# Control system error based on differential process value

In a basic PID controller, you measure the process value y (such as temperature) directly; then the error e is equal to the difference between the process value and the set point r. The error feeds a PID controller C which in turn outputs a control signal u to an effector, in this case maybe a heating element, controlling the process P.

But what about a peak-finding system such as an antenna tuner? Here, it's still closed-loop but there is no defined "set point", and rather than being able to measure the process value directly, we can only measure some non-directional figure of merit such as signal strength. We simply try to adjust for peak carrier strength, where the effector could be a tuning capacitor. The error could be set as

$$e = - \frac {\Delta y} {\Delta u}$$

That is to say, for some positive perturbation in the effector, if it improves the signal strength, then decrease the error.

Is there such a control system already? If so what's its name so that I can do further reading?

• FM? AM? Suppressed carrier? SSB? – Andy aka May 22 '18 at 13:53
• AM SSB with full carrier – Reinderien May 22 '18 at 14:02
• Tricky I believe! – Andy aka May 22 '18 at 14:04
• Such automatic antenna tuners are common in wireless comms (ham radio, e.g.). Some use pi networks with 3 variables (2xC + 1xL) and an algorithm to minimise VSWR. A single variable would be a much easier task. – Chu May 22 '18 at 15:57