## Designing linear control systems with MATLABWritten as a companion volume to the author's Solving Control Engineering Problems with MATLAB, this indispensable guide illustrates the power of MATLAB as a tool for synthesizing control systems, emphasizing pole placement, and optimal systems design. |

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### Contents

POLE PLACEMENT AND DESIGN OF | 24 |

POLE PLACEMENT AND DESIGN OF | 92 |

DESIGN OF OPTIMAL CONTROL SYSTEMS | 145 |

Copyright | |

1 other sections not shown

### Common terms and phrases

Ackermann's formula arbitrary pole placement assume completely state controllable computed Consider the system continuous-time control sequence control signal controllability matrix deadbeat response designed system desired characteristic equation desired characteristic polynomial desired closed-loop poles desired eigenvalues determined discrete-time control systems eigenvectors Enter matrices enter the following example feedback gain matrix following command format short full-order observer full-order state observer given by Eq grid Gx(k Hence Hu(k identity matrix inverted pendulum Lagrange multiplier MATLAB Program matrix exponential minimizes minimum minimum-norm solution minimum-order observer minimum-order state observer nilpotent matrix nonsingular matrix num,den observability matrix observer gain matrix optimal feedback gain output equation plot pole-placement poly(J quadratic optimal control quadratic performance index Referring to Eq sampling periods servo system shown in Figure solve step response symmetric matrix system defined system is completely transfer function transformation matrix type 1 servo variables x-y plot x(oo x3 versus xb(k zero