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Control of SMPS - A refresher How to measure the control loop of a SMPS
Control of SMPS - A refresher
How to measure the control loop of a SMPS
Hello, and welcome to part three of this three-part talk on the control of switched-mode power supplies. My name is Colin Gilmor, and I'm an applications engineer with Texas Instruments based in Cork in Ireland. In this final part, I want to talk about how to test a control loop and how to evaluate its stability. Then I'll present a summary.
So, having designed and built the control loop, it's necessary to measure its performance. I'm going to use gain phase measurements and load transient testing as examples of how this might be done.
There are two main ways to measure control loop performance, gain phase measurements or Bode plots and load transient tests. The main difference between these methods is that the gain phase measurements give a clear, quantitative measurement of the gain and phase margins of the system under small signal conditions.
And transient tests show the system response to large signal changes in an operating point. Typically, it's much easier to set up the system for a load transient test than for a gain phase measurement, but both are useful, and both should be included in any loop stability test program.
A Bode plot gives a clear indication of whether the gain and phase margins are adequate. Opinions vary, but, typically, a 2 dB to 10 dB gain margin and a phase margin between 45 and 80 degrees is acceptable. The Bode plot is a frequency domain check, which tests the loop response at a single operating point. Ideally, multiple plots should be taken under different conditions to verify stability over the full range of operating conditions.
The transient response is a time domain test that checks the system response to a large change in its operating conditions. This helps expose any nonlinear behaviors that may be a problem. For example, a 0% load to 100% load transient may show that the controller cannot maintain the output voltage within acceptable limits. Transient tests are easy to do and relatively easy to interpret, as we can see shortly. It's also worth noting that there is a strict mathematical relationship using Laplace transforms between the time domain and frequency domain responses.
The main consideration when setting up for a gain phase measurement is selection of a suitable point to inject the test signal. Ideally, the injection point should have a low impedance looking back into the loop, Z2 and Z2 prime, and a high impedance looking forward into the loop, Z1 and Z1 prime. The reason for this is that the true loop gain-- this is T of s-- is a function of the measured gain, M of s, and of these impedances.
Now, normally, these impedances are almost impossible to determine. So, if Z1 is much greater than Z2, their effect may be ignored. And the background of this requirement is explained in reference 10. Two suitable injection points are identified here. The one at the output is normally preferred.
If peak current mode control is used, then normally it is not necessary to check the stability of the inner current loop, other than to make sure that there is enough slope compensation. If average current mode control is used, then the inner current loop must be tested as well. And reference 14 shows how this can be done.
Now a load step forces the control loop to adjust from one operating condition to another. And the response of the system can be easily measured at the output. There are only a few constraints on the test.
The rate of change of the load current must be significantly faster than the loop bandwidth. There is no upper bound on how fast this step can be.
Typically, a 25% to 75% and back to 25% load transient is used. This operates the loop over most of its control range and avoids mode transitions into light load, burst, or sleep modes. The transient amplitude can be easily adjusted for tests from 0% to 100% to 0% load. And the same test setup can be easily modified to check entry into and recovery from overcurrent conditions.
The amplitude of the response can be quite small and even buried in the output noise. The strategy in this case would be to repeat the transients and average the result, using the current step as the trigger source.
As I mentioned earlier, there is a formal relationship between the gain phase results plotted on a Bode plot and the transient response. And this means that the phase margin can be estimated from the shape of the transient response. The plots here show the approximate relationship. The book by Ericson and Maksimovic, reference 11, gives more detail on how these curves were derived and the approximations used.
There is a trade-off between the phase margin and the speed of response of the system. The response time is the time needed to move from the initial condition at V tau equal to 0 to the final condition or V tau equal to 1. The response with a phase margin of 77 degrees is optimally damped. And the plot with a 52 degrees phase margin shows a slight overshoot, but it does have a significantly faster response time.
Phase margins less than about 45 degrees become unacceptably oscillatory and don't provide any margin against component-to-component variation or aging effects. Phase margins greater than 77 degrees can have an unnecessarily slow response.
Now for a summary of the material I have presented-- the iceberg analogy, so please bear in mind that, just because a switched-mode power supply is unstable, it may not be due to a loop with insufficient gain or phase margin. Here is a list of other possible causes of instability. And the first thing to do if you are faced with an unstable power supply is to try to understand the reason for the instability before blaming the control loop.
Now, to summarize, control theory is often thought to be difficult to understand. And theoretical approaches usually have lots of mathematics and talk about new gain, complex frequency, H of s, and G of s and so on and so forth. I have tried to show here that it is possible to gain a qualitative understanding and feel for analog control of switched-mode power supplies without using too much mathematics.
We have seen how the various pieces of the control loop puzzle are designed and how they are put together in a functioning switched-mode power supply system and described loop compensation strategies using type 2 and type 3 compensation networks and how sloped compensation is used to stabilize the current loop. I discussed the gain phase measurement and load transient test methods used to verify that a design is stable and indicated what the limits for acceptance might be.
Please remember the iceberg analogy, that, just because a power supply is oscillating, it does not always follow that the feedback loop has insufficient phase margin. There are many other causes for system instability.
Finally, there is a lot of good information available on control theory, and I included a list of the ones I used in this presentation at the end. Here are some useful reference sources. So this is a list of the sources used in this presentation.
If you want to choose one only, then I would recommend the [? application ?] [? note ?] by Sheehan, reference number three. Mammano's book, reference two, is a good all-around introduction to switched-mode power supply design, while reference 11, Erickson and Maksimovic's book, is an in-depth treatment of the subject. Reference 12 is a book dedicated to control theory and is a good reference for further study.
Thanks for your attention, and I hope you found this talk useful. Please feel free to contact me directly at this email address if you have any questions or if you have any suggestions for improvements that I could make. Thank you very much.
April 8, 2019
In this series of videos I want to show that it is possible to gain a good qualitative understanding and feel for analog control of SMPS without using too much mathematics. I will show how a functioning Switched Mode Power Supply control system is designed and how the loop is stabilised. I will discuss the Gain Phase and Load transient test methods used to verify that a design is stable and indicated what the limits for acceptance might be.