 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| M. Ya. Izrailovich, "Damping of forced quasi-harmonic oscillations in nonlinear systems," Mech. Solids. 38 (6), 1-7 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
6 |
Pages |
1-7 |
| Title |
Damping of forced quasi-harmonic oscillations in nonlinear systems |
| Author(s) |
M. Ya. Izrailovich (Moscow) |
| Abstract |
A feedback control law is constructed for damping of forced quasi-harmonic oscillations in a one-dimensional nonlinear dynamical system. The control variable is subjected to an integral quadratic constraint. To solve the control problem, we utilize harmonic linearization combined with the method of moments. The solution yields a linear control law. If stable modes of motion, different from the designed one, are possible in the system, we utilize a modified (multiplicative stabilizing) control law that eliminates extraneous modes and stabilizes the designed quasi-optimal mode.
The complexity of synthesis of active feedback controls for suppression of oscillations in nonlinear systems is due to the fact that the synthesized system can allow extraneous stable modes, some of which can have even higher intensity than that of oscillations occurring in the absence of the control. Thus, the introduction of an oscillation damping control can lead to the negative effect.
In the present paper, we propose a method for constructing laws for controlled damping of oscillations that do not allow extraneous modes and provide only the designed mode of quasi-harmonic forces oscillations in one-dimensional mechanical systems of any order with local nonlinearities. This method generalizes the approach of [1] for the reduction of extraneous modes to the case of forced oscillations. |
| References |
| 1. | M. Ya. Izrailovich, "Stabilization and removing ambiguity of controlled self-sustained oscillation modes. A multiplicative stabilizer," Doklady AN, Vol. 377, No. 1, pp. 25-29, 2001. |
| 2. | M. Ya. Izrailovich, "Control of forced oscillations of mechanical systems allowing harmonic linearization,"
Problemy Mashinostroeniya i Nadezhnosti Mahsin, No. 5, pp. 18-27,
1994. |
| 3. | M. Ya. Izrailovich and A. V. Sinev, "Synthesis of one class of active vibration isolation systems,"
Izv. AN. Teoriya i Sistemy Upravleniya,
No. 6, pp. 153-156, 1999. |
| 4. | E. P. Popov, Applied Theory of Control Processes in Nonlinear
Systems [in Russian], Nauka, Moscow, 1973. |
| 5. | N. N. Krasovskii, Theory of Control of Motion: Linear Systems
[in Russian], Nauka, Moscow, 1968. |
| 6. | M. Z. Kolovskii, Nonlinear Theory of Vibration Isolation Systems
[in Russian], Nauka, Moscow, 1966. |
|
| Received |
30 May 2001 |
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