Discrete-Time PID https://jp.mathworks.com/help/control/ug/discrete-time-proportional-integral-derivative-pid-controller.html

pidstd2.h

#pragma once
#include <integrator.h>
template<typename T>
class PIDStd2 {
	T Kp;
	T Ti;
	T Td;
	T N;
	T b;
	T c;
	T Ts;
	DescreteTimeIntegrator<T> IF;
	DescreteTimeIntegrator<T> DF;
public:
	PIDStd2(T kp, T ti, T td, T n, T b, T c, T ts, T reference=T(), T initial=T()) : Kp(kp), Ti(ti), Td(td), N(n), b(b), c(c), IF(1, ts), DF(1, ts) {
		IF.reset(reference - initial);
		DF.reset(c * reference - initial);
	}
	T update(T reference, T input) {
		auto u = Kp * ( (b * reference - input) + 1 / Ti * IF.update(reference - input) + Td / (Td / N + DF.update(c * reference - input)) );
		return u;
	}
	void reset(T reference=T(), T initial=T()) {
		IF.reset(reference - initial);
		DF.reset(c * reference - initial);
	}
};