Open loop control
“How can we make a simple control system?”
Control systems can be very complicated in nature due to their reliance on feedback systems. However, if we want, we can make our systems much more flexible if we take away such a mechanism. This is known as an open loop control. An example of an open loop control is a movement mechanism that pushes an object towards a destination regardless of what is in the way. If we were to model this on a control diagram, then the input would go straight to the output and never come back (hence the name open loop)
Linear and Time Invariant Systems
“What is the most ideal form for controls systems?”
There is a motley of types of control systems out there. So before we begin any sort of analysis, let’s start with the most simple form, known as Linear and Time Invariant Systems. LTI systems have three properties.
- Homogeneity If an input signal is scaled by a constant then the output will be scaled by the same constant
- Superposition If two unique inputs are summed together, then the sum of their outputs will be produced.
- Time Invariance The system will perform the same way no matter what the time is.
Unfortunately, Most controls systems are not LTI systems, but they are still important to study due to their easy to solve structure.
“How can we take a function in the time domain and put it into the frequency domain?”
When dealing with signals, we are sometimes only given information about the time domain or frequency domain, even though it would be nice to see the other side. So how can we transform this information to suit our need? Well, let’s think about it. We know that we can decompose a continuous signal into multiple sine waves of varying frequency.
If we wanted to convert from frequency to time, what if we were to go through all of the frequencies, take the area under the curve to be an amplitude and multiply it by a sine wave with its prescribed period? Well, this is the fundamental idea behind an Inverse Fourier transform and can be represented by the equation f(s) = 1/(2pi) * (integral from -infinity to +infinity)f(omega)*e^(i*omega*t)d omega
The normal Fourier Transform simply goes in reverse and can be represented by the equation f(t) = (integral from -infinity to +infinity)f(omega)*e^(-2pi*i*omega*t)dt
Fourier transforms are the bedrock foundation of signal processing, making it possible for complex control systems to exist