Minimizing the gap between theory and practice

The theory-practice gap has existed for decades, and each of us must bridge this gap in all we do. Control is an essential element in all multidisciplinary systems, so let’s start there and begin to bridge the gap that exists between the theory of control and its digital implementation. The following points provide an overview of control theory for the practitioner.

First, remember that feedback control is a pervasive, powerful, and enabling technology. At first sight, it looks simple and straightforward, but it is amazingly subtle and intricate in both theory and practice. Also remember that you cannot instantaneously effect changes in a dynamic system, so applying an otherwise-correct control decision at the wrong time could result in catastrophe. Further, nonlinearities, including backlash, coulomb friction, saturation, hysteresis, quantization, deadband, and kinematic nonlinearities, are always present. You can use a linearized model to approximate a nonlinear system near an operating point.

When working with dynamic systems, keep in mind that they must have guaranteed stability. Closed-loop systems become unstable because of an imbalance between the strength of corrective action and the system’s dynamic lags. Stable systems must have adequate stability margins to work after you have built them. Stable systems also have a frequency response. If you apply a sinusoidal input to a stable linear system, then the steady-state output will be a sinusoid of the same frequency. The amplitude ratio and phase difference of the two sinusoids are frequency-dependent, however.

Keep in mind that the open-loop transfer function is the product of all the transfer functions in the loop, including the controller, actuator, plant, and ensor. The open-loop transfer function is much less complex than the closed-loop system-transfer function. The Nyquist criterion, a graphical technique for determining the stability of a system, and the root-locus procedure, which allows adjustment of the system poles by changing the feedback system’s static gain, allow you to use the open-loop transfer function to predict closed-loop system performance.

Once you have a stable, closed-loop system, the main reasons for using feedback control are command following, disturbance rejection, insensitivity to modeling errors, and insensitivity to unmodeled high-frequency dynamics and noise. Time delays can be deadly, however. Always conserve phase, the equivalent of time delay. Integral control adds 90° of phase lag at every frequency, and digital control adds time delay primarily due to digital-to-analog conversion. Imagine trying to make decisions using old information.

High control gain yields good command tracking and good disturbance rejection. However, areas of concern include roll-off, saturation, and noise. Even the most insignificant detail of control engineering may prove important. Real control systems must be reliable, especially if people’s lives depend on them.

Maybe you know all of this information, but it is worth repeating.


About the author
Kevin C. Craig, PhD, is the Robert C. Greenheck chairman in engineering design and a professor of mechanical engineering at the College of Engineering at Marquette University.