Transfer functions

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Mohd Shahrul Azmi b Mohamad Yusoff

I'm have a degree in Mech. Eng and I enjoy my control subjects and thesis very much. I did my bachelor thesis on control topic but since then I haven't had a chance to actually use my control knowledge on my work.

I was just wondering, what is the most difficult task that you will experience, is it to find the mathematical or differential equations that represent the system or something else.

What I know is that in order for you stabilise or to investigate the response of the system to an input is by using step response or bode plot or ....... So for you to do that you have to have a transfer function and for that you must have a differential equation that describe the system mathematically.

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John Coppini

Unless you are dealing with critical aerospace, certain robotic situations, or other precise, high performance applications, you will find that most industrial and process controls deals with simple appllication of 2-position sequence control and pre-canned PID continuous control. Most process engineer either have never heard of a differential equation or have long forgotten how to develop and solve one...good academic excercises, but not used very much in normal industrial applications.....sorry you wasted so much time in school!!!

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Bill Faber

I would have to agree with John for the most part, when it comes to process control. From the Motion Control perspective, the mathematical analysis does become useful when modeling as a multibody system. Compliences of mechanical linkages and couplings often times become the biggest issue, when you look at it from a practicle perspective. When faced with a problematic machine with many unknowns (material factors of components are not documented), instability resolution becomes a struggle through experimentation. Estimating parameters and system setup via a model equation can aid you in discovering the system weak points.

Step tests can tell a lot about a control systems performance (electrical and mechanical system), but its not always practicle when it comes to tuning - the most important outcome of the implementation.

All of this depends upon the relative degree of performance expected compared to the machines design. Most of the time your problems end up being gain limitations due to resonances. For that reason, the most demanding motion applications require that actual machine bode plots be measured. Measured bode plots tell how the machine is operating across a broad frequency range and provides much more information than a step response. At this point, pass and notch filters allow control bandwidths to excede machine practicality.

When it comes to mathematical analysis, check out VisSim (www.vissim.com), Matlab (www.mathworks.com), P-Spice (www.orcad.com), and ModelQ - these are modeling and simulation packages that 'ease your pain'.

Not sure I answered your question, but hopefully i gave you another viewpoint - if anything it will encourage more discussion!

Regards,
Bill Faber

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Pierluigi Moschetti

I have also studied much theory at University about system control and I have spent many hours to solve complicated differential equation systems.
After 4 years work I am also aware that the real world of automation does not matter about so much difficult mathematics. But I do not feel to have wasted my time and I can say that sometimes so big theoretical background helps me better understand what is going on!

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Tom Bullock

Once you have sized the motor to the load, the electrical and mechanical time constants can be computed. From these, a LaPlace transform transfer function for the motor/load combination can be written. This is now placed in your servo block diagram for the system analysis.

If you don't know how to do the above, the book "Industrial Servo Control Sysyems" written by George Younkin (he is on our staff) shows how.
He shows it for DC servo motors, but he also has a paper to show how to modify the equations for brushless AC.

Thomas B. Bullock, President
Bull's Eye Marketing Incorporated
Industrial Controls Consulting Division
104 S. Main Street, Suite 320
Fond du Lac, WI 54935
PH: 920: 929-6544
FX: 920: 929-9344
E-mail: [email protected]

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Curt Wilson

In my experience, the toughest thing in the technical practice of control engineering is figuring out when and where the elegant mathematics you used in school can be appropriately applied, and when it cannot. I have seen lots of bright engineers come out of school and blindly apply what they had learned, with often disastrous results.

In school, you deal almost exclusively with linear systems, because they are easy to teach. If you come out assuming that any system you are going to deal with just has linear behavior, you are going to get in trouble quickly. In many cases, the linear stuff is so well understood as to be trivial -- all the interesting and difficult stuff in the system is not amenable to plain linear analysis.

Unlike an earlier respondent, I don't think your education has been wasted -- it's exposed you to a field, to important concepts, and to a good method of thinking. Just don't expect that your approach to real-world problems will be the same as the approach to your coursework.

A few examples: I'm sure you've studied stability analysis and seen that in most feedback systems if you keep increasing the gain, your system will go unstable because closed-loop poles move into the right half-plane (root-locus analysis) or you lose your phase margin (Bode analysis, which says the same thing). In my field, industrial motion control, your gains are usually limited far short of this point. Why? The quantization noise from limited resolution, and the delays in the loop almost always get you first. These effects are non-linear, so they are difficult to analyze, and of course linear theory says nothing about them. But we get much more "bang for our buck" in improving performance by increasing resolution and decreasing loop delays than by implementing fancier linear routines.

In process controls, you often have huge delays that dominate the control response of the system. Trying to treat this as a linear effect that just introduces some phase lag can get you into a lot of trouble.

A recent specific example of mine that you might find interesting: A customer was developing a system with brushless servo motors. Performance was beautiful in normal operation, but when they asked it for an emergency stop, the current loop would go unstable, and this could even blow up the amplifier. They could not figure out why this would be. Our internal discussions suggested motor magnetic saturation could be the root of the problem, so I asked the motor manufacturer for a torque vs. current plot for the motor. When the plot was faxed to me, I could immediately see what the problem was, but the young engineer from our customer was mystified as to how I could see this.

My analysis was this: For a linear system -- a good motor with no saturation, the plot of T vs. I should have been a straight diagonal line. But this plot "rolled off" significantly at high currents, producing a more S-shaped curve. In a motor, the purpose of armature current is to produce magnetic flux linkage (Lambda) which interacts with the "field" to produce torque. In a brushless servo motor the "field" is produced by permanent magnets on the rotor of constant strength. Therefore, the plot of T vs. I is the same shape as the plot of Lambda vs. I.

Next, remember that the definition of inductance L is d(Lambda)/dI -- the slope of this curve. At high currents, the slope was significantly reduced -- in this case, the inductance at maximum current was only 20% of that at low current. This meant that the L/R time constant of the motor windings was reduced by 80% from the low current levels at which the current loop had been tuned. The current loop gains had to be significantly reduced to be able to operate in this state.

The point of the story (I hope it doesn't sound like bragging) is that I had to pull together the kind of formal analysis I learned in school with a real-world appreciation for how that analysis really needs to be applied.

Curt Wilson
Delta Tau Data Systems

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Richard Dale

Question. the angular posistion of a shaft is required to be controlled by a proportional servo-control system so that the shaft follows a reference angle signal. Derive the transfer function (at least 1st order) for one of the component blocks using physical laws and mathematical modelling. Explain each step of your derivation and state any assumptions you have made. Please can you help? If you cannot please let me know yours sincerely Richard Dale e-mail:[email protected]

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Abbas Habib

From Hydrocarbon process control perspective, the most difficult thing is understanding the process itself. That is why the most effective control engineers have process background. Implemting a single PID controller on a single input single output (SISO)process is simple enough and in most cases does not require knowledge of the transfer function of the process. However, even for SISO loops, tuning could be a challege and knowing the dynamics, such as dominant time constant and time delay, of the process will help great deal. Most processes are of high order dynamics, however, most can be reasonably modeled by first order plus dead time. Knowing the dominant time constant and dead time will enable the control engineer to improve PID control by adding some Lead lag compensation. Most Hydrocarbon processes are Multi Input Multi Output processes, i.e. changing the opening of one valve will most likely have an effect on two or more vaiables. Single PID controllers are not very effective in controlling MIMO processes. To handle the effect of intrecation, many techniques, such as decoupling,have been used. The most effective way of controlling a process with many inputs and many outpus is to implement Multi-Variable Controls (MVC). Implementing MVCs require good knowledge of modeling techniques. A dynamic model of the process is developed based on rigourous plant testing. An MVC model can be either FTIR or parametric. Understanding process dynamics is necessary to properly model the process. I have never used Bode plots and Nyquest diagrams in my practice as a control engineer.