Download Loop-shaping Robust Control by Philippe Feyel PDF

By Philippe Feyel

The loop-shaping technique comprises acquiring a specification with regards to the open loop of the keep an eye on from standards concerning quite a few closed loop transfers, since it is simpler to paintings on a unmarried move (in addition to the open loop) than on a large number of transfers (various loopings reminiscent of set point/error, disturbance/error, disturbance/control, etc.). The simplicity and adaptability of the technique make it rather well tailored to the economic context.
This ebook provides the loop-shaping process in its entirety, beginning with the declension of high-level necessities right into a loop-shaping specification. It then indicates the way it is feasible to completely combine this process for the calculation of strong and effective correctors with assistance from present suggestions, that have already been industrially attempted and proven, corresponding to H-infinity synthesis. the idea that of a spot metric (or distance among versions) is additionally offered in addition to its reference to the best components of a suite of platforms shaping a ball of versions, in addition to its connections with strong synthesis by way of loop-shaping, as a way to calculate effective and strong correctors. As H-infinity loop-shaping is usually not easy when it comes to the order of correctors, the writer additionally appears to be like at loop-shaping synthesis less than an ordering constraint. extra promising traces of analysis are offered, one utilizing stochastic optimization, and the opposite non-smooth optimization. ultimately, the e-book introduces the idea that of correction with levels of freedom through the formalism of leading factorization.
Avenues for destiny paintings also are spread out by means of the writer as he discusses the most drawbacks to loop-shaping synthesis, and the way those matters should be solved utilizing sleek optimization concepts in an more and more aggressive business context, according to ever extra complicated units of sensible necessities, linked to more and more huge stipulations of usage.


1. The Loop-shaping Approach
2. Loop-shaping H-infinity Synthesis
3. Degrees-of-Freedom Controllers
4. Extensions and Optimizations
Appendix 1. Demonstrative components at the Optimization of sturdy Stabilization with Order Constraint
Appendix 2. institution of genuine LMIs for the Quasi-Convex challenge of Optimization of the Weighting Functions

About the Authors

Philippe Feyel is an R&D Engineer for the high-tech corporation Sagem Défense Sécurité, a part of the defence and defense enterprise of the SAFRAN workforce, in Paris, France.

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Example text

3. Example 3: issue of flexible modes and high-frequency disturbances Consider H(s), a system comprising a distribution of flexible modes (succession of resonances/antiresonances): the frequencies of the resonances are denoted as ωS ; the frequencies of the antiresonant modes are denoted as ωS . We wish to set the value y at 0. The loop is subject to a disturbance at the model’s input Γ 1 ( s ) , the spectrum of which is centered on ωS and ωS ; to compound the issue, the servoloop is also subject to a white noise-type disturbance at the model’s output Γ 2 ( s ) whose frequency spectrum naturally encapsulates ωS and ωS .

2. 1.

If D=0, then the Riccati equations are simply written AT X + XA − XBB T X + C T C = 0, F = − B T X AY + YAT − YC T CY + BB T = 0, L = −YC T We recognize the two equations from LQG synthesis (state feedback F and Kalman filter gain L). The eigenvalues of the matrices Ac = A+BF and Ao = A+LC have a negative real part, which ensures the stability of the two factors. 3. 4. Set of stabilizing controllers – Youla parameterization of stabilizing controllers Examine the system H ( s ) = [ A, B, C , D ] ; let us consider F and L such that the state matrices A+BF and A+LC are stable.

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