The thing about non-fraudulent, wealth-backed money is that there is no barrier to entry, nor is there a barrier to exit. Unlike usury-based money, a wealth-backed currency can cleanly decrease in usage, down to zero. People withdraw wealth pledged to created the money, by returning the amount of money created, and then take their wealth elsewhere.
Thus, if people don't like the valuations arrived at by the "basket" underlying the value of each unit of money (ie. something becomes undesirably in/deflationary), they can move to another form of money -- ideally, one that constitutes its "basket" based on a more representative set of the society's basic commodities. In the ideal embodiment, this basket would evolve over time (eg. as energy production moves from coal to oil to natural gas to nuclear to renewables over the years, for example, the energy commodity component of the basket would be revised automatically).
As for the PID loop, there are much more advanced controls methodologies that improve error rejection (eg. Kalman filtering), stability (Model Predictive or State Space control), etc. Furthermore, limits on the introduction (or withdrawal) of wealth (and hence newly created units of money) should reflect the current size of the ecosystem to limit shocks that would adversely interfere with the control stability. (ie. you can't create 10x the current size of the economy in newly issued money all at once.)