Controller tuning map

These graphs give you an idea of the effect of changing gain and integral time constant in a PI controlled system. The process which was controlled was third-order, made up of three first-order sub-processes each with a time constant of 1. The test input was a setpoint change of 1. Obviously, the absolute values of gain and time constant required will change with the system to be controlled. For comments on the responses, move the mouse over the relevant plot.

	T_I=0.6	T_I=0.3	T_I=0.15
K_c=4	This is a bit oscillatory, but the thing to notice is that the oscillations are initially centred underneath the setpoint - integral action isn't pulling up the controlled variable quickly enough	The response is oscillatory, but the oscillations are approximately centred on the setpoint - integral action is probably OK, but the gain needs to be reduced	This is clearly unstable. In cases like this I'd get rid of the integral action and reduce the proportional gain. Once I was happy I'd cut the gain a bit and gradually add integral action
K_c=2	There's little oscillation here, but the effects of too little integral action are clear - it's taking ages to drag the controlled variable to setpoint	Quite a nice response. A fast rise time and rapid settling. I'm happy with this!	This kind of response can be difficult to distinguish from that which we get when we have too much gain. The best thing to do to try to improve it is to reduce the integral action - if we end up with the sort of responses on the left hand side, then increase the integral action (reduce the time constant) and decrease the gain
K_c=1	There's no power in the control action at all here - both proportional and integral action are too weak	The proportional action isn't strong enough to carry the controlled variable over the setpoint. If you tune the controller by sorting out proportional control first, this shouldn't happen!	This looks OK, but it has a much longer rise time, and the overshoot is slightly greater, than the properly tuned response