Robust Control Design with MATLAB® by Da-Wei Gu PhD, DIC, CEng, Petko Hristov Petkov PhD, Mihail
By Da-Wei Gu PhD, DIC, CEng, Petko Hristov Petkov PhD, Mihail Mihaylov Konstantinov PhD (auth.)
Robustness is usually of the most important value up to the mark process layout. genuine engineering platforms are at risk of exterior disturbance and dimension noise and there are regularly discrepancies among mathematical types used for layout and the particular method in practice.
Robust keep an eye on layout with MATLAB® is helping you how to use well-developed complex strong keep watch over layout tools in useful situations. To this finish, numerous lifelike regulate layout examples starting from teaching-laboratory experiments, reminiscent of a mass–damper–spring meeting, to advanced platforms like a flexible-link manipulator are given designated presentation. the entire layout routines are carried out utilizing MATLAB® powerful keep watch over Toolbox, keep watch over procedure Toolbox and Simulink®.
By sharing their reviews in business circumstances with minimal recourse to complex theories and formulae, the authors express crucial principles and worthwhile insights into strong commercial keep watch over structures layout utilizing significant H-infinity optimization and comparable tools permitting you fast to maneuver on along with your personal challenges.
• Hands-on, instructional presentation supplying you with the chance to copy the designs awarded and simply to change them to your personal courses.
• An abundance of examples illustrating crucial steps in powerful layout.
Robust keep an eye on layout with MATLAB® is for graduate scholars and practicing engineers who are looking to find out how to care for strong keep an eye on layout difficulties with no spending loads of time in gaining knowledge of complicated theoretical developments.
The demonstrations are present for MATLAB® model 7.01, powerful keep an eye on Toolbox model 3.0, keep watch over process Toolbox model 6.1 and Simulink® model 6.1.
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Extra resources for Robust Control Design with MATLAB®
The objective is to ﬁnd a stabilising controller K to minimise the output z, in the sense of energy, over all w with energy less than or equal to 1. Thus, it is equivalent to minimising the H∞ -norm of the transfer function from w to z. Fig. 2. 1 Mixed Sensitivity H∞ Optimisation P (s) = 37 P11 (s) P12 (s) P21 (s) P22 (s) it can be obtained directly z = [P11 + P12 K(I − P22 K)−1 P21 ]w =: Fl (P, K)w where Fl (P, K) is the lower linear fractional transformation of P and K. 2) ∞ and is referred to as the H∞ optimisation problem.
It has no speciﬁc structure. 2. The uncertainties under consideration would include unstructured uncertainties, such as unmodelled dynamics, as well as parameter variations. All these uncertain parts still can be taken out from the dynamics and the whole system can be rearranged in a standard conﬁguration of (upper) linear fractional transformation F (M, ∆). 18) where i=1 ri + j=1 mj = n with n is the dimension of the block ∆. We may deﬁne the set of such ∆ as ∆. The total block ∆ thus has two types of uncertain blocks: s repeated scalar blocks and f full blocks.
There are three special cases of the dimensions in which the solution formulae would be simpler. Case 1: p1 = m2 and p2 < m1 . In this case, the orthogonal transformation on D12 is not needed. 2 is reduced to γ > σ(D11 V211 −1 T T −1 DK = −D12 D11 V212 (D21 V212 ) Case 2: p1 > m2 and p2 = m1 . In this case, the orthogonal transformation on D21 is not needed. 2 is reduced to γ > σ(U121 D11 ), and −1 DK = −(U122 D12 )−1 U122 D11 D21 Case 3: p1 = m2 and p2 = m1 . In this case, both orthogonal transformations are not needed.