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Because sinusoids have some important mathemtical properties. The first being how they behave under differentiation and integration. $$\frac{d}{dt}\sin(\omega t+\varphi) = \omega\cos(\omega t+\varphi) = \omega\sin(\omega t+\varphi+\frac{\pi}{2})$$ In other words when we differentiate or integrate a sinusoid we get a sinusoid of the same frequency. The ...


26

Gain and phase margin are usually applied to systems that are amplifiers of some sort with negative feedback around them. The more negative feedback, the tighter the system is controlled. However, you don't want to provide feedback in such a way that the system will oscillate. The gain and phase margin are two metrics to tell you how close the system is ...


24

The main point of a stepper motor is that you get discrete steps. However, the cost is larger size and lower efficiency than a continuous motor of the same torque. Stepper motors also have a low upper speed. The advantage of discrete steps can outweigh the various disadvantages when the system can be controlled open loop. If you're going to provide ...


23

Introduction First, we need to consider what exactly is this thing called the impulse response of a system and what does it mean. This is a abstract concept that takes a little thinking to visualize. I'm not going to get into rigorous math. My point is to try to give some intuition what this thing is, which then leads to how you can make use of it. ...


20

If we apply a sinusoidal signal into a linear time-invariant system (LTI), the output of that system will also be sinusoidal, of same frequency, but possibly different phase and magnitude. If we apply an input that can be described as a sum of sinusoids, output will also be the sum of sinusoids of same frequency, possibly different phase and magnitude. This ...


19

These calculations are absolutely used by professional EEs, for some on a daily basis. However, for many this job has been given to simulation software, such as LTSpice, which is also used on a daily basis. Generally the simulation is much faster to complete, so it is much more productive than doing the calculations by hand. I generally use the formulas ...


19

No, e(t) being zero does not imply that u(t) is also zero. It only implies that the output of the "P" process is zero. Remember, the "I" and "D" processes have memory — they depend on the past behavior of e(t). u(t) is zero only if the sum of all three processes is zero.


15

Your problem is called Integral Windup, it's a common control problem. In a non-linear or otherwise bounded region, the controller can't track the setpoint, and the integral increases to a large value. This causes a large overshoot when the setpoint is finally reached, which is exactly what you have deduced is the problem. The simplest solution is to limit ...


15

A LDO is a control loop. And like all control loops, there is always room for instability. So how do you make a control loop stable ? You provide sufficient phase margin (difference in phase from when the gain crosses the 0 dB axis and 180. The slope of open loop plot should be -20db/dec when crossing the 0dB axis Provide sufficient gain margin If you ...


14

Avoid ceramic capacitors and ceramic components for applications under environmental conditions that include vibrations and shocks. If you can't avoid them, choose components that use materials or constructions techniques targeted to minimise the so-called "microphonics". Also, use microphonics minimisation design strategies on your own. Microphonics is an ...


14

A pure sine wave is an useful test signal because it has a special property, it contains only energy at a single frequency, while other waveforms contain energy on multiple frequencies. So depending on what is being tested, a sine wave or other waveforms may be used. With a sine wave generator and a tool that can simply measure amplitude of sine wave (e.g. ...


13

You refer to these basic formulae at first and then find the real world has a lot of non-linear characteristics like XOR phase detectors in a second PLL loop response when you exceed the phase limit or that all Low Pass filters cause Inter-Symbol-Interference (ISI) unless the filter resonates within the binary symbol then you apply "Raised Cosine" Filters ...


13

This is not actually particularly rare. In industrial systems, stepper motors with encoder feedback are relatively common. And for hobbyists, there is e.g. the Mechaduino project. There are several benefits to using feedback with stepper motors: Does not lose position when overloaded. Can handle higher torque loads, because the feedback keeps magnetic ...


11

This is exactly why I think people should study stability first using Nyquist plots, THEN using bode plots and the associated gain and phase margin diagrams. The gain/phase margins are just a convenient way of determining how close the system gets to having poles on the right side of the complex plane, in terms of how close the nyquist plot gets to -1, ...


11

Okay, after a lot more research, I think I've gotten to the bottom of this. Actually I'm certain it's only approaching the bottom, as I've found this topic area quite deep, but I think I've gotten close enough to shed some light. A basic misconception A turning point in my understanding was when I realized that the equation I led off with in the OP: $$ G =...


11

Only sine wave don’t have harmonics (frequency spectrum at integer multiples of the main periodic frequency), which have energy, and thus can radiate RF above and outside the fundamental frequency. See “Fourier”. Testing with a non-sinewave also tests at all those harmonic frequencies, which, if not being done intentionally, can end up messing up the test ...


10

"The older high-dropout regulators with N-type transistors didn't seem to have this problem. " The answer is as follows: The npn-type transistor used as a control element is operated in a common-collector configuration (collector potential must be higher than that of the emitter). In contrast - as shown in the figure (provided by efox29) - the pnp type has ...


10

How to tune a PID controller to a nonlinear process? You don't. You linearize the process, then have the PID controller work on the linear values. By "linearize the process", I don't mean to actually make the process itself linear. That usually can't be done due to physics. However, you can put something non-linear between the output of the PID ...


10

Feed forward refers to the direction of the signal flow. For feed forward, the direction is, well, forward :-) I think it is easier to show an example. I know that many "sigma-delta" ADCs (analog to digital converters) use a combination of feedback and feed forward. I found an example of a block diagram of such an ADC here in this article, about Higher-...


10

Mars rovers don't move very fast, that is an important part. The "drivers" from Earth plan a rover movement for months, testing out scenarios, studying the topography, etc. Specific movements are planned the day before and are coded up, simulated, and when everything checks out, are sent to the rover as commands. For example, the Spirit Rover was (is) on ...


9

A convention is that the normal arrows indicate data flow, and the 'through the box' arrow indicates changing the properties of the box. (A bit like the wiper arrow in a variable resistor or capacitor, or a thermistor (NTC).) This can of course be seen as just another type of data input, but it is often used to indicate an input that has more 'fundamental' ...


9

If you understood what those terms meant you wouldn't be asking this, so I'll explain open loop and closed loop. Open loop means you pick the set point of a system and whatever comes out comes out. No system is perfectly "stiff", so the output will vary somewhat, sometimes quite a lot, depending on load. Closed loop is when something is actively watching ...


9

This is talking about a simple proportional controller. The control output is merely the system output minus the control input times some constant:   C = K(I - S) Where I is the control input to the system, S the actual system response, C the control output that drives the system, and K the proportionality constant. The tank example above is a ...


9

A good example is driving a car around a curve. In a pure feedback system, you go straight until the error signal tells you that you're not in the center of the lane anymore, then adjust the steering to compensate. Humans look ahead and see that a curve is coming up, and actually turn the wheel a little before entering the curve. This pre-compensates for ...


9

For prototype devices (which should last several months and are OK to fail occasionally), it is usually enough to mount the PCB on rubber inserts instead of bare screws). This greatly reduces peak accelerations your PCB sees, while keeping your prototype accessible and requiring minimum design changes: For commercial products which should last 10 years or ...


9

Provided you don't miss a step, a stepper motor should give you a deterministic movement. You can run it N steps forwards and N steps backwards and it will be in the same place. This is because the steps are discrete. Problems arise if it jams or you try to drive it too fast. Many systems have a simple means of resetting to a known state through a limit ...


9

A control system is only as good as it's sensor, run the sensor open loop and remove the control input. Create your own input to the sensor and slide it slowly (or find a way to slide it slowly reliably) while taking position data to make sure it's not the sensor. If the sensor is noisy, then improve the performance of the sensor by getting a new sensor or ...


9

Both, the automatic washing machine and the traffic signal system are open-loop for the same reason the website mentions for the home heating system. An open-loop system usually has a timer which instructs the system to switch on the furnace for some time and then switch it off. The Washing machine uses a timer to turn on and turn off washing and drying ...


8

Other math intensive fields of electrical engineering are signal processing (which includes the detection of signals in noise as well as spectral analysis and reconstruction of distorted signals) and communications (which includes coding theory and cryptography). Also theoretical circuit analysis is highly mathematical.


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