Firstorder weighting function with specified DC gain, crossover frequency, and highfrequency gain
makeweight
is a convenient way to
specify loop shapes, target gain profiles, or weighting functions
for applications such as controller synthesis and control system tuning.
W = makeweight(dcgain,wc,hfgain)
W = makeweight(dcgain,wc,hfgain,Ts)
creates
a stable, firstorder, continuoustime statespace model whose frequency
response has the specified lowfrequency gain, crossover frequency,
and highfrequency gain. In other words, the response of W
= makeweight(dcgain
,wc
,hfgain
)W
satisfies:
$$\begin{array}{c}W\left(j\cdot 0\right)=\text{dcgain}\\ \leftW\left(j\cdot \text{wc}\right)\right=1\\ W\left(j\cdot \infty \right)=\text{hfgain}\text{.}\end{array}$$
The lowfrequency gain
and the highfrequency gain must satisfy either dcgain

< 1 < hfgain
 or hfgain

< 1 < dcgain
.
creates
a stable, firstorder, discretetime statespace model with the specified
sample time. The response of W
= makeweight(dcgain
,wc
,hfgain
,Ts
)W
satisfies:
$$\begin{array}{c}W\left({e}^{j\cdot 0\cdot \text{Ts}}\right)=\text{dcgain}\\ \leftW\left({e}^{j\cdot \text{wc}\cdot \text{Ts}}\right)\right=1\\ W\left({e}^{j\pi}\right)=\text{hfgain}\text{.}\end{array}$$
As in the continuoustime
case, the lowfrequency gain and the highfrequency gain must satisfy
either dcgain
 < 1 < hfgain

or hfgain
 < 1 < dcgain
.
In addition, the crossover frequency must satisfy wc*Ts
< π.
TuningGoal.LoopShape
 TuningGoal.WeightedGain
 TuningGoal.WeightedVariance
 dksyn
 hinfstruct
 hinfsyn
 ss