Relationship between closed-loop systems

Relationship between frequency response and time response for closed-loop systems... 

The key idea is to use the Youla parameterization of all closed-loop systems which is affine in a free transfer matrix, and to optimize the free parameter for convex performance criteria. Each relationship between the external signals w(.s) and the external output z s) which is attainable by a stabilizing controller can be described as ... 

Let Fo be the number of degrees of freedom of the tree-structure system, once the joints have been cut, and q the corresponding Foxl vector of joint coordinates. The components of q are not independent because they are related through the cut joint constraints. Let be the number of the degrees of freedom of the closed loop system and z the F(xl vector of independent joint coordinates. A linear relationship between the two sets of joint velocities must exist and can be written as... 

In a TDL sensor, long-term variations wifhin the laser can cause changes in the relationship between laser input control current and output wavelength. These changes can create apparent wavelength shifts in the absorption spectrum that in turn result in absorption measurement errors. To address this potential problem, the LTS-100 features a closed-loop absorption peak control system that automatically introduces adjustments to the laser current to ensure fixed positioning of fhe absorption peaks. 

In open-loop system identification, it is assumed that the controller and reference signal are not present, that is, the control loop has not been closed. In such a case. Fig. 6.1 reduces to Fig. 6.2. The relationship between the input and output can then be written as... 

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