Control Theory for Engineers: A Primer by Brigitte d'Andréa-Novel, Michel De Lara

By Brigitte d'Andréa-Novel, Michel De Lara

Control concept is on the middle of knowledge and communique applied sciences of complicated platforms. it could actually give a contribution to assembly the strength and environmental demanding situations we face.

The textbook is geared up within the manner an engineer classically proceeds to unravel a keep watch over challenge, that's, elaboration of a mathematical version taking pictures the method habit, research of this version and layout of a keep watch over to accomplish the specified targets.

It is split into 3 elements. the 1st a part of the textual content addresses modeling facets via nation house and input-output representations. The concept of the inner kingdom of a process (for instance mechanical, thermal or electrical), in addition to its description utilizing a finite variety of variables, can be emphasised. the second one half is dedicated to the soundness research of an equilibrium element. The authors current classical instruments for balance research, akin to linearization options and Lyapunov capabilities.

Central to manage idea are the notions of suggestions and of closed-loop, and the 3rd a part of the textbook describes the linear keep watch over synthesis in a continuing and discrete-time framework and likewise in a probabilistic context. Quadratic optimization and Kalman filtering are offered, in addition to the polynomial illustration, a handy method of reject perturbations at the procedure with no making the regulate legislation extra complicated. through the textual content, diverse examples are built, either within the chapters and within the exercises.

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This approach is restrictive, but adapted to our purposes. 2. 3. 4. 5. In what follows, we denote by (λ) and (λ) the real part and the imaginary part of the complex number λ ∈ C. Thecomplex conjugate of the complex number λ = (λ) + i (λ) is λ = (λ) − i (λ). 2 Definitions of State-Space Models Some dynamical systems may be described by a finite number of quantities that allow us to determine their future evolution. Let us illustrate this with two simple examples, where we introduce the notions of state, state-space, and state-model.

U m (t) dt ... d xn (t) = f n t, x1 (t), . . , xn (t), u 1 (t), . . , u m (t) . 4) The state-space is the set X (or Rn ). This state-model is said to be stationary if the functions f 1 , . . , f n do not explicitly depend on the time variable t. On the contrary, we speak of a non stationary state-model. In what follows, we also use the terminology of (continuous-time) state representation to denote a state-model. 4 Here, and throughout the text, the notation x has two interpretations, depending on the context.

The following definitions are very useful in practice. s. system is said to be of first-order if its transfer function is of the form k . s. 8) s + 2ζ ωn s + ωn2 where ζ is called the damping factor and f n = ωn /2π the natural frequency of the system. For positive ζ and ωn , the case ζ > 1 corresponds to a so-called hyperdamped system (that is, with two real distinct and strictly negative roots), the case ζ = 1 to a double real root equal to −ωn , and the case ζ < 1 to two complex conjugated roots −ζ ωn ± iωn 1 − ζ 2 .

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