In this thesis, experimental, analytical and numerical analysis are used for distributed parameter plate structure modeling, an infinite-dimensional and a very high-order plate mathematical transfer function model is derived based on modal analysis and numerical analysis results. A feed-through truncated plate model which minimizing the effect of truncated modes on spatial low-frequency dynamics of the system by adding a spatial zero frequency term to the truncated model is provided and numerical software MATLAB is used to compare the feed-through truncated plate model with traditional balanced reduction plate model which is used to decrease the dimensions and orders of the infinite-dimensional and very high-order plate model.

Active vibration control strategy is presented for a flexible plate structure with bonded three self-sensing magnetic transducers which guarantee unconditional stability of the closed-loop system similar as collocated control system. Both multi-mode SISO and MIMO control laws based upon positive position feedback is developed for plate structure vibration suppression. The proposed multi-mode PPF controllers can be tuned to a chosen number of modes and increase the damping of the plate structure so as to minimize the chosen number of resonant responses.

Stability conditions for multi-mode SISO and MIMO PPF controllers are derived to allow for a feed-through term in the model of the plate structure which is needed to ensure little perturbation in the in-bandwidth zeros of the model. A minimization criterion based on the H∞ norm of the closed-loop system is solved by a genetic algorithm to derive optimal parameters of the controllers. Numerical simulation and experimental implementation are performed to verify the effectiveness of multi-mode SISO and MIMO PPF controllers’ vibration suppression for the feed-through truncated plate structure.

**Contents**

**Chapter 1**

**Passive Control**

**Active Control**

**Open-loop Control**

**Closed-loop Control**

**Feed-forward Control**

**Feedback Control**

**Wave Control**

**Modal Control**

**Collocated Control**

**Uncollocated Control**

**PPF controller development**

**Modified PPF (MPPF)**

**Robust PPF**

**Adaptive PPF**

**PPF combine with Genetic Algorithms (GA)**

**PPF compare with other controllers**

**MIMO PPF**

**SISO vibration controller for plate or shell structure**

**decentralized MIMO vibration controller for plate or shell structure**

**MIMO vibration controller for plate structure**

**Chapter 2**

**(Experimental Model)**

**(Numerical Model)**

**Chapter 3**

**Chapter 4**

**Chapter 5**

**Theorem 5.1**

**Theorem 5.2**

**Theorem 5.3**

**Theorem 5.4**

**Theorem 5.5:**Consider the following second-order multivariable dynamical system:

**Theorem 5.3.**

**Theorem 5.6**: The negative feedback connection of (5.43) and (5.42) with (5.45) is

**Chapter 6**

**Chapter 7**

**11.11% 21.569% 2.5974% 12.253%**

**0.9**

**2.2**

**0**

**1.4**

**35.57% 21.45% 15.38% 18.75%**

**5.8**

**2.1**

**1.4**

**3.8**

**0**

**24.561% 16.228% 19.065%**

**-1.1**

**2.3**

**1.7**

**2.5**

**19.444% 27.64% 35.714% 14.137%**

**2**

**2.7**

**3.9**

**1.5**

**34.01%**

**19.27% 59.26%**

**18%**

**5**

**2**

**7.6**

**1**

**19.33% 33.333% 50.543% 29.091%**

**1**

**3.4**

**6.9**

**2**

**Chapter 8**

**active**

*adaptive*-
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