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Essentials of Control Techniques and Theory_9

Tham khảo tài liệu 'essentials of control techniques and theory_9', kinh doanh - tiếp thị, quản trị kinh doanh phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 202 Essentials of Control Techniques and Theory it can be rearranged as x3 3x3 4x2 2 x1 u This will be equivalent to x1 3X1 4x1 2x1 u If we take the Laplace transform we have s3 3s2 4s 2 X1 s U s That gives us a system with the correct set of poles. In matrix form the state equations are x1 0 1 0 x1 0 x2 0 0 1 x2 0 x _ -3 -4 -2 _ x _ _1 That settles the denominator. How do we arrange the zeros though Our output now needs to contain derivatives of x1 y 4x1 x1 x1 But we can use our first two state equations to replace this by y x1 x2 4x3 i.e. y 1 1 4 x We can only get away with this form y Cx if there are more poles than zeros. If they are equal in number we must first perform one stage of long division of the numerator polynomial by the denominator to split ofl2 a Du term proportional to the input. The remainder of the numerator will then be of a lower order than the denominator and so will fit into the pattern. If there are more zeros than poles give up. Now whether it is a simulation or a filter the system can be generated in terms of a few lines of software. If we were meticulous we could find a lot of unanswered questions about the stability of the simulation about the quality of Linking the Time and Frequency Domains 203 the approximation and about the choice of step length. For now let us turn our attention to the computational techniques of convolution. Q 14.7.1 We wish to synthesize the filter s2 s2 2s 1 in software. Set up the state equations and write a brief segment of program. This page intentionally left .