Why does time delay, and correspondingly phase lag, almost always cause a system to go unstable? Physically, an imbalance between the strength of the corrective action and the system dynamic lags results in the corrective action being applied in the wrong direction. Mathematically, when the denominator of the closed-loop transfer function equals zero, the system goes unstable. Since this denominator is equal to 1 + the open-loop transfer function, when the open-loop transfer function equals -1 (i.e., magnitude = 1 and phase angle = -180 degrees), the closed-loop system is marginally stable.
If a system is stable, how close is it to becoming unstable? Because of model uncertainties, it is not merely sufficient for a system to be stable. It must have adequate stability margins. Stable systems with low stability margins work only on paper. The way uncertainty has been quantified in classical control is to assume that either gain changes or phase changes occur. The tolerances of gain or phase uncertainty are the gain and phase margins.
A paradox is that the presence of delays may be either beneficial or detrimental to the operation of a dynamical system. Judicious introduction of a delay may stabilize an otherwise unstable system (e.g., a wait-and-act control strategy) or improve steady-state tracking error.
The impact of delays continues to grow in many fields, including the control of distributed systems such as energy and computing grids.
I really like how you emphasize the "judicious introduction" of time delays. I have seen some folks use time delays as a quick fix without carefully evaluating their effect on the entire system, which can either be a great solution or it can introduce other errors in subtle ways.
I have been involved in developing, improving and consulting anything related with control system for the last 15 years in electronics component testing and automation system. Time delay is really important and at some cases it is the only mean to solve the problems.
When the control loop is some derivative of a PID loop, maintaining phase is very good advice.
When there are unavoidable delays present in the system, your suggestion of some kind of "wait and act" strategy is probably good advice. When you think about it, adding a delay in the control loop is just another way to "conserve phase".
Truchard will be presented the award at the 2014 Golden Mousetrap Awards ceremony during the co-located events Pacific Design & Manufacturing, MD&M West, WestPack, PLASTEC West, Electronics West, ATX West, and AeroCon.
Robots that walk have come a long way from simple barebones walking machines or pairs of legs without an upper body and head. Much of the research these days focuses on making more humanoid robots. But they are not all created equal.
The IEEE Computer Society has named the top 10 trends for 2014. You can expect the convergence of cloud computing and mobile devices, advances in health care data and devices, as well as privacy issues in social media to make the headlines. And 3D printing came out of nowhere to make a big splash.
For industrial control applications, or even a simple assembly line, that machine can go almost 24/7 without a break. But what happens when the task is a little more complex? That’s where the “smart” machine would come in. The smart machine is one that has some simple (or complex in some cases) processing capability to be able to adapt to changing conditions. Such machines are suited for a host of applications, including automotive, aerospace, defense, medical, computers and electronics, telecommunications, consumer goods, and so on. This discussion will examine what’s possible with smart machines, and what tradeoffs need to be made to implement such a solution.