Abstract
In Chap. 5 a method for control system design is presented, which is known as the time response method. The main feature of such an approach is to suitably locate the closed-loop poles to ensure that the transient response satisfies the desired specifications. Fundamental for that method is to know how the transient response is affected by the closed-loop poles if these are real, complex conjugate, repeated or different, etc.
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Notes
- 1.
This is further explained later
- 2.
Recall that given three complex numbers z, x, y such that z = xy, the angle of z is given as the addition of the angles of x and y.
- 3.
The frequency where the compensated open-loop system must have a magnitude of 0[dB].
- 4.
According to Sect. 6.5, the phase margin and the gain margin are defined for minimum phase systems and, although the system studied here is non-minimum phase, (because of the unstable pole at s = 35.7377), the term phase margin is used to indicate the comparison of the system phase with respect to the fundamental phase − 180∘.
- 5.
Although the phase margin was introduced in Sect. 6.5 for minimum phase systems, this concept is also applicable in this example
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Hernández-Guzmán, V.M., Silva-Ortigoza, R. (2019). Frequency Response-Based Design. In: Automatic Control with Experiments. Advanced Textbooks in Control and Signal Processing. Springer, Cham. https://doi.org/10.1007/978-3-319-75804-6_6
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