Question

Problem 3 Figure 3: RC circuit and its step response. 1. Give an example of transfer functions $G$ and $K$ such that $\frac{1}{1+GK}$ and $\frac{G}{1+GK}$ are stable but $\frac{K}{1+GK}$ is not. 2. Give an example of transfer functions $G$ and $K$ such that $\frac{1}{1+GK}$ and $\frac{K}{1+GK}$ are stable but $\frac{G}{1+GK}$ is not. 3. (hard problem) Show that it is not possible to have both $\frac{K}{1+GK}$ and $\frac{G}{1+GK}$ to be stable with $\frac{1}{1+GK}$ unstable.

          Problem 3

Figure 3: RC circuit and its step response.

1. Give an example of transfer functions $G$ and $K$ such that $\frac{1}{1+GK}$ and $\frac{G}{1+GK}$ are stable but $\frac{K}{1+GK}$ is not.

2. Give an example of transfer functions $G$ and $K$ such that $\frac{1}{1+GK}$ and $\frac{K}{1+GK}$ are stable but $\frac{G}{1+GK}$ is not.

3. (hard problem) Show that it is not possible to have both $\frac{K}{1+GK}$ and $\frac{G}{1+GK}$ to be stable with $\frac{1}{1+GK}$ unstable.

Problem 3

Figure 3: RC circuit and its step response.

1. Give an example of transfer functions G and K such that (1)/(1+GK) and (G)/(1+GK) are stable but (K)/(1+GK) is not.

2. Give an example of transfer functions G and K such that (1)/(1+GK) and (K)/(1+GK) are stable but (G)/(1+GK) is not.

3. (hard problem) Show that it is not possible to have both (K)/(1+GK) and (G)/(1+GK) to be stable with (1)/(1+GK) unstable.

Added by Brooke A.

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