definitions 3
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| State-variable form | x=Fx+Gu
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| State of the system | the column vector x, it contains in elements for an nth-order system
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| System matrix | The quantity F is an n x n system matrix
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| Input matrix | G is an n x 1 input matrix
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| Output matrix | H is a 1 x n row matrix reffered to as the output matrix
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| Direct transmission term | J is a scalar called the direct transmission term
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| Transpose | X=[x1 x2…]^T
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| An integrator | a device whose input is the derivative of its ouput
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| components of an analog computer | Integrator, summer, potentiometer
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| 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.
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| Dynamic response from the state equations | G(S) = Y(s)/U(s) = H(sI-F)^-1 G + J
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| Estimator | computes an estimate of the entire state vector when provided with the measurements of the system
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| Observer | same as estimator
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| Compensation | the control law and the estimator together
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| finding the control law; | u = -Kx
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| introducing the reference input with full-state feedback). | With the reference input in place, the closed-loop system has input r and output y
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| Two methods of pole selection | select poles without regard for effect on control effort, second has balance between good system response and control effort
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| 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
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| 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
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| Summarize the comments on the methods | Some modification is always necessary to achieve desired balance of bandwidth, and other design requirements
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