Interconnection and damping assignment passivity-based control of an unmanned helicopter

Abstract

The field of passivity-based control is a relatively new study field. As such, literat- ure on the application of this optimal non-linear control technique to complex control problems is limited. Only as recently as 2014 has Interconnection and Damping As- signment Passivity-based Control (IDA-PBC) been applied to quad-rotor models [29, 30]. The main motivation for selecting this specific form of PBC is its ability to shape the total energy of the system and control both the Cartesian and orientation states of the system [29]. Within this work, IDA-PBC is applied to helicopter dynamics for the same purpose. This work serves to provide an introduction to the control design of such a heli- copter system for the purposes of trajectory tracking. The trajectory tracking case is a special case of regular IDA-PBC design, which serves primarily to control the system at a specified operating point that does not change continuously. For some aircraft systems, this is acceptable [29]. However, when the aircraft needs to track a dynamic trajectory, an alternate set of equations is used [30]. This work presents the informa- tion necessary to design a control system for both purposes. However, the ultimate controller design and validation tests are presented for the trajectory tracking case. The problem statement for the research is given as follows:

This study aims to apply Interconnection and Damping Assignment Passivity- based Control (IDA-PBC) to an unmanned helicopter platform with the aim to investigate if significant flight accuracy and energy efficiency benefits may be ob- tained, and to understand if there is merit in the further study of this optimal control technique for the field of RWUAVs.

The flight accuracy and energy efficiency mentioned here are two questions that arose from previous studies. It is well understood that non-linear controller design is often more difficult to implement. Also, the robustness of the control system stability is often questioned. It is necessary to understand whether this non-linear technique has its benefits in application or only within academic purposes. Also worth understanding is whether the “energy-based” control technique will ultimately provide increased energy efficiency during control. This study aims to answer those questions and also guide further research topics at the North-West University. Within this work, the reader will find a critical review of the literature on passivity- based control. The basic modelling of the helicopter is discussed, but with the addition of an explanation of how to set up the model for the port-Hamiltonian modelling framework that is used for IDA-PBC. The 6 degree-of-freedom (DOF) modelling of the helicopter is done with Newton’s equations, but allows for the rotating Earth reference frame. The model accepts forces and torques as inputs to produce the Cartesian and orientation variables as outputs. These are sufficient to describe a helicopter’s motion. The work continues to show the design of the trajectory tracking IDA-PBC controller. With some preliminary understanding of IDA-PBC of other mechanical systems, it is possible to select the appropriate energy function with ease. This energy function also serves as the cost function for the optimal control strategy. The IDA-PBC controller is designed with the help of MAPLE™ 18. The controller accepts reference trajectories as inputs for each DOF within the body reference frame. The outputs of the controller

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are signals describing the forces and torques necessary for the helicopter to fly such a reference trajectory. The controller makes use of the energy-based cost function to optimise tracking of reference trajectories. Such a controller is easily linked with the 6-DOF model to allow adequate simulation of the designed control strategy. The energy-based cost function incorporates several free parameters that are left to the designer to choose. Unfortunately, there is not yet an analytical technique that allows one to calculate the value of those gains as is the case with Ackerman’s formula for linear systems [6]. Instead, the values were determined empirically with the help of a simple optimisation strategy. The strategy was not the focus of this study and can be dramatically improved, but it served the purposes of this work. It may be mentioned here, that the free parameters may be optimised for more strict trajectory-tracking at the expense of the high gains that are associated with such conditions. Typically, increased gains may be associated with lowered energy efficiency, which is precisely what this study aimed to avoid with the optimal control technique. For this reason, the gains are selected as low as possible while maintaining excellent trajectory tracking. For validation of the control system, measured data of a piloted helicopter system were used to evaluate the performance of the controller. The measured data inputs from the pilot were processed with a human pilot transfer function from [26] to estim- ate the flight path that the pilot attempted to fly. This estimated trajectory was then supplied to the controller to see how the controller would follow the path in conjunc- tion with the derived helicopter model. Results showed excellent trajectory tracking. From this can be concluded that the system will provide control inputs as well as, if not better than, an experienced pilot, even for manoeuvres that test the non-linear abilities of the controller. This should make the designed control system suitable for routine surveillance flights as well as aggressive avoidance manoeuvres, if the refer- ence trajectories for these manoeuvres can be adequately estimated.