SEGUIMIENTO EXCAVACIÓN DE PILOTES PUENTES MAR

There have been very few methods that take the approach of using low gains for robustness and using an additional modification for improved transient tracking. The first method that explicitly states this objective was CGAC. Although first proposed in Yucelen and Johnson (2012a, 2012b) there have been very few quantitative results and no experimental results of this method in literature. The first study provided only a simple simulation of wing rock aircraft dynamics to illustrate the concept, while a more detailed simulation of the same dynamics was provided in Yucelen and Johnson (2013). Although it demonstrated the transient tracking improvements and smooth control signal of CGAC, it only provided qualitative results in the form of graphical plots. In Magree, Yucelen and Johnson (2012) qualitative simulation results were provided for CGAC applied to a high-fidelity autonomous helicopter model. CGAC was extended to enable the handling of state constraints in Schatz, Yucelen and Johnson (2013) and illustrated using simulations of lateral and the longitudinal motion of an aircraft. Further simulations of this extension for a helicopter model and wing rock dynamics are given in Schatz et al. (2013).

Apart from these studies there have been others that were derived from or related to CGAC. They include:

C h a p t e r 1 19 | P a g e 1. A modified version of the command governor based on the work of Yucelen and

Johnson (2012b) was combined with an adaptive backstepping controller in Sørensen, MEN and Breivik (2015). Although it was not an exact study on CGAC, it provides some quantitative data in the form of performance indices by using simulation of a marine surface vessel.

2. A command governor modification was developed without adaptive control as a form of robust control by De La Torre, Yucelen and Johnson (2016), with experimental results for fault tolerant control of a Hexarotor given in Falconí, Schatz and Holzapfel (2016). Although based on CGAC (De La Torre, Yucelen & Johnson 2016), it does not directly relate to the current study due to it being a non-adaptive control method.

3. Recently Na, Herrmann and Zhang (2017) proposed another modification for better transient performance without high adaptive gains using simulation results. A closer inspection of this method indicate that it is variant of CGAC, where the robustification filter that is separately added in CGAC has been incorporated into the command governor design.

Although not explicitly proposed for the purpose, another form of adaptive control that could be used to improve transient tracking at low gains is CMRAC. Although applied mainly as a modification that leads to smoother transient behaviour under high adaptation gain (Hovakimyan & Cao 2010), several studies show CMRAC improves tracking accuracy (Duarte-Mermoud, Rioseco & González 2005; Duarte-Mermoud, Rojo & Pérez 2002; Yu & Lloyd 1997), including one study that applied CMRAC to a UUV (Mrad & Majdalani 2003). In that work a variant named Bounded Gain Forgetting (BGF) CMRAC method was compared with standard adaptive control with only qualitative simulation results being provided. More recently, another variant of composite adaptive control was introduced by Lavretsky (2009). This method has several novel improvements over previous CMRAC methods including being applicable to a generic class of Multiple Input Multiple Output (MIMO) dynamical systems with matched nonlinear-in-state and linear-in-parameters uncertainties (Lavretsky 2009). Although it has shown promising results (Dydek, Annaswamy & Lavretsky 2013; Gregory, Gadient & Lavretsky 2011), it is mainly used with high learning rates to

20 | P a g e C h a p t e r 1 provide smoother control input and has thus far not been quantitatively assessed for tracking improvements under low learning rates.

Another composite variant named PMRAC was first proposed in Lavretsky, Gadient and Gregory (2010) and has the advantage of being applicable to a generic class of MIMO dynamical systems with matched nonlinear-in-state and linear-in-parameters uncertainties similar to CMRAC. It differed from CMRAC in that the prediction error is generated by a state predictor with an error feedback. Thus, its prediction component has the structural formulation of indirect Modified-MRAC (M-MRAC) (Stepanyan & Krishnakumar 2012b) or Closed-Loop Reference Model (CLRM) architecture (Gibson, Annaswamy & Lavretsky 2013). Lavretsky, Gadient and Gregory (2010) tested it in simulations for an aircraft pitch control under high adaptive gains and observed that while the tracking performance was similar to MRAC the oscillations in the control signal was reduced. A more detailed simulation study of PMRAC for a generic aircraft was reported in Campbell and Kaneshige (2010). In this study, PMRAC was simulated using the NASA Generic Transport Model (GTM) in a full nonlinear simulation for a doublet manoeuvre. Only a few qualitative results were presented with similar conclusions. PMRAC was also used in a more extensive study that looked at simulation based sensitivity analysis of seven different controllers for the same NASA GTM in Campbell et al. (2010b). It was followed by a pilot handling study of the same controllers using a flight simulator (Campbell et al. 2010a). In addition, Khosravi, Lachini and Sarhadi (2015) applied PMRAC to an automotive vehicle lateral control in simulation with only qualitative results, similar to Lavretsky, Gadient and Gregory (2010), presented with very similar conclusions. A closer look at these studies showed that they gave very few specific quantitative details of PMRAC and no experimental results.