = [e_e; e_est'];
	endfor
      endif
      
      ##Control
      if ( (p_c.Tau_u==[])&&(p_c.Tau_y==[]) )
	U = K_w*w - K_x*x_est;
      else
	## Input constraints 
	[Gamma_u, gamma_u] = \
	    ppp_input_constraints(p_c.A_u,p_c.Tau_u,p_c.Min_u,p_c.Max_u);
	
	## Output constraints
	[Gamma_y,gamma_y] = \
	    ppp_output_constraints(A,B,C,D,x_est,p_c.A_u,\
				   p_c.Tau_y,p_c.Min_y,p_c.Max_y);
	
	## Composite constraints - t=0
	Gamma = [Gamma_u; Gamma_y];
	gamma = [gamma_u; gamma_y];
	
	[u_qp,U] = ppp_qp (x_est,w,J_uu,J_ux,J_uw,Us0,Gamma,gamma,1e-6,1);
      endif
      

      ## Save data
      if Simulate
	t = [t;ti'];
	y = [y;yi'];
	u = [u;ui'];
      else
	t = [t;t_i];
	y = [y;y_i'];
	u = [u;u_i'];
      endif
      

      if strcmp(p_o.method, "intermittent")
	y_e = [y_e; y_new'];
	e_e = [e_e; e_est'];
	t_e = [t_e; t_i];
      endif
      if !Simulate
	delta_comp = time-tim;
	usleep(floor(1e6*(p_c.delta_ol-delta_comp-0.01)));
      endif
      
    endfor			# Main loop
    w = -w;
  endfor 			# Outer loop

  if !Simulate
    ppp_put_get(0*U); 		# Reset to zero
  endif

  
  if strcmp(p_o.method, "continuous")
    t_e = t;
︙︙

MTT: Model Transformation Tools
[ GitHub | SourceHut | Sourceforge | Fossil RSS ]