Adaptive Control of Nonsmooth Dynamic Systems by Mattias Nordin, Per Bodin, Per-Olof Gutman (auth.), Gang Tao

By Mattias Nordin, Per Bodin, Per-Olof Gutman (auth.), Gang Tao PhD, Frank L. Lewis PhD (eds.)

A whole connection with adaptive keep an eye on of platforms with nonsmooth nonlinearities such as:

• backlash;

• dead-zones;

• part failure;

• friction;

• hysteresis;

• saturation;

• time delays.

These nonlinearities in business actuators reason serious difficulties within the movement keep an eye on of commercial strategies, fairly in view of recent requisites for velocity and precision of flow, resembling ensue in semiconductor production, precision machining and somewhere else. Actuator nonlinearities are ubiquitous in engineering perform and restrict regulate procedure performance.

While common suggestions regulate by myself can't deal with those nonsmooth nonlinearities successfully, this e-book, with unified and systematic adaptive layout equipment constructed in sixteen chapters, indicates how such nonlinear features could be successfully compensated for through the use of adaptive and clever regulate suggestions. this enables wanted process functionality to be completed within the presence of doubtful nonlinearities.

With broad surveys of literature and complete summaries of assorted layout equipment the authors of the e-book chapters, who're specialists of their components of curiosity, current new ideas to a couple very important matters in adaptive keep an eye on of structures with numerous kinds of nonsmooth nonlinearities.

In addition to supplying ideas, the publication is additionally aimed toward motivating extra study actions within the very important box of adaptive keep an eye on of nonsmooth nonlinear business platforms 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

Sample text

If mr, mz' br, bl are known, by constructing v(t) as shown in Figure 2b, we can cancel the dead zone so that the output of the dead zone u( t) == Ud (t). Mathematically, the relation between v(t) and Ud(t), which specifies the dead zone inverse, is defined as follows: (4) It can be easily verified that with this choice of v(t), u(t) == Ud(t). The problem is that the parameters m r , ml, br, and bl are unknown. , mt, ;;;J;r and mlbl are the estimates of m r , ml, mrbr and mlbl respectively. And b;.

In this section we will use describing function analysis to indieate that the plant gain depends monotonieally on the input amplitude, A, and the backlash gap a for a proper choiee of input frequency WA. Using monotonicity, a gradient adaptation scheme can be applied to estimate a. Assurne for simplicity that r = 0 and Tl = O. A more detailed analysis of the case r -:j:. 0 and Tl -:j:. 0 can be found in [4,14]. Let 101< a 1012: a (59) be the describing function ofthe dead zone (57). Note that N(O) varies monotonieally from 0 to 1.

Freeman. The effect of speed dependent friction and backlash on the stability of automatic control systems. Transaction of the American lEE, 7:680690, 1959. 12. A. E. Vander Velde. Multiple-Input Describing Functions and Nonlinear System Design. McGraw-Hill, 1968. 13. J. H. Liversidge. Backlash and Resilience within Glosed Loop of Automatie Gontrol Systems. Academic Press, 1952. 14. M. Nordin. Uncertain systems with backlash: Analysis, identification and synthesis. Licenciate thesis, trita/mat-95-os3, Royal Institute of Technology, 1995.

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