Desired Eigenvalues Placement Research Articles

Tracking control for nonminimum phase MIMO micro aerial vehicle – a dynamic sliding manifold approach

Nonminimum phase output tracking has been addressed for a fixed-wing micro aerial vehicle. Nonminimum phase characteristics in an aircraft result from the fact that the process of generating upward vertical motion produces an initial downward force, causing the aircraft to lose altitude momentarily, and vice versa. This phenomenon leads to unstable internal dynamics in the plant model. A dynamic sliding-surface-based sliding mode control is chosen to stabilize the internal dynamics and to provide asymptotic output tracking error convergence to zero with desired eigenvalue placement. The control is designed in such a way that the output of the plant model should track a nonlinear time-varying reference trajectory generated at every time instant with a finite number of nonzero time derivatives. Design of second-order sliding-mode-based super twisting controller which ensures finite-time stability of the internal dynamics is proposed in this work. The proposed control methodology is applied in the design of an autolanding controller for a micro aerial vehicle with nonminimum phase behavior. MATLAB-based simulation results and discussions are presented to evaluate the performance of the controller and robustness of the sliding mode with respect to matched and unmatched disturbances. The proposed control algorithm has been successfully implemented in hardware-in-the-loop simulation and results are given.

Sliding Mode Control of Uncertain Time Delay System using Lambert W Function

Abstract This paper presents a robust sliding mode control law for time delay systems with parametric uncertainties and external disturbances. The uncertainties and disturbances are assumed to be matched. The method for designing a switching hyperplane using Lambert W function is proposed for generation of sliding motion in the system. This method includes desired eigenvalue placement for getting a stable sliding manifold. A controller is designed such that system trajectories reach sliding surface in finite time and remain there for all subsequent time. Simulation results are also shown on a numerical example to illustrate the effectiveness of the proposed method.

Eigenvalue Placement Approach to Synchronization of Networked Nonlinear Oscillators

This paper is concerned with synchronization of nonlinear oscillators coupled via a directed network. It is known that that the synchronization can be achieved by choosing the coupling weights such that nonzero eigenvalues of the weighted Laplacian are located inside a certain convex region. We present a design method of the coupling weights which achieves the desired eigenvalue placement based on the bilinear matrix inequality optimization. The present method improves the previously reported method by the authors (Hibi and Takaba (2012)) by introducing a more general convex region for the eigenvalue placement.

Aircraft Nonminimum Phase Control in Dynamic Sliding Manifolds

The approximate causal nonminimum phase output tracking problem is considered for an F-16 nonlinear sixdegree-of-freedom modelandaddressed via sliding modecontrol.Asymptoticoutputtracking-errordynamicswith desired eigenvalue placement are provided in case of tracking causal reference output proe le with a e nite number of nonzero time derivatives (piecewise polynomial spline model ) in the presence of unmatched disturbances of the same kind. A complete constructive algorithm for tracking controller design is built for a class of uncertain nonlinear multi-input/multi-output systems with known linear unstable internal dynamics. An analysis is made of the issue that the given nonlinear aircraft model yields to the approach developed.

Reusable Launch Vehicle Control in Multiple-Time-Scale Sliding Modes

A reusable launch vehicle control problem during ascent is addressed via multiple-time scaled continuous sliding mode control. The proposed sliding mode controller utilizes a two-loop structure and provides robust, de-coupled tracking of both orientation angle command profiles and angular rate command profiles in the presence of bounded external disturbances and plant uncertainties. Sliding mode control causes the angular rate and orientation angle tracking error dynamics to be constrained to linear, de-coupled, homogeneous, and vector valued differential equations with desired eigenvalues placement. Overall stability of a two-loop control system is addressed. An optimal control allocation algorithm is designed that allocates torque commands into end-effector deflection commands, which are executed by the actuators. The dual-time scale sliding mode controller was designed for the X-33 technology demonstration sub-orbital launch vehicle in the launch mode. Simulation results show that the designed controller provides robust, accurate, de-coupled tracking of the orientation angle command profiles in presence of external disturbances and vehicle inertia uncertainties. This is a significant advancement in performance over that achieved with linear, gain scheduled control systems currently being used for launch vehicles.

Nonminimum phase tracking in MIMO systems with square input–output dynamics via dynamic sliding manifolds

The approximate causal output tracking problem in nonlinear multi-input/multi-output (MIMO) nonminimum phase systems is addressed via sliding mode control. A class of MIMO nonlinear systems with matched nonlinearities as well as matched and unmatched disturbances, where the number of inputs, outputs, and the total relative degree are equal, is considered. The output tracking problem is solved using dynamic sliding manifold technique. The linear bounded error dynamics with desired eigenvalue placement forced by unmatched disturbance and causal reference output profile are provided. Addressing nonminimum phase condition, the sliding mode controller (SMC) joins features of a conventional SMC (insensitivity to matched nonlinearities and disturbances) and a conventional dynamic compensator (accomodation to unmatched disturbances). Theoretical results are demonstrated on a numerical example.