PID can’t be used for control of any device that uses a relay. PWM will have the effect of just changing the coil voltage. Even if you could switch a relay on/o

PID can’t be used for control of any device that uses a relay. PWM will have the effect of just changing the coil voltage. Even if you could switch a relay on/off quickly you’d just prematurely burn out the contacts. PID is only effective with solid state switching devices, which are not really common for residential heating/cooling.