FirstOrder.hpp

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#pragma once
 
#include <janus/janus.hpp>
 
namespace vulcan::tf {

template <typename Scalar> struct FirstOrderCoeffs {
    Scalar a;   
    Scalar b;   
    double tau; 
    double K;   
    double dt;  
};

template <typename Scalar>
FirstOrderCoeffs<Scalar> first_order(double tau, double K, double dt) {
    double a = std::exp(-dt / tau);
    double b = K * (1.0 - a);
    return FirstOrderCoeffs<Scalar>{static_cast<Scalar>(a),
                                    static_cast<Scalar>(b), tau, K, dt};
}

template <typename Scalar>
Scalar first_order_step(const FirstOrderCoeffs<Scalar> &coeffs,
                        const Scalar &state, const Scalar &input) {
    return coeffs.a * state + coeffs.b * input;
}

template <typename Scalar>
Scalar first_order_response(double tau, double K, const Scalar &t) {
    return static_cast<Scalar>(K) * (1.0 - janus::exp(-t / tau));
}
 
} // namespace vulcan::tf