Digital Control Systems by Prof. Dr.-Ing. Rolf Isermann (auth.)

By Prof. Dr.-Ing. Rolf Isermann (auth.)

Show description

Read Online or Download Digital Control Systems PDF

Similar control systems books

Modeling and Control of Complex Physical Systems: The Port-Hamiltonian Approach

Power alternate is a huge starting place of the dynamics of actual structures, and, for that reason, within the learn of complicated multi-domain structures, methodologies that explicitly describe the topology of strength exchanges are instrumental in structuring the modeling and the computation of the system's dynamics and its keep an eye on.

Intelligent Diagnosis and Prognosis of Industrial Networked Systems (Automation and Control Engineering)

In an period of in depth festival the place plant working efficiencies needs to be maximized, downtime as a result of equipment failure has develop into extra high priced. to chop working bills and elevate sales, industries have an pressing have to are expecting fault development and closing lifespan of business machines, tactics, and structures.

Fault Detection and Diagnosis in Engineering Systems

That includes a model-based method of fault detection and analysis in engineering structures, this e-book comprises up to date, useful info on combating product deterioration, functionality degradation and significant equipment harm. ;College or college bookstores might order 5 or extra copies at a different scholar fee.

Extra resources for Digital Control Systems

Example text

5-13) of a transfer function B (z) (3. 5-14) G(z) = A(z) leading to 1+w m-1 + ... 5-15) Multiplying by (1-w)m yields A (w) = ( 1+w) m + a 1 ( 1+w) ~1 ( 1-w) + ... +am ( 1-w) m (3. 5-16) Now the Hurwitz criterion can be applied for the polynomial :1\(w) = 0. 5-17) 38 3. Discrete-time Systems This criterion states that the coefficients have to exist and have to carry the same algebraic sign. Then the system is not monotonic unstable. To avoid oscillatory unstability the Hurwitz-determinants have to be positive for systems higher than second order (or the Routh criterion has to be falfilled).

6-27) are presented. A first possibility which corresponds to the recursive solution of difference equations for a given input signal u(k) and initial conditions ~ (0) is 3. ::_k~(O) + ~ (k) k L Ai- 1 b u(k-i). 6-44) homoge- particular solution (conneous solution volution sum) where Ak A•A ... A. --' k y(k) can finally be obtained from Eq. 6-27). If u(k) is given explicitely as a z-transform, a second possible solution can be used. The z-transform then furnishes }{~(k)} = ~(z) }{~(k+1)} = z[~(z)- ~(0)] (applying the theorem of shifting to the left) .

B) The exponential function: x(kT 0 ) = e z z-e-aTo -akT 0 (a is real) z c) The sine function: x(kT 0 ) With it follows, using the result of b) with a iw 1 , or with a that x(z) 2i [z_)w1To zsinw 1 T0 2 z +a 1 z+1 0 These examples have shown how the z-transforms of some simple functions can be obtained. In this way, a table of transforms of common functions can be assembled. A short table of corresponding continuous time functions, Laplace-transforms and z-transforms, is given in the Appendix. This table shows: --- a) There is a direct correspondence of the denominators of x(s) and x(z) (s-s 1 ) n (z-z 1 ) n with z 1 = T s e 0 1 b) There is no direct correspondence of the numerators of x(s) and x(z).

Download PDF sample

Rated 4.61 of 5 – based on 24 votes