By Masayoshi Toda
This e-book presents readers with substitute powerful methods to manage layout for a tremendous type of platforms regularly linked to ocean-going vessels and constructions. those structures, which come with crane vessels, on-board cranes, radar gimbals and a conductivity temperature and intensity winch, are modelled as manipulators with oscillating bases. One layout method is predicated at the H-infinity regulate framework exploiting an efficient mixture of PD regulate, a longer matrix polytope and a strong balance research strategy with a state-dependent coefficient shape. the opposite relies on sliding-mode regulate utilizing a few novel nonlinear sliding surfaces. The version demonstrates how profitable movement keep an eye on might be accomplished through suppressing base oscillations and within the presence of uncertainties. this is often very important not just for ocean engineering structures during which the issues addressed right here originate yet extra in most cases as a benchmark platform for strong movement keep an eye on with disturbance rejection.
Researchers drawn to the powerful regulate of mechanical structures working on volatile bases will locate this monograph helpful. MATLAB® and Simulink® courses can be found for obtain to make the tools defined within the textual content more straightforward to appreciate and to permit readers to adventure useful methods initially hand.
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Additional info for Robust Motion Control of Oscillatory-Base Manipulators: H∞-Control and Sliding-Mode-Control-Based Approaches
Let ν 0 = (ν01 , . . , ν0l ) ∈ ν with 0 ≤ ν0i < 1, and then there exist the unique ξ0i ’s such that ν0i = (1 − ξ0(i−1) ) l−1 j=i ξ0 j , which is obtained in the following recursive manner: 4 Motion Control Using an H∞ -Control-Based Approach 32 ξ0(l−1) = 1 − ν0l 1 ξ0(l−2) = 1 − ξ0(l−1) ν0(l−1) .. 1 ξ01 = 1 − ξ0(l−1) ξ0(l−2) ···ξ02 ν02 and 0 < ξ0i ≤ 1 is easily confirmed. Next, let us consider the case where ν0s = 1 (1 ≤ s ≤ l) and ν0i = 0 (i = s). In this case, by setting ξ0(s−1) = 0 and ξ0i = 1 (i = s−1, 0), ν0i can be represented by the same form ν0i = (1−ξ0(i−1) ) l−1 j=i ξ0 j .
7) where σ¯ (·) denotes the largest singular value. If there exists no Δ ∈ which makes the matrix singular, then μ (M) := 0. Furthermore, this notion can be extended to a linear time-invariant system matrix M(s) ∈ Cn×n as μ (M(s)) := sup μ (M(iω)). 8) The method to analyze robustness of the system using μ instead of ||M(s)||∞ = supω∈R (σ¯ /M(iω)) (when M(s) ∈ H∞ ) is called “μ-analysis”. As described above, when evaluating the robust stability of the feedback configuration of the structured Δ and Fl (M, K ), the method using only their H∞ norms will provide a conservative result.
The second one requires a control design method with which one can cope with robustness. When these two features are accounted for, the H∞ control framework can be naturally a powerful candidate. The H∞ © Springer International Publishing Switzerland 2016 M. 1007/978-3-319-21780-2_4 21 22 4 Motion Control Using an H∞ -Control-Based Approach control that we have employed is fundamentally for linear time-invariant systems. However, by adding some modifications, the nonlinearity can be reduced and be absorbed into the model uncertainty.