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#include "control.h"
#include <armadillo>
#include <cassert>
#include <cmath>
namespace ct
{
TransferFn::TransferFn()
: num(1)
, den(1)
{
num(0) = 1;
den(0) = 1;
}
TransferFn::TransferFn(math::PolyCx num, math::PolyCx den)
: num(num)
, den(den)
{}
complex TransferFn::dc_gain() const
{
arma::cx_vec z(1, arma::fill::zeros);
arma::cx_vec n = arma::polyval(num.coeffs, z);
arma::cx_vec d = arma::polyval(den.coeffs, z);
return n(0) / d(0);
}
bool TransferFn::is_proper() const
{
return den.degree() >= num.degree();
}
bool TransferFn::is_strictly_proper() const
{
return den.degree() >= num.degree();
}
TransferFn operator + (const TransferFn& g, const TransferFn& h)
{
TransferFn tf(g.num * h.den + h.num * g.den, g.den * g.den);
tf.canonicalize();
return tf;
}
TransferFn operator - (const TransferFn& g, const TransferFn& h)
{
TransferFn tf = g + (-1. * h);
tf.canonicalize();
return tf;
}
TransferFn operator * (const TransferFn& g, const TransferFn& h)
{
TransferFn tf(g.num * h.num, g.den * h.den);
tf.canonicalize();
return tf;
}
TransferFn operator / (const TransferFn& g, const TransferFn& h)
{
TransferFn hinv = TransferFn(h.den, h.num);
hinv.canonicalize();
TransferFn tf = g * hinv;
tf.canonicalize();
return tf;
}
TransferFn operator * (const complex k, const TransferFn& h)
{
TransferFn tf(k * h.num, h.den);
tf.canonicalize();
return tf;
}
TransferFn operator / (const TransferFn& h, const complex k)
{
TransferFn tf((1. / k) * h.num, h.den);
tf.canonicalize();
return tf;
}
TransferFn feedback(const TransferFn& tf, complex k)
{
const TransferFn unit(math::PolyCx({1.}), math::PolyCx({1.}));
const TransferFn ol = k * tf;
const TransferFn bo = unit - ol;
const TransferFn fb = unit / bo;
const TransferFn tf_cl = ol * fb;
// const TransferFn tf_cl = (k * tf) / (unit - k * tf);
return tf_cl;
}
void TransferFn::canonicalize()
{
complex an = den(0);
if (std::abs(an) > 0)
{
num.coeffs /= an;
den.coeffs /= an;
}
}
LocusSeries::LocusSeries(double start, double end, size_t nsamples)
: n_samples(nsamples)
, start(start)
, end(end)
, in(arma::logspace(log10(start), log10(end), n_samples))
// FIXME: do not hardcode one root locus
, out(1, n_samples, arma::fill::zeros)
{}
void rlocus(const TransferFn& tf, LocusSeries& ls)
{
using namespace arma;
CT_ASSERT(tf.is_proper());
CT_ASSERT(tf.den.degree() > 0);
// prepare output
ls.out = cx_mat(tf.den.degree(), ls.n_samples, fill::zeros);
// compute roots
for (int i = 0; i < ls.n_samples; i++)
ls.out.col(i) = (tf.den + ls.in(i) * tf.num).roots();
// sort the roots
}
SSModel::SSModel(size_t n_in, size_t n_out, size_t n_states)
: n_in(n_in)
, n_out(n_out)
, n_states(n_states)
, A(n_states, n_states)
, B(n_states, n_in)
, C(n_out, n_states)
, D(n_out, n_in)
{}
SSModel ctrb_form(const TransferFn& tf)
{
// TODO: change to proper by implementing D
CT_ASSERT(tf.is_strictly_proper());
int ord = tf.den.degree();
SSModel ss(1, 1, ord);
ss.B(ord - 1) = 1;
for (int i = 0; i < ord; i++)
{
ss.A(ord - 1, i) = tf.den(ord - i);
if (i < tf.num.coeffs.n_elem)
ss.C(i) = tf.num(i);
}
return ss;
}
TimeSeries::TimeSeries(double start, double end, size_t n_samples)
: n_samples(n_samples)
, start(start)
, end(end)
, dt((start - end) / (n_samples - 1))
, time(arma::linspace(start, end, n_samples))
// FIXME: do not hardcode SISO
, in(1, n_samples, arma::fill::zeros)
, out(1, n_samples, arma::fill::zeros)
{}
void response(const SSModel& ss, TimeSeries& ts)
{
using namespace arma;
CT_ASSERT(ts.in.n_rows == ss.n_in);
CT_ASSERT(ts.in.n_cols == ts.n_samples);
ts.out = cx_mat(ss.n_out, ts.n_samples, fill::zeros);
ts.state = cx_mat(ss.n_states, ts.n_samples, fill::zeros);
// FIXME: non-homogeneous initial condition
// For the current application we want this to be faster rather than
// accurate. Hence we use a simulation with ZOH input is cheap and probably
// good enough.
// FIXME: do not invert matrix like that
const cx_mat Ad = expmat(ss.A * ts.dt);
const cx_mat Bd = (Ad - eye(size(Ad))) * pinv(ss.A) * ss.B;
for (int k = 0; k < ts.n_samples - 1; k++)
ts.state.col(k + 1) = Ad * ts.state.col(k) + Bd * ts.in.col(k);
ts.out = ss.C * ts.state + ss.D * ts.in;
}
void step(const SSModel& ss, TimeSeries& ts)
{
ts.in = arma::cx_mat(ss.n_in, ts.n_samples);
ts.in.fill(1.);
response(ss, ts);
}
}
// vim: ts=2 sw=2 noet:
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