Question B.13.1: Digital Control Systems We can convert G1(s) in cascade with...

Control Systems Engineering [EXP-57621]

Digital Control Systems

We can convert $G_{1}(s)$ 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 assumes $G_{1}(s)$ in cascade with a z.o.h.We simply put $G_{1}(s)$ into the command (the z.o.h. is automatically taken care of) and the command returns G(z). Let us apply the concept to Example 13.4. You will enter T through the keyboard.

This Question has been Answered.

Already have an account?

Login

The 'Blue Check Mark' means that either the MATLAB code/script/answer provided in the answer section has been tested by our team of experts; or the answer in general has be fact checked.

Learn more on how do we answer questions.

This Question has a MATLAB Verified Solution/Answer as well.

Already have an account?

Related Answered Questions

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)

Verified Answer:

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

Verified Answer:

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

Verified Answer:

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

Verified Answer:

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

Verified Answer:

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) =

Verified Answer:

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

Verified Answer:

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

Verified Answer:

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.

Verified Answer:

We can test observability using the MATLAB command Om=obsv(A , C)to find the observability matrix given the system matrix (A) and the output matrix (C). This command is followed by rank (Om) to test the rank of the observability matrix (Om). Let us apply the commands to Example 12.6.

Verified Answer: