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By Derek Atherton

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6). 4. 3 Illustrative root locus plot. The gain range for the root locus plot is selected automatically but as for Ȧ in a frequency response may be selected if preferred by the command K=linspace(a,b,n), which generates n points linearly spaced from a to b, inclusive, and then use of the plotting command rlocus(G,K). When a root passes into the rhs s-plane the closed loop becomes unstable. com 63 More on Analysis of the Closed Loop System Control Engineering the imaginary axis coordinate. This condition is often referred to as being neutrally stable, since mathematically a constant amplitude oscillation exists.

12) jZ , and writing G ( jZ ) in the form X (Z )  jY (Z ) gives 2 and Y (Z ) (1  Z 2 ) 2  (1  Z 2 ) . Clearly as Z o 0 , X (Z ) o 2 , not the (1  Z 2 ) 2 imaginary axis, although the phase does tend to -90°. This will always be the case that the locus for a transfer function with one or more integrators will tend to an asymptote which in principle can be calculated. The Nyquist plot of this transfer function is obtained with the instruction nyquist(G). com 46 Frequency Responses and Their Plotting Control Engineering Information about where a Nyquist plot cuts the axes can be obtained from the facts that the real axis is cut when Y(Ȧ) = 0 or arg G(jȦ) = 0° or 180°, and the imaginary axis when X(Ȧ) = 0 or arg G(jȦ) = -90° or +90°.

For example, if the output controlled variable is a temperature and the control system error channel uses voltage then H will have units of °C/V. The importance of H cannot be underestimated since if the sensor is supposed to give 5V at 50°C but actually gives 5V at 48°C the perfect control system with its reference set to 50°C will control the temperature at 48°C. In other cases H will contain dynamics of the sensor and/or loop compensation dynamics. Some sensors introduce a significant noise level into the loop and this can be represented by the signal, N, shown.

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Control Engineering - An introduction with the use of Matlab by Derek Atherton

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