# Control Theory Application?

KiltedEngineer
Hello Everybody,

Im a third year MechE student and I am focusing my studies on thermodynamics and control theory. I am getting really deep into the controls right now and after taking some introductory courses there are so many things that puzzle me even though I understand the actual theory.

This may sound stupid but I have no idea how to apply all of this theory that I have learned. For instance, I have learned about impulse response and how it demonstrates in the simplest way how a system responds to an input. However, I struggle with realizing why this is important. It seems that controlling an electric motor is as simple as switching it on and off or using something analog tomcontrol speed. Our teacher always says that wenused State Space (which I have only heard of, not studied) ro get to the moon, but what exactly does that mean?

The other thing that really puzzles me is how to interpret the mathematics. For example in Thermo, we can calculate the temperature ofmamstatenin a cycle and use that data to choose/design a suitable material in order to withstand that temperature. However control theory does not seem as clear cut. How to we translate the datanwe received into an actual application. Like if we analyze a problem in matlab, what do we use to put it into the real world? How do we use a transfer function to design a control system and why?

I probably sound very stupid, and the question may not be very clear but any response is appreciated.

Thanks

Homework Helper
Gold Member
That right thumb banging "n" and "m" instead of the space bar is enough to drive me nuts.
How do we use a transfer function to design a control system and why?
The "How" and the "Why?"
Let's invert that and deal with the "Why" or whole point/object/goal of controlling a process. How many times a day do you turn on a tap to fill a glass of water? How often do you spend five to ten minutes waiting for water to dribble in to fill the glass? How many times is the glass smashed from your hand into the bottom of the sink by a 500 psi jet? Somebody at the water works is applying control theory/state space to the water distribution system. Natural gas distribution, electric power production, transmission, voltage and frequency regulation. Thermostats for HVAC, ovens, refrigerators.
"How?" You pick a "set point" for a system in "state space" for that system, and design/engineer a graceful approach (or departure) to (from) that set point for start-up (or shut-down). That "set point" may be fixed as for utilities like water, gas, or electric power, or variable as for "smart weapon systems" or navigation systems (avionics, marine auto-pilots). You have a range of control outputs for approaching/maintaining set points ranging from "on/off" (bang/bang steering) through proportional (to error signal), then proportional plus integral, to proportional plus integral plus derivative (requiring a second error input "anticipating" variations in feedstock composition/quality for process streams, or heating values of fuels for furnaces/boilers, or other "upset" conditions). The analog methods are more from my era, and have been replaced by digital mimicry and possibility some improved algorithms with which I am not familiar, and that's what you are studying.
Hopefully, that helps you a little with the "how and why."

Mentor
That right thumb banging "n" and "m" instead of the space bar is enough to drive me nuts.

:-)

arunsjunk
The difference in the example you gave between thermodynamics and control theory is in the way you learn about systems. The way you learned thermodynamics is prescriptive, i.e., if X happens, do Y. Control theory is in developing the prescription itself. It is possible for engineers to learn engineering completely prescriptively, basically learning rules of thumb. However to truly understand engineering, physics and any other subject you have to go beyond practical rules of thumb, by understanding how a system behaves. You know you understand a system if you can predict its states over time in some prescribed environment.

Control theory provides tools to understand how a system behaves in an environment, and state space is one type of system representation. Transfer functions (impulse response) are one way to represent how a system behaves in frequency (time) domain given some actuation, e.g., turning on a motor. By measuring the system response to actuator input(s), we could develop a model to predict the system response if we actuated the system over time in a certain way. More importantly, if we desire the system to respond in a certain way, we could derive the actuator input as a function of time to achieve it. So, instead of just turning the motor on/off, we could provide a motor more/less power to achieve some objective more efficiently and reliably (turning a motor on/off could induce wear and tear).