By C.A. Rabbath, N. Léchevin
This designated publication offers a bridge among electronic keep watch over idea and automobile information and regulate perform. It provides useful ideas of electronic redecorate and direct discrete-time layout appropriate for a real-time implementation of controllers and counsel legislation at a number of premiums and with and computational ideas. the idea of electronic keep watch over is given as theorems, lemmas, and propositions. The layout of the electronic tips and regulate structures is illustrated via step by step strategies, algorithms, and case experiences. The platforms proposed are utilized to sensible versions of unmanned platforms and missiles, and electronic implementation.
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Extra resources for Discrete-Time Control System Design with Applications
Example text
DACs and ADCs ensure the transition between the two domains. 3 Operators in the Discrete-time Domain Two operators are of interest in this book: the shift and delta operators. They act upon discrete-time signals. The numerical properties of these operators depend on the value of T . The context dictates whether one is preferred over the other. To present the main characteristics of shift and delta operators, consider a discretetime signal f : N → R n . The signal is also represented as f (k, T ), where T ∈ R + is the sampling or update period and k ∈ N is the time step.
4b presents the response of the hold for each input sample. The total response of the hold is a sum of the contributions, which is shown in Fig. 4c. In this example, hold responses are cumulated within time intervals [0, T ) and [T , 2 T ). With the structural interpretation of Tustin’s method, the state-space expression of Eq. 7) is obtained as follows. For the sake of simplicity, the initial state is assumed to be the origin. Let the output of the instantaneous sampler in Fig. 3a be the state x(k, T ).
24 2 Review of Signals and Systems Lifted signal Partitioning CTL 0 0 T 2T 3T time T 0 0 T 0 T T 2T time Fig. 1 Continuous-time Lifting Continuous-time lifting, or CTL, of a bounded continuous-time function f (t) is visualized as a partitioning of its time trajectory into an infinite number of functions, each of which being a copy of f (t) within the time interval [kT , (k + 1)T ), with k being an index in Z, the set of integers. 8 presents an example of CTL for a scalar signal defined over t ≥ 0.