Question B.4.4: (Antenna Control Case Study) We now use MATLAB to plot the s...

(Antenna Control Case Study) We now use MATLAB to plot the step response requested in the Antenna Control Case Study.

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Let us now use MATLAB to design a digital lead compensator. The s-plane design was performed in Example 9.6. Here we convert the design to the zplane and run a digital simulation of the step response. Conversion of the s-plane lead compensator, Gc(s)=numgcs/dengcs, to the z-plane compensator, Gc(z)

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We now use the root locus to find the gain to meet a transient response requirement.AfterMATLAB produces a z-plane root locus, alongwith damping ratio curves superimposed using the command zgrid, we interactively select the desired operating point at a damping ratio of 0.7, thus determining the

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We now use the root locus to find the gain for stability. First, we create a digital LTI transfer-function object forG(z) = N(z)/D(z), with an unspecified sampling interval. The LTI object is created using tf(numgz, dengz,[ ]), where numgz represents N(z), dengz represents D(z), and [ ] indicates

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Wecan useMATLAB’s commanddcgain(Gz)to find steadystate errors. The command evaluates the dc gain of Gz, a digital LTI transfer function object, by evaluating Gz at z = 1. We use the dc gain to evaluate, Kp, Kv, and Ka. Let us look at Example 13.9 in the text. You will input T, the sampling interval

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We can use MATLAB to find the gain for stability. Let us look at Example 13.6 in the text.

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We also can use MATLAB to convert G(z) to G(s) when G(s) is not in cascade with a z.o.h. First, we create a sampled LTI transfer function, as discussed in ch13p3. The command F=d2c(H,’zoh’) transforms H(z) to F(s) in cascade with a z. o.h., where H(z) = ((z – 1)/z)z{F(s)/s}. If we consider F(s) =

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Creating Digital Transfer Functions Directly Vector Method, Polynomial Form A digital transfer function can be expressed as a numerator polynomial divided by a denominator polynomial, that is, F(z) = N(z)/D(z). The numerator, N(z), is represented by a vector, numf, that contains the coefficients

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We also can use MATLAB to convert G(s) to G(z) when G(s) is not in cascade with a z.o.h. The command H=c2d(F , T , ‘zoh’)transforms F(s) in cascade with a z.o.h. to H(z), where H(z) = ((z – 1)/z)*z{F(s)/s}. If we let F(s) = sG(s), the command solves for H(z), where H(z) = ((z – 1)/z)*z{G(s)}. Hence

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Digital Control Systems We can convert G1(s) in cascade with a zero-order hold (z.o.h.) to G(z) using MATLAB’s G= c2d (G1 ,T ,’ zoh’)command, where G1 is an LTI continuous-system object and G is an LTI sampled-systemobject. T is the sampling interval and ‘zoh’is a method of transformation that

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We can design observer gains using the command l = acker (A’ ,C’ , poles)’ without transforming to observer canonical form. Let us look at Example 12.8 in the text.

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