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Essentials of Control Techniques and Theory_7

Tham khảo tài liệu 'essentials of control techniques and theory_7', kinh doanh - tiếp thị, quản trị kinh doanh phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 148 Essentials of Control Techniques and Theory Figure 11.1 Oscilloscope measurement of phase. favorite. Soon time-domain and pseudo-random binary sequence PRBS test methods were adding to the confusion but they have no place in this chapter. 11.2 The Nyquist Plot Before looking at the variety of plots available let us remind ourselves of the object of the exercise. We have a system that we believe will benefit from the application of feedback. Before closing the loop we cautiously measure its open loop frequency response or transfer function to ensure that the closed loop will be stable. As a bonus we would like to be able to predict the closed loop frequency response. Now if the open loop transfer function is G s the closed loop function will be Gk 11.1 This is deduced as follows. If the input is U s and we subtract the output Y s from it in the form of feedback then the input to the inner system is U s Y s . So Y S G S U S - Y S i.e. 1 G s Y s G s U s so Y s 1G u s We saw that stability was a question of the location of the poles of a system with disaster if any pole strayed to the right half of the complex frequency plane. Where will we find the poles of the closed loop system Clearly they will lie at the More Frequency Domain Methods 149 values of 5 that give G s the value -1. The complex gain -1 j0 is going to become the focus of our attention. If we plot the readings from the phase-sensitive voltmeter the imaginary part against the real with no reference to frequency we have a Nyquist plot. It is the path traced out in the complex gain plane as the variable s takes value jw as 0 increases from zero to infinity. It is the image in the complex gain plane of the positive part of the imaginary s axis. Suppose that G s -- 1 s then G j WTh7 1 j 1 - j 1 2 1 2 j 1 2 If G is plotted in the complex plane as u jv then it is not hard to show that u2 v2 u 0 This represents a circle though for genuine frequencies with positive values of w we can only plot the lower .