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Control Systems with Saturating Inputs: Analysis Tools and - download pdf or read online

By Maria Letizia Corradini, Andrea Cristofaro, Fabio Giannoni, Giuseppe Orlando

ISBN-10: 1447125053

ISBN-13: 9781447125051

Saturation nonlinearities are ubiquitous in engineering structures: each actual actuator or sensor is topic to saturation due to its greatest and minimal limits. enter saturation is an working situation that's popular to the keep an eye on neighborhood for its “side effects”, which reason traditional controllers to lose their closed-loop functionality in addition to keep an eye on authority in stabilization. for this reason, the sensible program of keep an eye on conception can't steer clear of making an allowance for saturation nonlinearities in actuators, explicitly facing constraints up to the mark design.

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Extra resources for Control Systems with Saturating Inputs: Analysis Tools and Advanced Design

Example text

3) imposing ψ±M (t) = 0 we get x1 (t) = −mx2 (t) − q. The equation ψ±M (t + 1) = 0 can be written as ψ±M (t + 1) = x2 (t) + m(−a1mx2 (t) − a1q + a2x2 (t) ± M) + q = 0. 1 The SISO Planar Case We obtain 35 ⎧ mM ⎪ ⎨q = ± a1 m − 1 ⎪ ⎩ a1 m2 − a2 m − 1 = 0. 4) the expression a22 + 4a1 is non negative if and only if A has real eigenvalues. In particular we have m= 1 1 λ 1 + λ 2 ± |λ 1 − λ 2 | ∈ − ,− −2λ1λ2 λ1 λ2 . 1 , E 2 the (unbounded) strips We denote by EM M 1 = x ∈ R2 : x 1 − EM M 1 x2 < λ1 |λ 1 λ 2 − λ 1 | 2 EM = x ∈ R2 : x 1 − M 1 x2 < .

23). 6. 18) is BM = lim S j = j→∞ S j =: S∞ j∈N Proof. 4 and for sake of brevity the detailed proof is omitted. 1. 1 shows a plot of the saturated maximal region of attraction. 5 Fig. 1. Example of saturated maximal region of attraction with λ1 = 1, λ2 = 3 and M = 4. 2. 2. 2. x2 2 1 2 1 1 2 x1 1 2 Fig. 2. 2 and M = 2. 3. Let us consider the antistable system (A, B) with ⎛ ⎞ ⎛ ⎞ 0 1 0 0 A = ⎝ 0 0 1 ⎠, B = ⎝ 0 ⎠. 5, λ3 = 1. Setting the saturation level M = 1, the starting points for the algorithm are given by x± 0 = ±(10, 0, 0).

Xn ) ∈ Rn . In view of the controllability assumption, without loss of generality, the pair (A, B) is given in canonical form. Given a real positive value M > 0, the system is said to be subject to saturation at level M if the control variable u(k) is forced to have norm less than M. By the notation WM will indicate the set of admissible control functions: WM = u ∈ ∞ (Z) : u ∞ = sup |u(k)| ≤ M . e. BM = x ∈ Rn : ∃u ∈ WM : lim φ (k, x, u) = 0 . k→+∞ The set WM∗ ⊂ WM is the set of admissible switching control functions WM∗ = {u ∈ WM : u(k) ∈ {M, −M} ∀k ∈ Z} .

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Control Systems with Saturating Inputs: Analysis Tools and Advanced Design by Maria Letizia Corradini, Andrea Cristofaro, Fabio Giannoni, Giuseppe Orlando


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