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Automatic Control 3

definitions 3

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