Abstract
In the following chapter, the non-identifier based adaptive speed and position control problem (as introduced in Sect. 3.1) will be solved for industrial servo-systems with stiff and elastic coupling, respectively.
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Notes
- 1.
To obtain \(M_{\varvec{z}}\) and \(M_{\dot{V}}\), the augmented 2MS (11.41), (11.42), (11.48) must be transformed into BIF to allow for a computation of \(|\hat{a}_1|\), \(\Vert \hat{\varvec{a}}_2 \Vert \), \(\Vert \hat{\varvec{a}}_3 \Vert \), etc. (see proof of Proposition 11.9). The details are omitted.
- 2.
Another common approach to avoid overshoots for PID position control is to smooth the reference signal by a first-order filter (see [300, p. 81 f.]). However, then, set-point tracking of a reference step—as required for Experiment PC2—is not feasible anymore.
- 3.
To compute M as in (9.128) for the feasibility check, the augmented 2MS (11.27), (11.28), (11.72) must be transformed into BIF (see proof of Proposition 11.17) such that \(|\hat{a}_1|\), \(\Vert \hat{\varvec{a}}_2 \Vert \), etc. are available for evaluation of \(M_{\dot{V}}\) as in (9.97) and \(M_{\varvec{z}}\) as in (9.98). The details are omitted.
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Hackl, C.M. (2017). Speed and Position Control of Industrial Servo-Systems. In: Non-identifier Based Adaptive Control in Mechatronics. Lecture Notes in Control and Information Sciences, vol 466. Springer, Cham. https://doi.org/10.1007/978-3-319-55036-7_11
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DOI: https://doi.org/10.1007/978-3-319-55036-7_11
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