"Wisdom begins in wonder" – Socrates
Category: Mathematics
Minimum Phase Systems
08/20/17
“What do we call systems that have all poles and zeros inside the unit circle?”
Systems that have all poles and zeros inside the unit circle are very special. Why? Well, because with these systems, their causal system will be completely stable and will have a phase lag less than a system of identical magnitude. Since these systems are so special, controls and signal engineers have termed them Minimum Phase Systems.
Unity feedback
08/19/17
“When is the output unchanged from the input of a control block?”
In control systems, the output of a control block is usually modified from the input. However, when there is no change, the process is said to be in unity feedback
Closed-loop Summing Points
08/19/17
“What are the points on a control diagram for comparing the output and the setpoint?”
What makes a closed-loop control system truly closed loop is the comparison of the output and setpoint for making the error value. However, how is this represented on a control diagram? Well, Control Engineers like to use something called a Closed-loop Summing Point. Closed-loop Summing Points are small circular elements on a diagram that takes in an input on one quadrant, the setpoint on another and then produce the error term. Depending on the signs of the quadrant, the input value might be positive (for a + sign) or negative (for a – sign)
Tracking control
08/18/17
“How can we measure the disturbance between a setpoint and an output?”
When a closed loop control system sends an output, it must be compared to an initial setpoint. This process is known as tracking control and is one of the most fundamental parts of every control system
Closed-loop Control Systems
08/18/17
“How can we have a self-correcting control system?”
Open loop control systems may be affordable, but the lack of control over them (pun intended) makes them useful for only select applications. So how can we fix this problem? Well, what if every time our system was to produce an output, we compare it to our setpoint, and then modify the process to achieve our desired result accordingly? This is the fundamental idea behind a closed-loop control system and is used in a vast array of controls applications from electric vehicle battery life monitoring to drones and even laundry machine monitoring.
Controls gain
08/18/17
“What is the amplification of a controls system?”
When a signal passes through a transfer function, its output will be modified in an according way depending on its frequency. So what do we call the change of magnitude of the signal? Well, after much debate, controls researchers have settled on the idea of gain to describe this. Gain is defined as the ratio of the new magnitude to the old magnitude, such that a system that is twice as large will have a magnitude of 2 and half the size would be 1/2
Final Value Theorem
08/17/17
“How can we convert from the s to time domain without using a Laplace transform?”
Taking an inverse Laplace transform of a function from the s to time domain is very useful but quite difficult, so is there a way that we can get around it for specific case? Well, after years of hard work, mathematicians have discovered that if you multiply the frequency function by s and take its limit as it approaches zero (lim s–>0 s*f(s)) then it would actually be equal to the value of the time domain function at infinity! The proof is shown in the picture above
Dead Reckoning
08/17/17
“How can we make a location history using past velocities?”
Making a location history can be very difficult. Having to make active GPS measurements for a cycle of intervals is very taxing on resources. However, is there a way that we could circumvent this and make a new less resource intense system? Well, let’s start off by thinking back to basic physics. We know that velocity multiplied by time equals a change in distance. So what if were to start off with an initial GPS location and then build an array of all of the measured velocities after that? Well, this is the fundamental ideas behind a technique known as Dead Reckoning and is commonly implemented in control systems and machines that are equipped to go into no-GPS locations.
Integral Control
08/17/17
“How can control systems be based on the summation of error levels over time?”
Control systems respond to an error between feedback and setpoints by making changes to the next output. However, sometimes the error does not change fast enough or it changes too quickly. So how could we devise a mechanism to solve this issue? Well, let’s start with a simple idea. We know that if an error value were to persist over time it would show easily on a graph. So what if we were to just take the area of the error under this graph and modify our outputs accordingly? This is the fundamental idea behind integral control and is one of the prime factors in the ever so often used PID control system.
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