How can the proper controller adjustments be quickly determined on any control application?
I am afraid that the question you pose is too general. There are many control books describing a wide variety of control strategies and each of which is "adjusted/tuned" in a specific way. You may want to be more specific with your question in order to get an answer that can be useful. (e.g. control application, control strategy, control requirements....)
there is a field in control is named optimal control.
in this field you must define a cost function. cost function include the control variables that you want they become minimum.
see this link
http://www.amazon.com/Optimal-Control-Theory-Introduction-Engineering-ebook/dp/B00CWR4MX0
Before selecting a method of design a controller, the plant has to be specified, for instance, is it linear or nonlinear, time-varying or time invariant , SISO or MIMO, etc. The second step is to recognize the certainty of the plant parameters, also the type of input. Finally, what are the desired specification. On the other hand, in general, the methods of design can be either of the two categories, model-based methods or non model-based. Therefore, the topic is very wide as Enrique said.
Indeed, most of the time people want a fast response and (almost) no overshoot. A lot of systems are integrating in nature and have some delay (cumulated small first order, calculating time, sample and actuation time). A PI controller will have 40% overshoot just before oscillatory damped response (time constant of corner of the PI 5.5 times dead time. If a the high frequencies are attenuated 2 times in the set value (poles and zeroes), the step response can be made without overshoot. Surprisingly, the same response can be made by a high pass filter (high frequencies two times higher) in the feedback (a soft D-action). Integrating time of process*integrating time of integration= 10*dead time^2, in this way the I-action of the controller can be evaluated. I used such tricks many times during years, it corresponds to some phase margin of 50°, but the tuning works better in the time domain. In fact it is sufficient to know a maximal dead time of the process and a maximal gain (smallest integrating time) of the process to get it stable, but is the gain is too low, the response will be sluggish. If done well, 50% of final step response is obtained in about 2.5 times the dead-time.
If one step response is obtained, a second loop can be built around (one takes an equivalent delay at the time when half the peak value of the response is obtained.
One can consecutively get from voltage to current (=proportional to torque), to speed, from speed to position in nested loops.
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