diff --git a/docs/@lti_pole.html b/docs/@lti_pole.html index 6f6d230..c5ca114 100644 --- a/docs/@lti_pole.html +++ b/docs/@lti_pole.html @@ -98,7 +98,7 @@

For SISO transfer functions, pole uses Octave’s roots. MIMO transfer functions are converted to - a minimal state-space representation for the + a minimal state-space representation for the computation of the poles.

diff --git a/docs/@lti_zero.html b/docs/@lti_zero.html index 2195fbf..5f1746d 100644 --- a/docs/@lti_zero.html +++ b/docs/@lti_zero.html @@ -182,7 +182,7 @@

For SISO transfer functions, zero uses Octave’s roots. MIMO transfer functions are converted to - a minimal state-space representation for the + a minimal state-space representation for the computation of the zeros.

References
diff --git a/docs/assets/control.png b/docs/assets/control.png index f08d195..912d77a 100644 Binary files a/docs/assets/control.png and b/docs/assets/control.png differ diff --git a/docs/assets/pzmap_101.png b/docs/assets/pzmap_101.png index 11879a2..d45b7a8 100644 Binary files a/docs/assets/pzmap_101.png and b/docs/assets/pzmap_101.png differ diff --git a/docs/assets/pzmap_201.png b/docs/assets/pzmap_201.png index 49e4756..73cd8ca 100644 Binary files a/docs/assets/pzmap_201.png and b/docs/assets/pzmap_201.png differ diff --git a/docs/assets/sgrid_101.png b/docs/assets/sgrid_101.png index 46b832e..9c49a28 100644 Binary files a/docs/assets/sgrid_101.png and b/docs/assets/sgrid_101.png differ diff --git a/docs/assets/sgrid_201.png b/docs/assets/sgrid_201.png index 97b7c19..f03635a 100644 Binary files a/docs/assets/sgrid_201.png and b/docs/assets/sgrid_201.png differ diff --git a/docs/assets/sgrid_301.png b/docs/assets/sgrid_301.png index 69c7232..80fb091 100644 Binary files a/docs/assets/sgrid_301.png and b/docs/assets/sgrid_301.png differ diff --git a/docs/assets/zgrid_101.png b/docs/assets/zgrid_101.png new file mode 100644 index 0000000..702b098 Binary files /dev/null and b/docs/assets/zgrid_101.png differ diff --git a/docs/gram.html b/docs/gram.html index 87f33e4..eaa35df 100644 --- a/docs/gram.html +++ b/docs/gram.html @@ -79,8 +79,8 @@

gram (sys, "o") returns the observability gramian of the (continuous- or discrete-time) system sys. gram (a, b) returns the controllability gramian - Wc of the continuous-time system dx/dt = a x + b u; - i.e., Wc satisfies a Wc + m Wc’ + b b’ = 0. + Wc of the continuous-time system d×/dt = a× + b u; + i.e., Wc satisfies a Wc + m Wc’ + b b’ = 0.

diff --git a/docs/index.html b/docs/index.html index 42ea30e..255d41d 100644 --- a/docs/index.html +++ b/docs/index.html @@ -61,7 +61,7 @@

control

- 3.5.2 2023-04-05 + 3.6.0 2023-05-20

Computer-Aided Control System Design (CACSD) Tools for GNU Octave

@@ -783,6 +783,14 @@

Singular values of frequency response. + + + + zgrid + + + Display an grid in the complex z-plane. +

diff --git a/docs/mixsyn.html b/docs/mixsyn.html index 6cd0eb8..97ea784 100644 --- a/docs/mixsyn.html +++ b/docs/mixsyn.html @@ -91,23 +91,23 @@

    -
  1. For disturbance rejection make +
  2. For disturbance rejection make \(\overline{\sigma}(S)\) small. -
  3. For noise attenuation make +
  4. For noise attenuation make \(\overline{\sigma}(T)\) small. -
  5. For reference tracking make +
  6. For reference tracking make \(\overline{\sigma}(T) \approx \underline{\sigma}(T) \approx 1\) -
  7. For input usage (control energy) reduction make +
  8. For input usage (control energy) reduction make \(\overline{\sigma}(K S)\) small. -
  9. For robust stability in the presence of an additive perturbation +
  10. For robust stability in the presence of an additive perturbation \(G_p = G + \Delta\) make \(\overline{\sigma}(K S)\) small. -
  11. For robust stability in the presence of a multiplicative output perturbation +
  12. For robust stability in the presence of a multiplicative output perturbation \(G_p = (I + \Delta) G\) make \(\overline{\sigma}(T)\) diff --git a/docs/ncfsyn.html b/docs/ncfsyn.html index d006c21..6c418f0 100644 --- a/docs/ncfsyn.html +++ b/docs/ncfsyn.html @@ -85,19 +85,19 @@

      -
    1. For disturbance rejection make +
    2. For disturbance rejection make \(\underline{\sigma}(W_2 G W_1)\) large; valid for frequencies at which \(\underline{\sigma}(G_S) \gg 1\) -
    3. For noise attenuation make +
    4. For noise attenuation make \(\overline{\sigma}(W_2 G W_1)\) small; valid for frequencies at which \(\overline{\sigma}(G_S) \ll 1\) -
    5. For reference tracking make +
    6. For reference tracking make \(\underline{\sigma}(W_2 G W_1)\) large; valid for frequencies at which \(\underline{\sigma}(G_S) \gg 1\) -
    7. For robust stability to a multiplicative output perturbation +
    8. For robust stability to a multiplicative output perturbation \(G_p = (I + \Delta) G\) make \(\overline{\sigma}(W_2 G W_1)\) @@ -121,7 +121,7 @@

      [K, N] = ncfsyn (G, W1, W2, f) The function ncfsyn - the somewhat cryptic name stands - for normalized coprime factorization synthesis - allows the specification of + for normalized coprime factorization synthesis - allows the specification of an additional argument, factor f. Default value f = 1 implies that an optimal controller is required, whereas f > 1 implies that a suboptimal controller is required, achieving a performance that is f times less than optimal. @@ -159,7 +159,7 @@

      K

      State-space model of the H-infinity loop-shaping controller. - Note that K is a positive feedback controller. + Note that K is a positive feedback controller.

      N
      diff --git a/docs/optiPID.html b/docs/optiPID.html index 10d0170..1716ad5 100644 --- a/docs/optiPID.html +++ b/docs/optiPID.html @@ -106,11 +106,11 @@

      \(r(t) = \varepsilon (t)\) in the time domain. In the frequency domain, the sensitivity \(M_s = ||S(jw)||_{\infty}\) - is minimized for good robustness, where S(s) denotes the sensitivity transfer function + is minimized for good robustness, where S(s) denotes the sensitivity transfer function $$ S(s) = \frac{1}{1 + L(s)} = \frac{1}{1 + P(s)\,C(s)} $$ The constants \(\mu_1,\, \mu_2 \mbox{ and } \mu_3\) - are relative weighting factors or «tuning knobs» + are relative weighting factors or «tuning knobs» which reflect the importance of the different design goals. Varying these factors corresponds to changing the emphasis from, say, high performance to good robustness. The main advantage of this approach is the possibility to explore the tradeoffs of diff --git a/docs/sgrid.html b/docs/sgrid.html index 72d42b5..10e8e3f 100644 --- a/docs/sgrid.html +++ b/docs/sgrid.html @@ -82,10 +82,8 @@

      Control the display of s-plane grid with :

        -
      • - zeta lines corresponding to damping ratios and -
      • - omega circles corresponding to undamped natural frequencies +
      • zeta lines corresponding to damping ratios and +
      • omega circles corresponding to undamped natural frequencies

      The function state input may be either "on" or "off" @@ -99,13 +97,9 @@

      where Z and W are : -

      -
        -
      • - Z vector of constant zeta values to plot as lines - -
      • - W vector of constant omega values to plot as circles +

          +
        • Z vector of constant zeta values to plot as lines +
        • W vector of constant omega values to plot as circles

        Example of usage: @@ -114,10 +108,8 @@

        sgrid toggle the s-plane grid visibility sgrid ([0.3, 0.8, …], [10, 75, …]) create:
         
          -
        • - zeta lines for 0.3, 0.8, … 
- 
        • - omega circles for 10, 75, … [rad/s] 
+
        •  zeta lines for 0.3, 0.8, … 
+ 
        •  omega circles for 10, 75, … [rad/s] 
  
         
         sgrid (hax, "on")   create the s-plane grid for the axis 
@@ -125,7 +117,8 @@

        See also: -grid +grid, + zgrid

        Source Code: sgrid diff --git a/docs/zgrid.html b/docs/zgrid.html new file mode 100644 index 0000000..8b39c72 --- /dev/null +++ b/docs/zgrid.html @@ -0,0 +1,169 @@ + + + + Computer-Aided Control System Design: zgrid + + + + + + + + + +

        +
        + +
        +
        +
        +
        +
        +
        +
        +

        + Function Reference: zgrid +

        +
        +
        +
        +
        +
        +
        Function File: zgrid
        +
        Function File: zgrid on
        +
        Function File: zgrid off
        +
        Function File: zgrid (z, w)
        +
        Function File: zgrid (hax, …)
        +
        +

        Display an grid in the complex z-plane. +

        +
        +

        Control the display of z-plane grid with : +

          +
        • zeta lines corresponding to damping ratios and +
        • omega lines corresponding to undamped natural frequencies +
        + +

        The function state input may be either "on" or "off" + for creating or removing the grid. If omitted, a new grid is created + when it does not exist or the visibility of the current grid is toggled. +

        +

        The zgrid will automatically plot the grid lines at nice values or + at constant values specified by two arguments : +

        +
         
         zgrid (Z, W)
+
        + +

        where Z and W are : +

          +
        • Z vector of constant zeta values to plot as lines +
        • W vector of constant omega values to plot as circles +
        + +

        Example of usage: +

         
         zgrid on	  create the z-plane grid
+ zgrid off 	remove the z-plane grid
+ zgrid		  toggle the z-plane grid visibility
+ zgrid ([0.3, 0.8, …], [0.25*pid, 0.5*pi, …])   create:
+
         
          +
        •  zeta lines for 0.3, 0.8, … 
+ 
        •  omega lines for 0.25*pi/T, 0.5*pi/T, … [rad/s] 
+
        +
        +
         zgrid (hax, "on")   create the z-plane grid for the axis 
+                     handle hax
+
        + +

        See also: +grid, + sgrid +

        +

        Source Code: + zgrid +

        +
        +
        +
        +
        +
        +

        + Example: 1 +

        +
        +
        +
        +
        +
        +
        + + + +
         
        +
+ clf;
+ num = [1 0.25]; den = [1 -1.5 0];
+ sys = tf(num, den, 1);
+ rlocus(sys,0.01,0,3.5);
+ ylim([-1.1,1.1]);
+ zgrid on;
+
+
        +
        + plotted figure +

        + +
        +
        +
        +
        +
        + + +
        +
        +
        + + +