Create continuous-time weighting functions by specifying the low-frequency gain, high-frequency gain, and magnitude of the gain at some intermediate frequency.

For instance, create a weighting function with a gain of 40 dB at low frequency, rolling off to –20 dB at high frequency. Specify further that the gain is about 10 dB at 1 rad/s by putting these values in a vector [freq,mag]. Specify all the gains in absolute units.

Wl = makeweight(100,[1,3.16],0.1);

Create a weighting function with a gain of –10 dB at low frequency, rising to 40 dB at high frequency. Specify a 0 dB crossover frequency of 10 rad/s. To specify a 0 dB crossover frequency, you can use the crossover frequency as the second input argument instead of the vector [freq,mag].

Wh = makeweight(0.316,10,100);

Plot the magnitudes of the weighting functions to confirm that they meet the response specifications.

bodemag(Wl,Wh)
legend
grid on

Create a gain profile that rolls off at high frequency without flattening. Specify a gain of 40 dB at low frequency and a crossover frequency of 10 rad/s.

W = makeweight(100,[10 1],0);

Specifying a high-frequency gain of 0 ensures that the frequency response rolls off at high frequencies without leveling off. Plot the gain profile to confirm this shape.

bodemag(W)
grid on

Create discrete-time weighting functions by specifying the low-frequency gain, high-frequency gain, magnitude of the gain at some intermediate frequency, and sample time.

Create a weighting function with a sample time of 0.1 s. Specify a gain of 40 dB at low frequency, rolling off to –20 dB at high frequency. Specify further that the gain is about 10 dB at 0.01 rad/s. Provide all gains in absolute units.

Wl = makeweight(100,[0.01,3.16],0.1,0.1);

Create a weighting function with a gain of –10 dB at low frequency, rising to 40 dB at high frequency. Specify a 0 dB crossover frequency of 2 rad/s and a sample time of 0.1 s. To specify a 0 dB crossover frequency, you can use the crossover frequency as the second input argument instead of the vector [freq,mag].

Wh = makeweight(0.316,2,100,0.1);

Plot the magnitudes of the weighting functions to confirm that they meet the response specifications.

bodemag(Wl,Wh)
grid on

The high-frequency leveling of Wh is distorted due to the proximity of its crossover frequency to the Nyquist frequency.

By default, makeweight creates first-order weighting functions. If you want a sharper transition between the low-frequency and high-frequency gains, you can specify the order with the last input argument. For instance, suppose you want to create a weighting function with a sample time of 0.1 s. The function has a gain of –10 dB at low frequency, rising to 40 dB at high frequency. Additionally, the gain passes through 6 dB at 1 rad/s. For comparison, create both a third-order and a first-order function with these specifications.

W3 = makeweight(0.316,[1 2],100,0.1,3);
W1 = makeweight(0.316,[1 2],100,0.1);
bodemag(W3,W1)
legend('location','northwest')
grid on

For the first-order function, the high-frequency leveling is distorted due to the proximity of its crossover frequency to the Nyquist frequency. Using a sharper, higher-order transition ensures that the function has leveled out before reaching the Nyquist frequency.

To create continuous-time weighting functions of higher order, set Ts = 0. For instance, create continuous-time weighting functions with the same gain specifications as W1 and W3.

W3c = makeweight(0.316,[1 2],100,0,3);
W1c = makeweight(0.316,[1 2],100);
bodemag(W3c,W1c)
legend('location','northwest')
grid on