Consider the plant defined by (Y(z))/(U(z))=(0.6 z+0.5)/((z-1)^2) Using the polynomial equations

Step 1: First, we need to find the difference equation that represents the given plant. The tran

Question

Consider the plant defined by $$ \frac{Y(z)}{U(z)}=\frac{0.6 z+0.5}{(z-1)^2} $$ Using the polynomial equations approach, design a control system such that the system will behave like the following model, $G_{\text {model: }}$ $$ G_{\text {medet }}=\frac{2 z-1}{z^2} $$ Obtain the unit-step response and unit-ramp response of the designed system (which is the same as $G_{\text {model }}$ ) The sampling period $T$ is $1 \mathrm{sec}$.

   Consider the plant defined by
$$
\frac{Y(z)}{U(z)}=\frac{0.6 z+0.5}{(z-1)^2}
$$
Using the polynomial equations approach, design a control system such that the system will behave like the following model, $G_{\text {model: }}$
$$
G_{\text {medet }}=\frac{2 z-1}{z^2}
$$

Obtain the unit-step response and unit-ramp response of the designed system (which is the same as $G_{\text {model }}$ ) The sampling period $T$ is $1 \mathrm{sec}$.

Discrete-Time Control Systems (Pie)

Katsuhiko Ogata 2nd Edition

Chapter 7, Problem 8

Instant Answer

Step 1

The transfer function of the plant is given as $$ \frac{Y(z)}{U(z)}=\frac{0.6 z+0.5}{(z-1)^2} $$ To find the difference equation, we can use the inverse Z-transform. The inverse Z-transform of $\frac{0.6 z+0.5}{(z-1)^2}$ is $0.6(n+1)u(n)+0.5(n+1)u(n)$, where Show more…

Show all steps

Thanks for your feedback!

Consider the plant defined by $$ \frac{Y(z)}{U(z)}=\frac{0.6 z+0.5}{(z-1)^2} $$ Using the polynomial equations approach, design a control system such that the system will behave like the following model, $G_{\text {model: }}$ $$ G_{\text {medet }}=\frac{2 z-1}{z^2} $$ Obtain the unit-step response and unit-ramp response of the designed system (which is the same as $G_{\text {model }}$ ) The sampling period $T$ is $1 \mathrm{sec}$.

Play audio

Feedback

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later

Please give Ace some feedback