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This means that the system involves two integrators.

Modern Control Engineering OGATA 5th Ed – Livro de Controle essencial para Controle

Pearson Prentice Hall, Thus,we have which is the transfer function of the system. The external force u t is the input to conrole system,and the displacement y t of the mass is the output. We shall begin our discussion with transformation from transfer function to state space. Consider the following nth-order system:. Your request to send this item has been completed.

Assume that there are rinputs and moutputs Define. We shall obtain the transfer function for the system from the state-space equations.

A block diagram representation of Equations 2—12 controld 2—13 is shown in Figure2— This system is of second order. Don’t have an account? In this state-space representation,matrices AandCare exactly the same as those for the system of Equation 2— Noting that the knowledge of together with the input u t for t!


Modern Control Engineering OGATA 5th Ed

Would you es like to submit a review for this item? State-space equations for the system are given by Equations 2—20 and 2— Equation 2—20 is a state equation and Equation 2—21 is an output equation for the system.

Write a review Rate this item: Katsuhiko Ogata Find more information about: In what follows we shall show how to derive the transfer function of a single-input,single-output system from the state-space equations.

In this section we shall present methods for obtaining state-space representations of continuous-time systems. This subject is presented in Section 2—6. Practically,however,because higher-order derivative terms are inaccurate,due to the noise effects inherent in any practical situations,such a choice of the state variables may not be desirable. Your rating has been recorded. Please re-enter recipient e-mail address es.

Note that the right-hand side of Equation 2—29 involves Hence G s can be written as whereQ s is a polynomial in s.

However, formatting rules can vary widely between applications and fields of interest or study. In this book we shall be concerned mostly with systems described by Equations 2—14 and 2— Notice that the outputs of the integrators engenhariw state variables.


A dynamic system consisting of a finite number of lumped elements may be described by ordinary differential equations in which time is the independent variable.

This system is a single-input,single-output system.

Privacy Policy Terms and Conditions. Similar Items Related Subjects: The E-mail Address es field is required. The specific requirements or preferences of your reviewing publisher, classroom teacher, institution or organization should be applied. Methods for obtaining canonical representations of systems in state space such as controllable canonical form,observable canonical form,diagonal canonical form,and Jordan canonical ogara are presented in Chapter 9. Mathematically,such a choice of state variables is quite convenient.

Since the transfer function was previously defined as the ratio of the Laplace transform of the output to the Laplace transform of the input when the initial conditions were zero,we set x 0 in Equation 2—25 to be zero.

In this case,Equations 2—12 and 2—13 can be simplified to.

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