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Kane's Method of Linearization Applied to the Dynamics of a Beam in Large Overall Motion
Published in Arun K. Banerjee, Flexible Multibody Dynamics, 2022
This chapter is based on a paper [1] that deals with the issue of linearization with respect to modal coordinates associated with vibration mode shapes, for a beam executing small vibrations in a reference frame that is itself undergoing large motion. Study of the behavior of flexible bodies attached to moving supports has been vigorously pursued for over 60 years in diverse disciplines, such as machine design, robotics, helicopter dynamics, and spacecraft dynamics. In particular, beams attached to moving bases have received attention in hundreds of technical papers dealing variously with elastic linkages, rotating machinery, robotic manipulator arms, aircraft propellers, helicopter rotor blades, and spinning satellites with flexible appendages. Indeed, the existing literature is so voluminous as to preclude a comprehensive review even within the confines of a chapter. A 1974 review by Modi [2] of the literature on rigid bodies with flexible appendages contains more than 200 references, and we will add to it with relatively later pertinent publications, as the discussion proceeds. Here, we will derive equations of motion of beams in large overall motion, by Kane's method [3], for small deformations about a frame undergoing large motion. The method forms linearized equations, without deriving the non-linear equations, but requires keeping non-linear terms up to a certain point in the analysis.
A high bandwidth control system for the helicopter in-flight simulator ATTHeS – modelling, performance and applications
Published in Mark B. Tischler, Advances in Aircraft Flight Control, 2018
Wolfgang von Grünhagen, Gerd Bouwer, Heinz-Jürgen Pausder, Frohmut Henschel, Jürgen Kaletka
Manned simulation continues to be the important tool for flying qualities research as well as in systems design approach. The implementation of highly augmented flight control systems, new controller types and pilot information systems will give designers more flexibility to alter the response characteristics of the overall helicopter system and to tailor the desired flying qualities. This capability is also a two-edged possibility, in as far as it has to have adequate guidance from flying qualities specifications, concerning which types of helicopter dynamics are desirable for various piloting tasks. The demands placed upon the engineers continue to emphasize a strong need for realistic simulation. The pitfalls inherent in the exclusive use of ground-based pilot-in-the-loop simulation will become evident during the development of the next generation of rotorcraft. For this reason, an integrated approach, using both ground and in-flight simulators throughout the design process and the flying qualities research, is important.
Optical Flow Sensing and Its Precision Vertical Landing Applications
Published in Yallup Kevin, Basiricò Laura, Iniewski Kris, Sensors for Diagnostics and Monitoring, 2018
Mohammad K. Al-Sharman, Murad Qasaimeh, Bara J. Emran, Mohammad A. Jaradat, Mohammad Amin Al-Jarrah
This section briefly details the small-scale flybarless helicopter model. The nonlinear model of the Maxi Joker 3 helicopter is used in this study (Figure 13.2). Elaborated details on modeling the Maxi Joker 3 helicopter using the top-down modeling approach can be found in [4, 15]. This approach models the helicopter dynamics in four major blocks. The actuator dynamics, the flapping and thrust dynamics, the force and torques, and the rigid body equations are modeled in a Matlab (R) Simulink environment. The modeling of the flybarless helicopter is thoroughly illustrated in [4].
Sliding mode observer-based fault detection for helicopter system
Published in Journal of Control and Decision, 2022
M. Raghappriya, S. Kanthalakshmi
With inherent non-linearity, cross-coupling effects, unmodelled dynamics, and parametric uncertainty, helicopter dynamics are complex. Because of the system's complicated dynamics, fault detection is critical for ensuring safety and reliability while maintaining acceptable performance. In the literature, a number of model-based fault diagnosis methods have been presented. The use of observers is one of the model-based Fault Detection and Identification (FDI) methods. Observers generate residuals which are used to detect faults. Residual generation employs a system model into which the actuator control inputs and the sensor outputs of the system are injected in order to forecast the system's behaviour and compare it to the actual behaviour. In fault-free condition, residuals should be close to zero and in faulty condition, residual deviates from zero. With some statistical tests or thresholds, fault decision signals are generated. Because of the relation between state feedback control and full-order observer design, fault detection problem becomes an equivalent state feedback control problem. Sliding mode observers (SMOs) are a type of non-linear observer that tries to reconstruct the fault rather than identify the presence of a fault using residual signals (Edwards et al., 2000; Spurgeon, 2008).
Control for cooperative transport of a bar-shaped payload with rotorcraft UAVs including a landing stage on mobile robots
Published in International Journal of Systems Science, 2020
Javier Gimenez, Lucio R. Salinas, Daniel C. Gandolfo, Claudio D. Rosales, Ricardo Carelli
The UAV model used is a 6DoF dynamic model of a mini-helicopter named MIT's X-Cell .60 extracted from Gavrilets (2003) with nominal parameters. It adequately represents the mini-helicopter dynamics in both hovering and low-speed flight envelope (up to 20 [m/s] forward flight). The model considers wind effects and non-ideal dynamics such as flapping, drag, and actuator dynamics (see Gavrilets, 2003; Gimenez et al., 2018 for more details). For each UAV, the connection between the input commands for the dynamic model and the kinematic formation control law is made via an adaptation stage conformed by two stages: a velocity frame change and a PID-based cascade control (see details in Gandolfo et al., 2016; Gimenez et al., 2018; Salinas et al., 2014). An important advantage of this proposal is that the same controller can be used for other types of miniature rotorcraft (such as quadrotors (Gandolfo et al., 2017)) by only modifying the adaptation stage.
Fast finite-time backstepping for helicopters under input constraints and perturbations
Published in International Journal of Systems Science, 2020
Along (5)–(6), helicopter dynamics (2) and (4) can be rewritten as follows: where . , . The parameter , , and are the approximate values of the main control coefficients. The lumped disturbances and involve external perturbations, parameter uncertainties and unmodelled dynamics. In (7)–(8), just the main control coefficients are needed for designing the controller, which greatly reduces the workload of identifying the helicopter dynamics. Practically, the real control inputs are also subjected to saturation nonlinearities due to the physical limitations of actuators. The input constraints are expressed as where ; is our designed control command; and are the minimum and maximum constraints of the input commands, respectively. This input saturation problem would potentially give rise to system performance degradation or even loss of stability. Thus it is necessary to quickly deal with the adverse effects when input saturation occurs.