www.gusucode.com > control 案例程序 matlab源码代码 > control/PlotSectorIndexVersusFrequencyExample.m
%% Plot Sector Index Versus Frequency % Plot the sector index to visualize the frequencies at which the I/O % trajectories of $G\left( s \right) = \left( {s + 2} \right)/\left( {s + % 1} \right)$ lie within the sector defined by: % % $$ S = \left\{ {\left( {y,u} \right):0.1{u^2} < uy < 10{u^2}} \right\}. $$ %% % In U/Y space, this sector is the shaded region of the following diagram. %% % % <<../sector_diagram1.png>> % %% % The Q matrix for this sector is given by: a = 0.1; b = 10; Q = [1 -(a+b)/2 ; -(a+b)/2 a*b]; %% % A trajectory $y\left( t \right) = G{\kern 1pt} u\left( t \right)$ lies % within the sector _S_ when for all _T_ > 0, % % $$0.1\int_0^T {u{{\left( t \right)}^2} < } \;\;\int_0^T {u\left( t % \right)y\left( t \right)dt < } \;\;10\int_0^T {u{{\left( t \right)}^2}dt} % .$$ %% % In the frequency domain, this same condition can be expressed as: % % $${\left( {\begin{array}{*{20}{c}} {G\left( {j\omega } \right)}\\ 1 % \end{array}} \right)^H}Q\left( {\begin{array}{*{20}{c}} {G\left( {j\omega % } \right)}\\ 1 \end{array}} \right) < 0.$$ % %% % To check whether |G| satisfies or violates this condition at any % frequency, plot the sector index for |H = [G;1]|. G = tf([1 2],[1 1]); sectorplot([G;1],Q) %% % The plot shows that the sector index is less than 1 at all frequencies. % Therefore, the trajectories of G(s) fit within in the specified sector Q % at all frequencies.