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Automatic Control 3
definitions 3
| Question | Answer |
|---|---|
| State-variable form | x=Fx+Gu |
| State of the system | the column vector x, it contains in elements for an nth-order system |
| System matrix | The quantity F is an n x n system matrix |
| Input matrix | G is an n x 1 input matrix |
| Output matrix | H is a 1 x n row matrix reffered to as the output matrix |
| Direct transmission term | J is a scalar called the direct transmission term |
| Transpose | X=[x1 x2…]^T |
| An integrator | a device whose input is the derivative of its ouput |
| components of an analog computer | Integrator, summer, potentiometer |
| Block diagrams and canonical forms; | For G=b(s)/a(s) roots of b are zeros and roots of a are poles. There is control canonical form, modal canonical form and normal mode and observer canonical form. |
| Dynamic response from the state equations | G(S) = Y(s)/U(s) = H(sI-F)^-1 G + J |
| Estimator | computes an estimate of the entire state vector when provided with the measurements of the system |
| Observer | same as estimator |
| Compensation | the control law and the estimator together |
| finding the control law; | u = -Kx |
| introducing the reference input with full-state feedback). | With the reference input in place, the closed-loop system has input r and output y |
| Two methods of pole selection | select poles without regard for effect on control effort, second has balance between good system response and control effort |
| dominant second-order poles; | we can choose the closed-loop poles for a higher-order system as a desired pair of dominant second-order poles |
| symmetric root locus (SRL). | For u = -Kx the optimal value of K is that which places the closed-loop poles at the stable roots of the SRL |
| Summarize the comments on the methods | Some modification is always necessary to achieve desired balance of bandwidth, and other design requirements |
Created by:
delafuente
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