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num-rat-resultant-sqrt-subst

eq1: (x-x1)^2+(y-y1)^...

eq2: (x-x2)^2+(y-y2)^...

eq3: rat(eq1-eq2,y,x);

Calculate

num

eqn: 1444/16;

a: num(eqn);

b: den(eqn);

Calculate

num-rat-rhs-solve

eqa: (x-xa)^2+(y-ya)^...

eqb: (x-xb)^2+(y-yb)^...

eqc: (x-xc)^2+(y-yc)^...

Calculate

num-plot2d-sin
plot2d(aInitialValue_num + sin(aCurrentTime_num / aDuration_num * %pi*2 - %pi/2),[aCurrentTime_num,0,aDuration_num]);

aInitialValue_num: 1.0;

aFinalValue_num: 1.0;

aDuration_num: 4.0;

Calculate

num-plot2d
plot2d(aCurrentTime_num^6,[aCurrentTime_num,0,aDuration_num]);

aInitialValue_num: 0.0;

aFinalValue_num: 1.0;

aDuration_num: 1.0;

Calculate

num-sum

sum((k*23/3 -77/3), k...

Calculate

num-plot2d
plot2d(aInitialValue_num + (aFinalValue_num - aInitialValue_num) * 2 / (aDuration_num * aDuration_num) * aDuration_num * aCurrentTime_num - (aFinalValue_num - aInitialValue_num) * 2 / (aDuration_num * aDuration_num) * aCurrentTime_num * aCurrentTime_num / 2,[aCurrentTime_num,0,aDuration_num]);

aInitialValue_num: 1.0;

aFinalValue_num: 1.0;

aDuration_num: 4.0;

Calculate

num-plot2d-sin
plot2d(aInitialValue_num + 0.5 + 0.5*sin(aCurrentTime_num / aDuration_num * %pi*2 - %pi/2),[aCurrentTime_num,0,aDuration_num]);

aInitialValue_num: 1.0;

aFinalValue_num: 1.0;

aDuration_num: 4.0;

Calculate

num-plot2d
plot2d(-(aCurrentTime_num - aDuration_num/2) ^ 2 + lSignedAmplitude_num,[aCurrentTime_num,0,aDuration_num]);

aInitialValue_num: 1.0;

aFinalValue_num: 1.0;

aDuration_num: 4.0;

Calculate

num-plot2d-sin
plot2d(aInitialValue_num + sin(aCurrentTime_num * aDuration_num - %pi/2),[aCurrentTime_num,0,aDuration_num]);

aInitialValue_num: 1.0;

aFinalValue_num: 1.0;

aDuration_num: 4.0;

Calculate

num

Run Example
(%i1)eq1:Kp*(1+1/(Ti*s)+Td*s);
                                  1
(%o1)                        Kp (---- + s Td + 1)
                                 s Ti
(%i2) eq2:s = 2/T *((z-1)/(z+1));
                                     2 (z - 1)
(%o2)                            s = ---------
                                     (z + 1) T
(%i3) eq3:factor(subst(eq2,eq1));
            2  2        2    2         2                       2
(%o3) (Kp (z  T  + 2 z T  + T  + 2 Ti z  T - 2 Ti T + 4 Td Ti z  - 8 Td Ti z
                                           + 4 Td Ti))/(2 Ti (z - 1) (z + 1) T)
(%i4) num(eq3);
           2  2        2    2         2                       2
(%o4) Kp (z  T  + 2 z T  + T  + 2 Ti z  T - 2 Ti T + 4 Td Ti z  - 8 Td Ti z
                                                                     + 4 Td Ti)
(%i5) denom(eq3);
(%o5)                       2 Ti (z - 1) (z + 1) T
(%i6) 
Run Example
aInitialValue_num: 1.0;
(%o1)                                 1.0
(%i2) aFinalValue_num: 1.0;
(%o2)                                 1.0
(%i3) aDuration_num: 4.0;
(%o3)                                 4.0
(%i4) lMaxNormalizedDeviation_num: 0.14;
(%o4)                                0.14
(%i5) slow: 1.5;
(%o5)                                 1.5
(%i6) plot2d(aInitialValue_num + aFinalValue_num * (aCurrentTime_num / aDuration_num) + lMaxNormalizedDeviation_num * 0.5 * (1 - cos((aCurrentTime_num / aDuration_num)^slow * 2 * %pi)),[aCurrentTime_num,0,aDuration_num]);
plotplot2d(aInitialValue_num + aFinalValue_num * (aCurrentTime_num / aDuration_num) + lMaxNormalizedDeviation_num * 0.5 * (1 - cos((aCurrentTime_num / aDuration_num)^slow * 2 * %pi)),[aCurrentTime_num,0,aDuration_num]);
Run Example
kill(all);
(%o0)                                done
(%i1) nodev1: 0 = g*(v0 - k*v1 - v2) - (gc*(v1 - 0) - ic1eq), gc=1;
(%o1)                0 = g (- v2 - k v1 + v0) - v1 + ic1eq
(%i2) nodev2: 0 = g*(v1 - 0) - (gc*(v2 - 0) - ic2eq), gc=1;
(%o2)                       0 = - v2 + g v1 + ic2eq
(%i3) sln1: (first(solve([nodev1, nodev2], [v1, v2]))[1]);
                               g v0 - g ic2eq + ic1eq
(%o3)                     v1 = ----------------------
                                           2
                                    g k + g  + 1
(%i4) sln2: (first(solve([nodev1, nodev2], [v2, v0]))[1]);
(%o4)                          v2 = g v1 + ic2eq
(%i5) sln3: substitute(sln1, sln2);
                         g (g v0 - g ic2eq + ic1eq)
(%o5)               v2 = -------------------------- + ic2eq
                                       2
                                g k + g  + 1
(%i6) rat(second(sln3));
                       2
                      g  v0 + g ic2eq k + ic2eq + g ic1eq
(%o6)/R/              -----------------------------------
                                        2
                                 g k + g  + 1
(%i7) rat(num(second(ratsimp(sln3))));
                       2
(%o7)/R/              g  v0 + g ic2eq k + ic2eq + g ic1eq
(%i8) rat(denom(second(ratsimp(sln3))));
                                        2
(%o8)/R/                         g k + g  + 1
(%i9) 

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