Delay in control systems
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There are first-order lag and second-order lag in control systems; what is the difference between them?
Lag variables are often used in time series analysis. This is because the difference between time series analysis and systems of equations lies in the fact that systems of equations consider the relationships between variables from the perspective of causality, whereas time series analysis focuses on the characteristics of the sequence itself. Therefore, for a time series, the values at each point in time are all information that affects the model’s determination of future values. Here, the variable value at a later time point is the lagged variable. In other words, using a certain time as a reference point, the previous time point is at a first-order lag with respect to this reference time, while the time point before that is at a second-order lag.
It is explained in the book on automatic control; it’s mainly due to the differences in parameters – one is fast, and the other is slow
The output Y(T) of a discrete control system at time T is determined not only by the input R(T) at that time, but also by the inputs and outputs from earlier times: R(T‑t), Y(T‑t), R(T‑2t), Y(T‑2t), R(T‑3t), Y(T‑3t), and so on. By using a zero-order holder in the control system, the influence of inputs and outputs from times far away from T on Y(T) can be reduced, thereby minimizing high-frequency disturbances; however, inputs and outputs from times closer to T, such as T‑t and T‑2t, still have an impact on the output at time T
Simply put, first-order lag refers to a single-volume lag; the transfer function is 1/(T1*s+1), and the step response curve has no inflection points； Second-order lag is a double-volume lag, equivalent to two volume elements connected in series, with a value of 1/((T1*S+1)*(T2*S+1)); the response curve has an inflection point. ============ The above explanation is not an exact concept; it is merely intended to aid in simple understanding. Installing Matlab and giving it a try is the most straightforward approach.
First-order lag and second-order lag – I heard about them for the first time; it’s quite informative. I only know that there is a pure lag: L.