Prognosis and Health Management
The Prognosis and Health Management ([62, 74, 84]) or PHM has recently emerged as a key technology which uses data analysis or model based techniques to assess the actual health conditions of an engineered system (health reasoning) and predict how and when the system is likely to fail (health prognosis) by evaluate the lifetime of the system. In addition, the necessity of PHM is being considered by the growing demand of Condition based Maintenance (CBM) and extension of operational life in high-value engineered systems like nuclear power plants, wind turbines, pipelines, satellites and aircraft. One of the main objectives of the PHM is to predict how the system will behave in the future in order to know if more stress or changes in the nominal operations on the system will likely cause an acceleration towards a certain undesirable event or failure condition, and the time when such event will occurs. The obtained prediction is used to compute the Remaining Useful Life (RUL) of the component and/or system. According to  the PHM is developed by executing four basic functions:
Health Sensing: acquire sensor signals for an engineered system by in-situ monitoring techniques and to ensure a high likelihood of damage detection.
Health Reasoning: extract health-relevant system information from the acquire sensor signals using feature extraction techniques and to classify system health states by using health classication techniques.
Health Prognosis: dene a threshold for each unusual or abnormal state and predict the RUL, i.e., the amount of time remaining before the system can not longer performance its required functions.
Health Management: enable optimal decision making on maintenance of the system based on the RUL prediction to minimize the Life Cycle Cost (LCC).
In addition, other works like  dene that the necessary steps to develop the PHM includes:
Data acquisition: collect measurements data from sensors and process them to extract useful features for diagnosis.
Diagnostics: a fault is detected for any abnormal state, isolated to determine which component is failing and identied in order to know how severe it is with respect to the failure threshold.
Prognostics: predict how long it will take until failure under the current operating conditions.
Health Management: manage in optimal manner the maintenance scheduling and logistics support.
Among previous steps, prognostics is the key enabler that permits the reliability of a system to be evaluated in its actual life cycle conditions. In other works, it predicts the time at which a system or a component will no longer perform its intended function, thus giving users the opportunity to mitigate system level risks while extending its useful life.
Nowadays, most maintenance systems applied to engineered systems are either corrective (repairing or replacing a system after it fails) or preventive (inspecting a system on a routine schedule regardless of whether inspection is actually needed). The former strategy is called corrective maintenance (CM) and the latter is called preventive maintenance (PM). Both approaches are expensive and incur high LCCs. PHM meanwhile, uses sensor signals from a system in operation to assess the actual health of the system and predict when and how the system is likely to fail. The health and life information provide by PHM enables eld engineers to take a maintenance action only when needed. This is referred to as a condition based maintenance (CBM) strategy. CBM often results in a lower LCC than CM and/or PM strategies as it can be seen in Figure 2.2.
Short and Long term predictions
As it was mentioned in previous paragraph, the main objective of PHM is to increase the system performances by improving the system maintenance time. Such task is carried out by monitoring the actual health state of the system and to determine possible future deviations of its nominal operation. Usually, two fundamental situations make that the system is out of its nominal operations, the fault occurrence and degradation caused by fatigue due to constant usage or operation. The eect of fault occurrence can be addressed by rstly using fault diagnosis methods to detect, isolate and identify the fault. Then the fault eect can be mitigated by generate fault tolerant control system in order to guarantee the system operation. On the other hand, the degradation caused by continuous use is determined by computing the actual health state of the system and compare it with the Begin of Life (BoL) value. With this, it is possible to dene what is the degradation level and its evolution. Once the actual degradation trend and its causes are known, it is possible to make progression and to predict its future evolution for both short and long term predictions. The use of short or long term predictions depends on the system dynamics, lifetime of the system or component and accuracy of the prediction ([131, 175]). Figure 2.5 shows the prediction of the possible trend that the performance of a system could have. The solid dark blue line represents the past evolution of the system behavior until present time ta, and the brown area is the Safety Zone (SZ) or the nominal operational limit. According to dierent factors such as the inputs of the system, aging, or even external disturbances, the system behavior could be progressed until reach values outside of its nominal operation. In that sense, if such factors are known, the future trajectory of the system behavior can be predicted until reaching the SZ (segmented blue lines).
PHM in multirotor UAV
In addition, the PHM is useful to determine the actual and future evolutions of system performances considering short and long term predictions. However the predictions executed around the PHM approaches are not limited to evaluate only the system health. In UAV applications, the PHM have been used to improve the ight performance by developing health management systems which allows designers to examine optimal fault accommodation techniques that can increase availability, improve safety, and optimize maintenance resource planning for complex vehicle systems ([48, 60, 107, 208]). On the other hand, one emerging application for UAV PHM electrically powered is the prognosis of battery performance and prediction of ight endurance.
A multirotor is a particular helicopter lifted and propelled by two or more BLDCMs with vertical take o and landing capabilities (). Usually, the multirotors are classied as rotorcraft, as opposed to xed-wing aircraft, because their lift is generated by a set of revolving narrow-chord airfoils. Unlike most helicopters, multirotors generally have symmetrically pitched blades. Control of vehicle motion (position and orientation) is achieved by modifying the rotation rate and/or the axis of rotation direction of one or more BLDCMs, thereby changing its torque load and thrust/lift characteristics. According to number of BLDCMs it is possible to get dierent design congurations and ight modes, e.g. in Figure 3.1 two Trirotors ight conguration are shown where (a) all rotors are co-rotating or (b) one of the rotors (green one) counter-rotates.
Position and orientation controller design
In order to keep the orientation of the vehicle stable during the ight and at the same time to follow a reference trajectory around x-y-z axis describing the xed inertial frame, several control strategies have been developed using dierent methods and techniques which are based on the mathematical model of the vehicle. Generally such control techniques can be classied in two types: linear ([93, 112, 174]) and nonlinear ([67, 95, 96, 129]) controllers.
According to , multirotors are multivariable highly coupled nonlinear systems. The use of linear control for this system consists of an algebraic manipulation for state variables of linear model under certain environmental conditions. For trajectory tracking, the linear control can be applied only if the trajectory and the ying conditions for the quadrotor are not complex and dicult. In such cases, the coupled nature of the system requires high variations in the angular velocities and fast variations in the altitude, which cannot be realized by such controllers. For such linear controller techniques, the most common are the Proportional Integral Derivative (PID) controller ([5, 11, 91, 118, 142]), the Linear Quadratic Regulator (LQR) ([8, 66, 79, 87, 88, 171]) and H-Innity controller ([7, 126, 143]).
On the other hand, the nonlinear controller are based on nonlinear mathematical representation of multirotor vehicle. They are able to manage the stabilization problem taking into account the nonlinear coupling of orientation dynamics around Euler angles, and the trajectory tracking considering complex ying conditions as well as obstacle avoidance. Among nonlinear controller techniques applied to multirotor the following are the most common: Sliding Mode Control, Backstepping Control ([32, 92, 146]), Feedback Linearization ([18, 92, 186]), Neural Network and Fuzzy Logic ([81, 157, 189]), Model Based Predictive Control (MBPC) ([85, 135, 140]), Adaptive Control ([76, 115, 123]) and Robust Control Algorithms ([4, 15, 90]).
In the next section, the development of a Cascade Control Loop (CCL) for both stabilization of hexarotor orientation and tracking of a reference position based on a classical PID controller strategy will be explained. In addition, the eect of the battery discharge will be analyzed considering the impact on the control signals and the angular speed of BLDCM by adding the dynamics of propulsion system.
Cascade Control Loop (CCL) development
Since the objective of this work is not to develop an advanced control law, the trajectory tracking controller is based on a position and orientation classical Cascade Control Loop (CCL) as it can be seen in Figure 3.11. The implementation of this control loop is developed by split the hexarotor dynamics described by (3.17) into translational and rotational dynamics. The rotational dynamics describes the orientation ofthe vehicle from Euler angles [ ]T and the translational dynamics represents the position around the x y z axis of xed inertial frame and it also depends on the Euler angles variation. As it can be not from Figure 3.11 on left side, the position and orientation controllers generates the reference control signals (thrust force and torques) denoted by U i. In addition, the position controller also generates the roll (r) and pitch (r) reference angles (inputs of the orientation controller) by considering that a variation on roll and pitch angles generate a movement around and y and x position respectively. On the other hand, the yaw ( ) reference angle is generated externally. The reference control signals are distributed around of BLDCMs and the angular speed generated by them produce the control inputs denoted by Ui. The coupling between the propulsion system and the reference control signals will be explained in Subsection 3.4.2.
Table of contents :
1 Generalities of topic thesis
1.3 Objectives and aims of topic thesis
1.5 Contributions and publications
1.6 Thesis organization
2 State of the Art
2.1 Prognosis and Health Management
2.1.1 Prognosis methods
2.1.2 Short and Long term predictions
2.1.3 PHM in multirotor UAV
2.2 Mission planning
2.3 Path planning
3 Mathematical model of UAV hexarotor
3.1 Multirotor congurations
3.2 Hexarotor dynamics
3.3 Propulsion system
3.3.1 Lithium Polymer battery dynamics
3.3.2 BrushLess DC Motor dynamics
3.4 Position and orientation controller design
3.4.1 Cascade Control Loop (CCL) development
3.4.2 Integration of Propulsion system in CCL
4 Prognosis and Health Management of multirotor UAV
4.1 Prognosis module
4.1.1 State Estimation
4.1.2 Propagation and Prediction of estimated states
4.2 Multirotor Flight Endurance
4.2.1 Endurance model
4.2.2 Flight Endurance Prediction
4.2.3 SoC estimation
4.3 Battery Health prediction
5 Energy aware mission planning
5.1 Mission planning strategy
5.1.1 Energy consumption of hexarotor
5.1.2 Path generation based on energy consumption
5.2 Simulation results
6 Conclusions and perspectives
6.1 Prognosis and Health Management module
6.2 Mission planning and path planning
Appendix A. Parametrization of lithium battery