By Mattias Nordin, Per Bodin, Per-Olof Gutman (auth.), Gang Tao PhD, Frank L. Lewis PhD (eds.)
A entire connection with adaptive keep watch over of platforms with nonsmooth nonlinearities such as:
• part failure;
• time delays.
These nonlinearities in business actuators reason critical difficulties within the movement keep watch over of business strategies, relatively in view of contemporary standards for pace and precision of circulation, akin to happen in semiconductor production, precision machining and in different places. Actuator nonlinearities are ubiquitous in engineering perform and restrict keep an eye on approach performance.
While commonplace suggestions keep watch over on my own can't deal with those nonsmooth nonlinearities successfully, this ebook, with unified and systematic adaptive layout equipment constructed in sixteen chapters, indicates how such nonlinear features may be successfully compensated for through the use of adaptive and clever keep watch over thoughts. this permits wanted procedure functionality to be accomplished within the presence of doubtful nonlinearities.
With wide surveys of literature and complete summaries of assorted layout tools the authors of the e-book chapters, who're specialists of their components of curiosity, current new options to a few very important matters in adaptive regulate of platforms with quite a few varieties of nonsmooth nonlinearities.
In addition to offering suggestions, the ebook can be geared toward motivating extra learn actions within the very important box of adaptive keep an eye on of nonsmooth nonlinear commercial structures by way of formulating a number of tough open difficulties in comparable areas.
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Additional info for Adaptive Control of Nonsmooth Dynamic Systems
The input u(t) is the output of a flexible tube connected to apressure bottle with an inlet and an out let valve as controls. The characteristies from control valves to the output u(t) are well modeled by a non-symmetric dead zone  and moreover, u(t), the output of the dead zone is readily measurable by apressure transducer. We would also like to point out that relaxing the measurability assumption on the dead zone does not trivialize the problem. Note that the idea of an adaptive dead zone inverse is built on the certainty equivalence principle.
In Symposium: Modelling and Simulation tor Control 0/ Lumped and Distributed Parameter Systems, pages 107~113, Lilie, 1986. IMACS-IFACS. 4. G. Brandenburg, H. Hertie, and K. Zeiselmair. Dynamic influence and partial compensation of coulomb friction in a position- and speed-controlled elastic two-mass systems. In IFAC World Congress, Munieh, 1987. 30 Mattias Nordin, Per Bodin and Per-Olof Gutman 5. G. Brandenburg and U. Schäfer. Influence and partial compensation of backlash for a position controlled elastic two-mass system.
To see that, we divide -bi< v < br into three cases, Ud > 0, Ud < 0, and Ud = 0. Adaptive Dead Zone Inverses Case 1) Ud > O. Note that sgn Ud This implies 0 < v < br . = sgn v, U = 0, Ud = Llu, and v 41 > O. Case 2) Ud < O. Note that in this case, -bi < v < O. Thus --CPlT-() = rn/v + rn/b/ - rn/b/ - rn/v = Llu - rn/(b/ + v) < Llu < 0 Case 3) Ud = O. This implies v(t) = 0, and Llucp[e = 0 = Llu. In all three cases, we have -(Llu)cp[e :::; _(LlU)2. Hence V :::; -Llu 2. This shows that the parameter estimates error is bounded and Llu E L 2.
Adaptive Control of Nonsmooth Dynamic Systems by Mattias Nordin, Per Bodin, Per-Olof Gutman (auth.), Gang Tao PhD, Frank L. Lewis PhD (eds.)