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#pragma once
#include "armadillo/include/armadillo"
#include <utility>
#include <complex>
#include <cassert>
#include <cmath>
#include <cstddef>
#ifndef CONTROL_H
#define CONTROL_H
#define CT_ASSERT(x) (assert(x))
#define CT_SMALL_TOL 1e-6
#define CT_SMALL(x) (std::abs(x) < CT_SMALL_TOL)
#define CT_ASSERT_SMALL(x) (assert(CT_SMALL))
namespace ct
{
typedef std::complex<double> complex;
typedef std::size_t size_t;
namespace math
{
template<typename T>
struct Poly
{
arma::Col<T> coeffs;
Poly(size_t n_elem) : coeffs(n_elem) {}
Poly(arma::Col<T> c) : coeffs(c) {}
template<typename U>
Poly(std::initializer_list<U> l) : coeffs(l.size())
{
int i = 0;
for (const U& u : l)
coeffs(i++) = T(u);
}
int degree() const { return coeffs.n_elem - 1; }
void add_root(T r) { (*this) = (*this) * Poly({1., -r}); }
arma::Col<T> roots() const { return arma::roots(coeffs); }
template<typename IndexT>
T& operator () (IndexT idx) { return coeffs(idx); };
template<typename IndexT>
T operator () (IndexT idx) const { return coeffs(idx); };
};
template<typename T>
Poly<T> operator * (const Poly<T>& p, const Poly<T>& q)
{
arma::Col<T> coeffs = arma::conv(p.coeffs, q.coeffs);
CT_ASSERT(!coeffs.has_nan());
return Poly<T>(coeffs);
}
template<typename T, typename R = T>
Poly<T> operator * (R scalar, const Poly<T>& p)
{
Poly<T> q(p.coeffs * scalar);
CT_ASSERT(!q.coeffs.has_nan());
return q;
}
template<typename T, typename R = T>
Poly<T> operator / (R scalar, const Poly<T>& p)
{
Poly<T> q(p.coeffs / scalar);
CT_ASSERT(!q.coeffs.has_nan());
return q;
}
template<typename T>
Poly<T> operator + (const Poly<T>& p, const Poly<T>& q)
{
const Poly<T>& big = (p.degree() > q.degree()) ? p : q;
const Poly<T>& small = (p.degree() > q.degree()) ? q : p;
Poly<T> s(small);
int rel = big.degree() - small.degree();
s.coeffs.insert_rows(0, rel);
CT_ASSERT(!s.coeffs.has_nan());
return Poly<T>(big.coeffs + s.coeffs);
}
template<typename T>
Poly<T> operator - (const Poly<T>& p, const Poly<T>& q)
{
return p + (-1. * q);
}
typedef Poly<complex> PolyCx;
}
struct TransferFn
{
math::PolyCx num;
math::PolyCx den;
TransferFn(void);
TransferFn(math::PolyCx num, math::PolyCx den);
TransferFn(const TransferFn& other)
: num(other.num)
, den(other.den) {}
inline void add_pole(complex p) { den.add_root(p); }
inline void add_zero(complex z) { num.add_root(z); };
complex dc_gain() const;
bool is_proper() const;
bool is_strictly_proper() const;
void canonicalize();
TransferFn& operator = (const TransferFn& other);
};
TransferFn operator + (const TransferFn& g, const TransferFn& h);
TransferFn operator - (const TransferFn& g, const TransferFn& h);
TransferFn operator * (const TransferFn& g, const TransferFn& h);
TransferFn operator / (const TransferFn& g, const TransferFn& h);
TransferFn operator * (const complex k, const TransferFn& h);
TransferFn operator / (const TransferFn& h, const complex k);
// inline TransferFn operator / (const TransferFn&
TransferFn cancel_zp(const TransferFn& tf, double tol = CT_SMALL_TOL);
TransferFn feedback(const TransferFn& tf, complex k = -1);
struct LocusSeries
{
size_t n_samples;
double start, end;
arma::vec in;
arma::cx_mat out;
LocusSeries() = delete;
LocusSeries(double start, double end, size_t n_samples);
};
void rlocus(const TransferFn& tf, LocusSeries& ls);
void nyquist(const TransferFn& tf, LocusSeries& ls);
struct SSModel
{
size_t n_in, n_out, n_states;
arma::cx_mat A, B, C, D;
SSModel() = delete;
SSModel(size_t n_in, size_t n_out, size_t n_states);
};
SSModel ctrb_form(const TransferFn& tf);
// SSModel obsv_form(const TransferFn& tf);
// SSModel eigm_form(const TransferFn& tf);
struct TimeSeries
{
size_t n_samples;
double start, end, dt;
arma::vec time;
arma::cx_mat in, out;
arma::cx_mat state;
TimeSeries() = delete;
TimeSeries(double start, double end, size_t n_samples);
};
void response(const SSModel& ss, TimeSeries& ts);
void step(const SSModel& ss, TimeSeries& ts);
}
#endif // CONTROL_H
// vim:ts=2 sw=2 noet:
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