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In particular, we distinguish several parameters of the camera to determine the point mapping mathematically. These parameters comprise a model of the camera applied. In particular, such a model represents a mathematical description of how the light reflected or emitted at points in a 3D scene is projected onto the image plane of the camera. In this Section we will be concerned with a projective camera model often referred to as a pinhole camera model. It is a model of a pinhole camera having its aperture infinitely small (reduced to a single point).
Green indicates that the real value is larger then that used for controller design. The red dot marks the location in case of no variation. Since the factors kTel and k v are linearly scaled the plots reveal the sensitivity to parameter variation. The actual damping of the outer loop is affected heavily by parameter mismatch. The step response in fig. 9 illustrates the performance loss. Errors in the delay are again more critical. 2 0 Time 0 Time Fig. 9: Step response of closed loop. Left: Variation of mass.
For sake of simplicity inverter dynamics have been neglected. A consideration can be found in (Levant & Friedman, 2002) showing that dynamics are pushed to sliding of order two with similar dynamics. Comparing sliding mode to linear control design reveals an offset in disturbance rejection for classical sliding mode control, which can be coped with integral action, cf. eq. (25) and (26). It can be seen that chosen parameters lead to similar closed loop dynamics as input balancing, however being nonlinear.