Optimal Placement and Active Control Methods for Integrating Smart Material in Dynamic Suppression Structures
Abstract
:1. Introduction
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- Modeling of intelligent constructs execution of control in oscillation suppression.
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- Uncertainties in dynamic loading.
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- Measurement noise.
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- Appropriate selection of weights for complete suppression of oscillations.
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- Using various choice places to stifle oscillations.
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- Results in the frequency domain as well as the time-space domain.
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- Introduction of the uncertainties in the construction’s mathematical model.
2. Modeling
3. Controller Synthesis
- K-step. Create a controller for the scaled issue. with fixed D(s).
- D-step. Find D(jω) to minimalize at each frequency with fixed N.
- Fit the degree of each factor of D(jω) to a stable and the lowest phase transfer function D(s) and move to Step 1.
4. Results
4.1. Results in Simulation and Analysis of the Smart Structural Control
4.2. Results for the Open Loop (Initial Condition without Control)
4.3. Results with LQR Control
4.4. Results with Hinfinity Control
5. Discussion
- On the modeling of uncertainty in smart constructions.
- In the creation of advanced control techniques.
- In the complete suppression of vibrations under dynamic loading.
- Analytical explanation of the equations used in programming.
- Advanced programming techniques have been used to make the simulations.
- The model has been worked both in simulation and in advanced programming.
- It is not possible in one article to present both the modeling and the experimental results in such detail. For this reason, they will be presented in future research papers.
6. Conclusions
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- Modeling of intelligent constructs execution of control in oscillation suppression.
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- Using various choice places to stifle oscillations.
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- Results in the frequency domain as well as the time-space domain.
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- Introduction of the uncertainties in the construction’s mathematical model.
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- The integration of smart structures using methods for optimal placement and active control.
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- Uncertainties in dynamic loading.
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- Measurement noise, appropriate selection of weights for complete suppression of oscillations.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
M | Mass Matrix | ψi(t) | Displacement deflection |
K | Stiffness Matrix | x(t) | The state vector of our system |
D | Viscous damping Matrix | y(t) | Output vector of our system |
fe(t) | piezoelectric force | d31 | Piezoelectric constant |
n | Number of nodes in finite element formulation | cp | Piezoelectric constant |
u(t) | Control voltages of actuators | K(s) | Hinfinity Controller of the system |
Fe | Matrix with piezoelectric constant | KlQ | LQR controller of the system |
wi(t) | Rotation deflection | P(s) | Augment Plant of the smart system |
μ | Singular value | e(t) | The error of the system |
d(t) | Disturbances of the system | n(t) | Noise of the system |
A, B, G, H | Matrices of our system | D, G-K | D-K interaction in the frequency domain |
Tde, Tne, Tdu, Tnu | The transfer function disturbance error, noise error, disturbance control, noise control | We | The error Weight for Hinfinity control |
Wn | The noise Weight for Hinfinity control | Wu | The control Weight for Hinfinity control |
Wd | The disturbance Weight for Hinfinity control | N | The transfer function for the smart system |
Δ | The Uncertainty of the system | δM t | The Uncertainty terms for the mass matrix |
δκ | The Uncertainty terms for the stiffness matrix | kp, mp | Numerical constant from zero to one |
J | Matrix which is utilized to select states that we are concerned with controlling | Q, R | The weight vectors for LQR control |
κ(jω) | Frequency-dependent condition number | F | Fractional transformation |
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Parameters | Values |
---|---|
L, for Beam length | 1.00 m |
W, for Beam width | 0.08 m |
h, for Beam thickness | 0.02 m |
ρ, for Beam density | 1600 kg/m3 |
E, for Young’s modulus of the Beam | 1.5 × 1011 N/m2 |
bs, ba, for Pzt thickness | 0.002 m |
d31 the Piezoelectric constant | 280 × 10−12 m/V |
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Moutsopoulou, A.; Stavroulakis, G.E.; Petousis, M.; Pouliezos, A.; Vidakis, N. Optimal Placement and Active Control Methods for Integrating Smart Material in Dynamic Suppression Structures. Vibration 2023, 6, 975-1003. https://doi.org/10.3390/vibration6040058
Moutsopoulou A, Stavroulakis GE, Petousis M, Pouliezos A, Vidakis N. Optimal Placement and Active Control Methods for Integrating Smart Material in Dynamic Suppression Structures. Vibration. 2023; 6(4):975-1003. https://doi.org/10.3390/vibration6040058
Chicago/Turabian StyleMoutsopoulou, Amalia, Georgios E. Stavroulakis, Markos Petousis, Anastasios Pouliezos, and Nectarios Vidakis. 2023. "Optimal Placement and Active Control Methods for Integrating Smart Material in Dynamic Suppression Structures" Vibration 6, no. 4: 975-1003. https://doi.org/10.3390/vibration6040058