Modern control theory (3rd ed.)
Modern control theory (3rd ed.)
Linear Optimal Control Systems
Linear Optimal Control Systems
| Hi-index | 22.14 |
The absolute minimum input 'energy' vector and corresponding energy function, are derived in explicit form, for total open-loop suppression of identified peak responses in time-invariant linear structural dynamic systems. There is no obvious way, for arbitrarily large order systems, to obtain these explicit results using well-known optimal control solutions derived via state-space formulation. Instead, the input vector and energy function are obtained directly using the original second-order equations, by superposition of optimal infinite-terminal-time modal excitation functions and optimisation via a Lagrange multiplier. Explicit results can be obtained this way for normal mode systems, but only by using one very specific choice of quadratic cost weighting matrix. This absolute minimum input energy function can be used to construct a simple benchmark criterion for assessing the performance efficiencies of various open- and closed-loop peak suppression strategies, of relevance to active vibration control. A numerical example is given to demonstrate this criterion applied to an LQR strategy for suppressing motion in a 10-state conveyor-positioning system.