In this paper we have considered a prey-predator model with Holling type of predation and independent harvesting in either species. The purpose of the work is to offer mathematical analysis of the model and to discuss some significant qualitative results that are expected to arise from the interplay of biological forces. Our study shows that, using the harvesting efforts as controls, it is possible to break the cyclic behaviour of the system and drive it to a required state. Also it is possible to introduce globally stable limit cycle in the system using the above controls.
In this paper, the fault tolerant capabilities of the neural aided sliding mode controller for autolanding under actuator failures and severe winds developed earlier are improved significantly by incorporating a novel anti-windup strategy and a phase compensation scheme. This controller further increases the size of the fault tolerance envelope for various types of control surface stuck faults and provides complete coverage at every point within the envelope boundaries. Earlier work by the authors showed the existence of a neural-aided sliding mode controller which could handle a wide range of actuator stuck faults. One of the major drawbacks of this earlier controller is that it does not ensure that all points within the range of minimum and maximum bounds of the fault tolerance envelope are covered. The anti-windup proposed in this paper is a generalization of the scheme used for proportionalderivative-integral controllers to the cascaded trajectory following controllers designed by the authors. This scheme can handle requirements of state limiting as well as multiple redundant control surface saturation. The proposed anti-wind up design is a simplification over the command filter approach used for adaptive backstepping. The approach is demonstrated for a fixed-wing aircraft undergoing unknown actuator stuck failures and subject to severe wind disturbances during autolanding. An example of three control surface failures (both ailerons and rudder) handled by this controller is also presented.
A novel formulation of the flight dynamic equations is presented that permits a rapid solution for the design of trajectory following autopilots for nonlinear aircraft dynamic models. A robust autopilot control structure is developed based on the combination of the good features of the nonlinear dynamic inversion (NDI) method, integrator backstepping method, time scale separation and control allocation methods. The aircraft equations of motion are formulated in suitable variables so that the matrices involved in the block backstepping control design method are diagonally dominant. This allows us to use a linear controller structure for a trajectory following autopilot for the nonlinear aircraft model using the well known loop by loop controller design approach. The resulting autopilot for the fixed-wing rigid-body aircraft with a cascaded structure is referred to as the diagonally dominant backstepping (DDBS) controller. The method is illustrated here for an aircraft auto-landing problem under unknown actuator failures and severe winds. The requirement of state and control surface limiting is also addressed in the context of the design of the DDBS controller.
This paper presents a dynamic model of a rotating flexible beam carrying a payload at its tip. The model accounts for the driving shaft and the arm root flexibilities. The finite element method and the Lagrangian dynamics are used in deriving the equations of motion with the small deformation theory assumptions and the Euler-Bernoulli beam theory. The obtained model is a nonlinear-coupled system of differential equations. The model is simulated for different combinations of shaft and root flexibilities and arm properties. The simulation results showed that the root flexibility is an important factor that should be considered in association with the arm and shaft flexibilities, as its dynamics influence the motor motion. Moreover, the effect of system non-linearity on the dynamic behavior is investigated by simulating the equivalent linearized system and it was found to be an important factor that should be considered, particularly when designing a control strategy for practical implementation.
A nonlinear flight controller is developed using dynamic inversion principles. The nonlinearities in the equations of motion arising from inertia coupling and the gravity vector are compensated by dynamic inversion. Control and state decoupling is demonstrated for conventional aileron, elevator and rudder control surfaces using a static control allocation matrix and choice of stability axis rates for feedback respectively. We demonstrate that the right hand sides of the equations of motion can be approximated by using flight path variables and traditional feedback signals like normal and lateral accelerations. Further, except for the inertia compensation and gravity compensation terms which contain sine and cosine functions, the remainder of the controller can be designed in the linear domain. The simulation results are presented for a case where a nonlinear high performance fighter aircraft is undergoing a high angle of attack stability axis roll maneuver. This maneuver exercises the aircraft over a very wide dynamic range in a short time and demonstrates the capabilities of the nonlinear controller.
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