【正文】 d controlled are considerably large than they were when the first edition of this book was written. The second impact of the puter technology has to so with the proliferation and wide availability of the microputers in homes and I the work place, classical control theory was dominated by graphical methods because at the time that was the only way to solve certain problems, Now every control designer has easy access to powerful puter packages for systems analysis and design. The old graphical methods have not yet disappeared, but have been automated. They survive because of the insight and intuition that they can provide, some different techniques are often better suited to a puter. Although a puter can be used to carry out the classical transforminverse transform methods, it is used usually more efficient for a puter to integrate differential equations directly. The third major impact of the puters is that they are now so monly used as just another ponent in the control systems. This means that the discretetime and digital system control now deserves much more attention than it did in the past. Modern control theory is well suited to the above trends because its timedomain techniques and its mathematical language (matrices, linear vector spaces, etc.) are ideal when dealing with a puter. Computers are a major reason for the existence of state variable methods. Most classical control techniques were developed for linear constant coefficient systems with one input and one output (perhaps a few inputs and outputs). The language of classical techniques is the Laplace or Ztransform and transfer functions. When nonlinearities ad time variations are present, the very basis for these classical techniques is removed. Some successful techniques such as phaseplane methods, describing function s, and other ad hoc methods, have been developed to alleviant this shorting. However, the greatest success has been limited to loworder systems. The state variable approach of modern control theory provides a uniform and powerful method of representing systems of arbitrary order, linear or nonlinear, with timevarying or constant coefficient. It provides an ideal formulation for puter implementation 3 and is responsible for much of the progress in optimization theory. Modern control theory is a recent development in the field of control. Therefore, the name is justified at least as a descriptive title. However, the foundations of modern control theory are to be found in other wellestablished fields. Representing a system in terms of state variables is equivalent to the approach of Hamiltonian mechanics, using generalized coordinates and generalized moment. The advantages of this approach have been wellknown I classical physics for many years. The advantages of using matrices when dealing with simultaneous equations of various kinds have long been appreciated in applied mathematics. The field of linear algebra also contributes heavily to modern control theory. This is due to the concise notation, the generality of the results, and the economy of thought that linear algebra provides. Mechanism of Surface Finish Production There are basically five mechanisms which contribute to the production of a surface which have been machined. There are: (1) The basic geometry of the cutting process. In, for example, single point turning the tool will advance a constant distance axially per revolution of the work piece and the resultant surface will have on it, when viewed perpendicularly to the direction of tool feed motion, a series of cusps which will have a basic form which replicates the shape of the tool in cut. (2) The efficiency of the cutting operation. It has already been mentioned that cutting with unstable builtupedges will produce a surface w