### 6.7. BODE-DIAGRAM APPROACH

The Bode-diagram approach [8] is one of the most commonly used methods for the analysis and synthesis of linear feedback control systems. This method, which is basically an extension of the Nyquist stability criterion, has the same limitations and uses as the Nyquist diagram. The presentation of information in the Bode-diagram approach, however, is modified to permit relatively quick determinations of the effects of changes in system parameters without the laborious calculations associated with the Nyquist diagram.

**Table 6.6. MATLAB Program for Converting from the Transfer Function to the State-Space Form**

num = [0 0 0 1]; |

den = [1 2 1 0]; |

[A, B, C, D] = tf2ss(num,den) |

A= |

−2 −1 0 |

1 0 0 |

0 1 0 |

B = |

1 |

0 |

0 |

C = |

0 0 1 |

D = |

0 |

**Table 6.7. MATLAB Program for Determining the Nyquist Diagram from the State-Space Form**

A = [−2 −1 0; 1 0; 0; 0 1 0];
B = [1;0;0]
C = [0 0 1];
D = [0];
nyquist(A,B,C,D)
axis([−1.8 0 −2.5 2.5])
grid
title(‘Nyquist plot of G(s) ∗ H(s) = 1/[s ∗ (s + 1)^2]’) |

The Nyquist diagram gives the amplitude and phase of the open-loop transfer function *G*(*s*)*H*(*s*) as *s* traverses a contour that encloses the right half-plane. As *s* traverses the positive imaginary axis, it has the value of real frequency *ω*, and the plot corresponds to *G*(*jω*)*H*(*jω*). We can illustrate the same amount of information by means of two diagrams ...