scholarly journals Deterministic Approaches to Transient Trajectory Generation

2020 ◽  
Author(s):  
Matthew A. Cooper
Keyword(s):  
Linear Time ◽  
Tracking Error ◽  
Trajectory Generation ◽  
Deterministic Approach ◽  
Van Der Pol ◽  
Linear Time Invariant ◽  
Tuning Method ◽  
Exponential Weighting ◽  
Strongly Nonlinear System ◽  
Optimal Linear

This chapter studies a deterministic approach to transient trajectory generation and control as applied to the forced Van der Pol oscillatory system. This type of system tends towards a strongly nonlinear system, which can be considered chaotic. A classical tuning method, targeted exponential weighting, and isolated trajectory fractionalization trajectory generation methods are examined. Illustrating the given deterministic approach via the Van der Pol system highlights the potentially iterative nature of deterministic methods, and that traditional optimal linear time-invariant control techniques are unable to perform as desired whereas even an idealized nonlinear feedforward control significantly outperforms at the steady-state. It will be shown that utilizing a-priori knowledge of the system dynamics will enable the isolated trajectory fractionalization method to minimize the nonlinear transient effects due to miss-modeled or unmodeled plant dynamics, and that this benefit can be coupled with the targeted exponential weighting approach for greatly decreased trajectory tracking error on the order of a 92% reduction of the objective cost function in the presented case study based on the forced Van der Pol system.

scholarly journals The Best Achievableℋ2Tracking Performances for SIMO Feedback Control Systems

2007 ◽  
Vol 2007 ◽  
pp. 1-12 ◽  
Author(s):  
Shinji Hara ◽  
Toni Bakhtiar ◽  
Masaaki Kanno
Keyword(s):  
Feedback Control ◽  
Control Systems ◽  
Linear Time ◽  
Tracking Error ◽  
Control Input ◽  
Discrete Time System ◽  
Time System ◽  
Linear Time Invariant ◽  
Augmentation Strategy ◽  
Feedback Control Systems

This paper is concerned with the inherentℋ2tracking performance limitation of single-input and multiple-output (SIMO) linear time-invariant (LTI) feedback control systems. The performance is measured by the tracking error between a step reference input and the plant output with additional penalty on control input. We employ the plant augmentation strategy, which enables us to derive analytical closed-form expressions of the best achievable performance not only for discrete-time system, but also for continuous-time system by exploiting the delta domain version of the expressions.

Adaptive Control for the Twin Rotor Helicopter with Actuator Faults

2012 ◽  
Vol 271-272 ◽  
pp. 1501-1505
Author(s):  
Shi Jun Zhang ◽  
Fu Yang Chen ◽  
Gang Tao
Keyword(s):  
Linear Time ◽  
Tracking Error ◽  
Adaptive Controller ◽  
Actuator Faults ◽  
Environmental Disturbances ◽  
Linear Time Invariant ◽  
Control Scheme ◽  
Modeling Errors ◽  
Time Invariant ◽  
Twin Rotor

For the linear time-invariant model of a twin-rotor helicopter, a new control scheme is proposed in the presence of actuator faults, environmental disturbances and modeling errors. Using the Lyapunov stability theorem, the system with proposed adaptive controller is proved to be stable, and the tracking error tends to zero asymptotically. Simulation results prove the effectiveness of this method.

Regularized Filtered Basis Functions Approach for Accurate Tracking of Discrete-Time Linear Time Invariant Systems With Bounded Random Uncertainties

2016 ◽  
Author(s):  
Keval S. Ramani ◽  
Chinedum E. Okwudire
Keyword(s):  
Discrete Time ◽  
Linear Time ◽  
Selection Process ◽  
Tracking Error ◽  
Basis Functions ◽  
Worst Case ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Time Invariant ◽  
Time Linear

This paper proposes a regularized filtered basis functions (RFBF) approach for robust tracking of discrete-time linear time invariant systems with bounded random (unstructured) uncertainties. Identical to the filtered basis functions (FBF) approach, studied in prior work by the authors, the RFBF approach expresses the control trajectory as a linear combination of user-defined basis functions with unknown coefficients. The basis functions are forward filtered using a model of the system and their coefficients are selected to fulfill the tracking control objective. The two approaches differ in the coefficient selection process. The FBF approach selects the coefficients such that the tracking error is minimized in the absence of uncertainties, whereas, the proposed RFBF approach formulates the coefficient selection problem as a constrained game-type problem where the coefficients are selected to minimize the worst case tracking error in the presence of model uncertainty. Illustrative examples are used to demonstrate significantly more accurate tracking of uncertain systems using RFBF compared with FBF.

scholarly journals Investigation into the optimal linear time-invariant lag correction for radar artifact removal

2011 ◽  
Vol 38 (5) ◽  
pp. 2398-2411 ◽  
Author(s):  
Jared Starman ◽  
Josh Star-Lack ◽  
Gary Virshup ◽  
Edward Shapiro ◽  
Rebecca Fahrig
Keyword(s):  
Linear Time ◽  
Artifact Removal ◽  
Linear Time Invariant ◽  
Optimal Linear ◽  
Time Invariant
Sign in / Sign up

Export Citation Format

Share Document