What is ODE and DDE?
In this paper, by considering ordinary differential equation (ODE) as a special case and a starting point of delay differential equation (DDE), we will show that some typical topological methods such as continuation theorems can be applied to detect some dynamics of DDE like periodic solutions.
What is delay in math?
A delay differential equation is a differential equation where the time derivatives at the current time depend on the solution and possibly its derivatives at previous times: Instead of a simple initial condition, an initial history function needs to be specified. The quantities and are called the delays or time lags.
What is a delay system?
A system can be built with an inherent delay. Delays are units that cause a time-shift in the input signal, but that don’t affect the signal characteristics. An ideal delay is a delay system that doesn’t affect the signal characteristics at all, and that delays the signal for an exact amount of time.
How do you fix a delayed differential equation in Python?
Say you have a delay differential equation like this: {y(t)=g(t),for t<0y′(t)=F(y,t),for t≥0, where F(y,t) can involve delayed values of y, of the form y(t−d). y = ddeint(F, g, t) # returns [y(t1), y(t2) …]
What is a pure delay?
In physical systems, causality is in reality associated with some time delay or lags between cause and effect. An example of a pure time delay occurs when monitoring the temperature or composition of a liquid flowing in a pipe. It takes a time delay for a unit of fluid to get from one point to another.
What is delay margin?
The delay margin is defined as the largest time delay such that, for any delay less than this value, the closed-loop stability is maintained.
What is a gain margin?
Gain margin is defined as the amount of change in open-loop gain needed to make a closed-loop system unstable. The gain margin is the difference between 0 dB and the gain at the phase cross-over frequency that gives a phase of −180°. 2.25, meaning a positive gain margin, then the closed-loop system is stable.
How is gain margin calculated?
The gain margin is the amount by which the actual gain must be multiplied before the onset of instability. Thus if the plot cuts the negative real axis at –x (Figure 12.12), it has to be multiplied by 1/x to give the value −1 and so the gain margin, which is expressed in dB, is 20 lg(1/x).
What does negative gain margin mean?
A positive gain margin means how much the control system gain can be increased, while a negative gain gain margin means how much the control system gain can be reduced. Therefore, in response to various uncertainties, the control system should satisfy negative and positive gain margin and phase margin.
Why gain margin should be positive?
Note that at the gain crossover frequency the phase margin is indeed positive in order for the stability of the system to be preserved. In conclusion, regardless of the sign of the margins you have to check the region where these changes occur and whether or not the magnitude plot is close to 0dB.
How do you calculate delay margin?
Multiply numerator and denominator by the complex conjugate of the denominator. = delay margin = time delay for the system to be on the verge of instability.
What does negative gain mean?
Negative gain means the output is inverted from the input. For the gain to be negative, the output would have to go down when the input goes up, which is clearly not happening in your case.
Is withdraw positive or negative?
If a positive number is a deposit to a bank account, then a negative number is a withdrawal from that bank account. If a positive number is a quantity of minutes in the future, then a negative number is a quantity of minutes in the past. If a positive number means addition, then a negative number means subtraction.
How do I gain from dB?
Gain is defined as the ratio of the output power to the input power in dB. Assume that the input power is 10 mW (+10 dBm) and the output power is 1 W (1000 mW, +30 dBm). The ratio will be 1000/10 = 100, and the gain will be 10 * log 100 = 20 dB.
What is 3dB gain?
The frequency response of a device or a circuit describes its operation over a specified range of signal frequencies by showing how its gain, or the amount of signal it lets through changes with frequency. These half power points corresponds to a fall in gain of 3dB (0.7071) relative to its maximum dB value.
What is the 3dB rule?
3dB rule when measuring noise at work When you measure noise levels with a noise meter, you measure the intensity of noise in units called decibels, expressed as dB(A). It is based on orders of magnitude, rather than a standard linear scale, so each mark on the decibel scale is the previous mark multiplied by a value.
Why 3dB is cut off?
The -3dB point is very commonly used with filters of all types (low pass, band pass, high pass…). It is just saying the filter cuts off half of the power at that frequency. The rate at which it drops off depends on the order of the system you are using. Higher order can get closer and closer to a “brick wall” filter.
How is 3dB calculated?
The cut-off frequency or -3dB point, can be found using the standard formula, ƒc = 1/(2πRC). The phase angle of the output signal at ƒc and is -45o for a Low Pass Filter.
What is 3dB loss?
A 3 dB loss means half the power. For example, a system with 40 watts of input power and a 6 dB insertion loss will only have 10 watts of output power. dB: Decibel, a logarithm (equal to 10 times) ratio of the difference between two values.
What is 3 dB bandwidth?
The 3 dB bandwidth is the frequency at which the signal amplitude reduces by 3 dB i.e. becomes half its value. The bandwidth of a bandpass filter is usually defined as the 3 dB bandwidth.