Transforms from differential equations to difference equations and vice-versa applied to computer control systems. (English) Zbl 1311.93030
Summary: This letter derives the transform relationship between differential equations to difference equations and vice-versa, applied to computer control systems. The key is to obtain the rational fraction transfer function model of a time-invariant linear differential equation system, using the Laplace transform, and to obtain the impulse transfer function model of a time-invariant linear difference equation, using the shift operator. Finally, we find the discrete-time models of the first-order, second-order and third-order systems from their continuous-time models and vice-versa and find the mapping relationship between the coefficients of discrete-time models and the continuous-time models using the bilinear transform. An example is provided to demonstrate the proposed model transform methods.
MSC:
| 93B40 | Computational methods in systems theory (MSC2010) |
| 93B17 | Transformations |
| 44A10 | Laplace transform |
Keywords:
differential equation; difference equation; continuous-time system; discrete-time system; bilinear transform; \(z\)-\(s\) transformReferences:
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