Ho Chul Lee

Decoupling and tracking control using eigenstructure assignment for linear time-varying systems

This work is concerned with the assignment of a desired PD-eigenstructure for linear time-varying systems. Despite its well-known limitations, gain scheduling control appeared to be a focus of the research efforts. Scheduling of frozen-time, frozen-state controllers for fast time-varying dynamics is known to be mathematically fallacious, and practically hazardous. Therefore, recent research efforts are being directed towards applying time-varying controllers. In this paper, (a) we introduce a differential algebraic eigenvalue theory for linear time-varying systems, and then (b) a novel decoupling and tracking control scheme is proposed by using the PD-eigenstructure assignment scheme via a differential Sylvester equation and a Command Generator Tracker for linear time-varying systems. The PD-eigenstructure assignment is utilized as a regulator. A feedforward gain for tracking control is computed by using the command generator tracker. The whole design procedure of the proposed PD-eigenstructure assignment scheme is systematic in nature. The scheme could be used to determine stability of linear time-varying systems easily as well as to provide a new horizon of designing controllers for the linear time-varying systems. The presented method is illustrated by numerical examples.

Autopilot Design for Agile Missile Using Time-Varying Control Technique

Abstract This paper is concerned with control allocation strategies with two time scale dynamic inversion which generate nominal control input trajectories. In addition, an robust flight control design method is proposed by using a time-varying control technique which is time-varying version of the pole placement of linear time invariant system for an agile missile with aerodynamic fin, thrust vectoring control, and side-jet thruster. The control allocation algorithms proposed in this paper are capable of extracting the maximum performance by combining each control effector. The time-varying control technique for the autopilot design enhances the robustness of the tracking performance for the wide angle of attack range. The main results are validated through the nonlinear simulations with aerodynamic data.

Efficient eigenvalue assignment for linear time-varying systems

This paper deals with the eigenvalue assignment for linear time-varying systems to achieve feedback stabilization. For this, we introduce the novel eigenvalue concepts. It is believed that this technique is the generalized version of the Ackerman formula for linear time-invariant systems. The advantages of the proposed Ackerman-like formula are that it does not require the transformation of the original system into the phase-variable form nor the computation of eigenvalues of the original system.

Ackerman-like formula for linear time-varying systems

Deals with the eigenvalue assignment for linear time-varying systems to achieve feedback stabilization. For this, we introduce novel eigenvalue concepts. Then, we propose the Ackerman-like formula for linear time-varying systems. It is believed that this technique is the generalized version of the Ackerman formula for linear time-invariant systems. The advantages of the proposed Ackerman-like formula are that it does not require the transformation of the original system into the phase-variable form nor the computation of eigenvalues of the original system.

Decoupling and tracking control for linear time-varying systems using eigenstructure assignment and CGT

This work is concerned with the decoupling and tracking control for linear time-varying systems such as missiles, rockets, fighters, etc. Despite its well-known limitations, gain-scheduling control appeared to be focus of the research efforts. Scheduling of frozen-time, frozen-state controller for fast time-varying dynamics is known to be mathematically fallacious, and practically hazardous. Therefore, recent research efforts are being directed towards applying time-varying controllers. In this paper, i) we introduce a differential algebraic eigenvalue theory for linear time-varying systems, and ii) a novel decoupling and tracking control scheme is proposed by using the PD-eigenstructure assignment scheme via differential Sylvester equation and CGT (command generator tracker) for linear time-varying systems. The presented method is illustrated by numerical examples.

PD-eigenstructure assignment control for decoupling and tracking of linear time-varying systems

Concerns the decoupling and tracking control for linear time-varying systems, such as missiles, rockets, fighters, etc. Despite its well-known limitations, gain-scheduling control appears to be a focus of the research efforts. The scheduling of a frozen-time, frozen-state controller for fast time-varying dynamics is known to be mathematically fallacious and practically hazardous. Therefore, recent research efforts are being directed towards applying time-varying controllers. In this paper, we introduce a differential algebraic eigenvalue theory for linear time-varying systems, and a novel decoupling and tracking control scheme is proposed by using the PD (parallel differential) eigenstructure assignment scheme via the differential Sylvester equation and a CGT (command generator tracker) for linear time-varying systems. The presented method is illustrated by numerical examples.

AUTOPILOT DESIGN FOR AGILE MISSILE USING LTV CONTROL AND NONLINEAR DYNAMIC INVERSION

Abstract This paper is concerned with autopilot design for an agile missile with aerodynamic fins, thrust vectoring control, and side-jet thrusters. Two-time scale dynamic inversion is used as a nonlinear flight control law. To deal with the inherently weak robustness property of dynamic inversion, Ackermann-like formula which is a time-varying version of Ackermann formula for LTI systems is applied to control the aerodynamic fins to stabilize LTV tracking error dynamics. In addition, control allocation algorithms for the effective distribution of the required total control efforts to the individual actuators are suggested, which are capable of extracting the maximum performance by combining each control effector. Finally, the main results are validated through nonlinear simulations with aerodynamic data.

Agile missile autopilot design via time-varying eigenvalue assignment

This paper is concerned with control allocation strategies with two-time scale dynamic inversion which generate nominal control input trajectories. In addition, a robust flight control design method is proposed by using a time-varying control technique which is time-varying version of the pole placement of linear time-invariant system for an agile missile with aerodynamic fin, thrust vectoring control, and side-jet thruster. The control allocation algorithms proposed in this paper are capable of extracting the maximum performance by combining each control effector. The time-varying control technique for the autopilot design enhances the robustness of the tracking performance for the wide angle of attack range. The main results are validated through the nonlinear simulations with aerodynamic data.

Robust mixed control with aerosurface and side thruster using LTV control technique

Abstract This paper is concerned with a mixed control with aerodynamic fin and side thrusters applied to an agile missile using two-time scale dynamic inversion and linear time-varying control technique. The nonlinear dynamic inversion method with the weighting function allocates the desired control inputs (aerodynamic fin and side thrusters) to track a reference trajectory, and the time-varying control technique guarantees the robustness for the uncertainties. Closed-loop stability is achieved by the assignment of the extended-mean of these linear time-varying eigenvalues to the left half complex plane. The proposed schemes are validated by nonlinear simulations

Eigenstructure-based robust stability analysis for linear time-varying systems

Stability robustness of a linear time-varying system with time-varying structured state space uncertainties is considered by using extended-mean theorem and Bellmans lemma. The extended-mean theorem is a necessary and sufficient exponential stability criterion based on the recently developed PD-eigenvalue and PD-eigenvector for a linear time-varying system. Our new result required that the extended-mean of each nominal PD-eigenvalue should be negative real, which is determined by a norm involving the structures of the uncertainty and the nominal left/right PD-eigenvectors. It is believed that this result is well suited for a design of control systems using PD-eigenvalue assignment or PD-eigenstructure assignment. The usefulness and correctness will be validated by a numerical example.