Output tracking via sliding modes in causal systems with time delay modeled by higher order pade approximations

Output tracking in a SISO causal uncertain nonlinear system with an output subject to a time delay is considered using sliding mode control. A higher order Pade approximation to a delay function with a known time delay is used to construct a model of a transformed system without a time delayed output and is employed in a feedback sliding mode control. This model functions as a predictor of the plant states and the plant output, but is of nonminimum phase due to the application of the Pade approximation. The method of the stable system center is used to stabilize the internal dynamics of this plant model, and a control is developed using a sliding surface to allow the plant to track an arbitrary reference profile given by an exogenous system with a known characteristic equation. Simulations of the system are performed for the plant model using a first, second and third order Pade approximations and a controller in plant feedback mode. Numerical examples for Pade approximations of increasing order are considered and compare

Second-order SM approach to SISO time-delay system output tracking

A fully linearizable single-input-single-output relative-degree n system with an output time delay is considered in this paper. Using the approach of Pade approximation, system center approach, and second-order sliding-mode (SM) control, we have obtained good output tracking results. The Smith predictor is used to compensate the difference between the actual delayed output and its approximation. A second-order supertwisting SM observer observes the disturbance in the plant. A nonlinear example is studied to show the effect of this methodology

Kuhn-Tucker-based stability conditions for systems with saturation

This paper presents a new approach to deriving stability conditions for continuous-time linear systems interconnected with a saturation. The method presented can be extended to handle a dead-zone, or in general, nonlinearities in the form of piecewise linear functions. By representing the saturation as a constrained optimization problem, the necessary (Kuhn-Tucker) conditions for optimality are used to derive linear and quadratic constraints which characterize the saturation. After selecting a candidate Lyapunov function, we pose the question of whether the Lyapunov function is decreasing along trajectories of the system as an implication between the necessary conditions derived from the saturation optimization, and the time derivative of the Lyapunov function. This leads to stability conditions in terms of linear matrix inequalities, which are obtained by an application of the S-procedure to the implication. An example is provided where the proposed technique is compared and contrasted with previous analysis methods

DISCRETE-TIME VARIABLE STRUCTURE CONTROLLER FOR AIRCRAFT FLIGHT ANGLE TRACKING

The paper presents the longitudinal, short-period aircraft dynamics and its application on the climb angle tracking. For the aircraft flight angle tracking the stable system centre technique is developed for controlling the output in a discrete-time non-minimum phase causal system using the sliding mode control. The developed discrete-time stable system centre technique transforms the output tracking problem to a corresponding state variable tracking problem by asymptotically identifying the ideal internal dynamics for the unstable internal states of a discrete-time system. A numerical simulation example is given to show the effectiveness of the method

Feedback linearization of nonminimum phase systems and control of aeroelastic systems and undersea vehicles

The thesis presents the design of feedback control systems for a class of nonminimum phase single input-single output nonlinear systems. The linearized system is assumed to have one unstable zero. Since asymptotic or exact tracking of output trajectory cannot be accomplished, an approximate output is derived by neglecting the unstable zero. Based on the inversion of the new input-output map, a feedback linearizing control is derived; These results are applied to control an aeroelastic system and a small undersea vehicle. For pitch angle control and plunge motion regulation, an inverse control system is designed for the aeroelastic system. Simulation results are shown for the pitch controller and the design is found to be robust to variation in the parameters. Dive plane control of an undersea vehicle is accomplished using an inverse control law. To attenuate the effect of the surface waves, a servocompensator has been designed. Later, a controller is also designed using the sliding mode control technique, to make the system more robust

The strengthening of Islamic values on students through the metaphor of accepting death: an Indonesian perception

Death is a sure entity for every human that cannot be avoided in human life. The purpose of this research was to reveal that the usage of metaphor technique called, “The Acceptance of Death” in group counselling can improve Islamic values on Muslim students. This study employed an action research using The Kemmis Model with the stages of planning, action, observation, and reflection. This research implemented group counselling with metaphor technique of accepting death by students. The research subjects were 20 female students of State Islamic University of Sultan Syarif Kasim Riau who lived in the campus dormitory. The selection of the research subjects was done randomly by choosing the female students who were willing to join the group counselling activity. The research results showed that the practice of metaphor technique of “The Acceptance of Death” in the group counselling can strengthen the Islamic values and their characteristics as Muslims. They understand their previous mistakes and are willing to be better for the sake of their life. They have the commitment to become the best students and the best Muslims

Flexible Modes Control Using Sliding Mode Observers: Application to Ares I

The launch vehicle dynamics affected by bending and sloshing modes are considered. Attitude measurement data that are corrupted by flexible modes could yield instability of the vehicle dynamics. Flexible body and sloshing modes are reconstructed by sliding mode observers. The resultant estimates are used to remove the undesirable dynamics from the measurements, and the direct effects of sloshing and bending modes on the launch vehicle are compensated by means of a controller that is designed without taking the bending and sloshing modes into account. A linearized mathematical model of Ares I launch vehicle was derived based on FRACTAL, a linear model developed by NASA/MSFC. The compensated vehicle dynamics with a simple PID controller were studied for the launch vehicle model that included two bending modes, two slosh modes and actuator dynamics. A simulation study demonstrated stable and accurate performance of the flight control system with the augmented simple PID controller without the use of traditional linear bending filters

Resource-aware motion control:feedforward, learning, and feedback

Controllers with new sampling schemes improve motion systems’ performanc