I cannot find out how you would show the unit circle centered at -1 on a Nyquist plot.

When I plot `nyquist(L)` with `L(s) = P(s)*C(s)` being my loop function, it only shows the nyquist plot itself. Using `grid on` also doesn't do this.

Once you create your Nyquist plot, use `hold on;` so we can draw a circle in MATLAB on top of your Nyquist plot. If you recall from polar co-ordinates, we can parameterize a point on a circle to be the following:

• `x = r*cos(theta);`
• `y = r*sin(theta);`

`r` would be the radius of your circle while `theta` is the angle it makes with respect to the origin. `theta` has its domain between `[0,2*pi]`. For the unit circle, `r = 1`. We would then substitute angles (`theta`) between 0 to `2*pi`. You also need to shift your circle so that the origin is at `Re = -1, Im = 0`. As such, do this:

``````n = 1000; %// Define number of points on circle
theta = linspace(0, 2*pi, n);
x = cos(theta);
y = sin(theta);
nyquist(L); %// Spawn Nyquist plot
hold on;
plot(x-1, y); %// Unit circle
``````

Here's a quick example for you. Using `L = tf(9, [1 6 9]);` to represent our transfer function of the open-loop system, using the above code produces the following plot: Bear in mind that I had to adjust the limits of the axis so you could see the unit circle. I did this by invoking`axis` in the following way after the plot was shown:

``````axis([-2 2 -1 1]);
``````

The real axis limits span from -2 to 2, and the imaginary axis limits span from -1 to 1.

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