Adaptive Time Delay-Based Control for Stabilizing Non-Collocated Oscillatory Systems with Constrained Actuators

Conceitos Básicos

An adaptive time delay-based control approach is proposed to effectively stabilize non-collocated fourth-order oscillatory systems with constrained actuators, overcoming the practical infeasibility of classical observer-based state-feedback control.

Resumo

The paper addresses the challenge of controlling fourth-order non-collocated oscillatory systems, where the control input is applied to the active body while the output of interest is measured from the passive, low-damped load. The authors first demonstrate the practical infeasibility of a classical observer-based state-feedback control design, even in the presence of low measurement noise, due to the constraints on the actuator's force and displacement.
To overcome this limitation, the authors propose an adaptive time delay-based control approach. The key aspects are:

Time delay-based control: This control strategy directly shapes the system's frequency response around the resonance frequency, effectively attenuating the oscillations without significantly altering the response at other frequencies.

Robust frequency estimation: An online adaptation of the oscillation frequency parameter is provided, extending a previously proposed robust frequency estimator. This allows the time delay-based control to be applied without requiring prior knowledge of the system's mass and stiffness parameters.

Experimental evaluation: The proposed adaptive time delay-based control is experimentally validated on a non-collocated fourth-order mechanical system with gravity disturbances and constraints on the actuator's input and output. The results demonstrate stable attenuation of the output oscillations and robust convergence of the frequency estimate, even in the presence of external disturbances.

The authors conclude that the adaptive time delay-based control provides a simple and effective solution for stabilizing non-collocated oscillatory systems with constrained actuators, overcoming the practical limitations of classical observer-based state-feedback control approaches.

Estatísticas

The system has the following key parameters:

Mass of the active body: m = 1 kg
Mass of the passive load: M = 0.5 kg
Stiffness coefficient: k = 333.33 N/m
Link damping coefficient: ζ = 0.012 Ns/m
Actuator's time constant: τ = 0.0012 s
Actuator's force constant: κ = 3.2811 N/V
Actuator's input and output constraints: u ∈ [0, 10] V, z ∈ [0, 0.021] m
Oscillation frequency: ω0 = 16.4 rad/s
Damping ratio: δ = 0.031

Citações

"Time delay based control, recently proposed for non-collocated fourth-order systems, has several advantages over an observer-based state-feedback compensation of the low-damped oscillations in output."
"The time delay based control relies on the knowledge of the oscillation frequency ω, and assumes the time delay constant θ = -arg(G(iω))/ω."
"The bias-canceling extension of the robust frequency estimator [12] was introduced, which allows for an online (adaptive) tuning of the time delay based controller."

Principais Insights Extraídos De

Adaptive time delay based control of non-collocated oscillatory systems

by Michael Rude... às arxiv.org 04-23-2024

https://arxiv.org/pdf/2311.14979.pdf

Perguntas Mais Profundas

How could the proposed adaptive time delay-based control be extended to handle more complex system dynamics, such as nonlinear stiffness or time-varying parameters?

In order to extend the adaptive time delay-based control to handle more complex system dynamics like nonlinear stiffness or time-varying parameters, several approaches can be considered:

Nonlinear Stiffness:

Introducing adaptive algorithms that can account for nonlinearities in the system's stiffness. This could involve using adaptive control techniques such as model reference adaptive control (MRAC) or nonlinear control strategies like sliding mode control to handle the nonlinear behavior of the system's stiffness.
Implementing online parameter estimation algorithms that can adapt to the changing stiffness characteristics of the system in real-time. This could involve using recursive least squares (RLS) or extended Kalman filter (EKF) algorithms to estimate the nonlinear stiffness parameters.

Time-Varying Parameters:

Developing adaptive algorithms that can track and adjust to time-varying parameters in the system. This could involve incorporating adaptive laws that update the controller parameters based on the changing dynamics of the system over time.
Utilizing robust control techniques that can provide stability guarantees in the presence of time-varying parameters. Robust adaptive control methods like robust model predictive control (MPC) or H-infinity control can be explored to handle uncertainties in the system's parameters.

Hybrid Control Strategies:

Combining the adaptive time delay-based control with other control strategies like fuzzy logic control or neural network-based control. This hybrid approach can enhance the system's ability to adapt to complex dynamics by leveraging the strengths of different control techniques.
Implementing adaptive observers that can estimate the system's internal states and parameters, allowing for more accurate control in the presence of nonlinearities and time-varying parameters.

By incorporating these strategies, the adaptive time delay-based control can be extended to effectively handle the challenges posed by nonlinear stiffness and time-varying parameters in complex system dynamics.

What other control strategies could be explored to address the practical limitations of observer-based state-feedback control for non-collocated oscillatory systems?

To address the practical limitations of observer-based state-feedback control for non-collocated oscillatory systems, several alternative control strategies can be explored:

Adaptive Control:

Implementing adaptive control techniques that can adjust the controller parameters based on the system's changing dynamics. Adaptive control algorithms like model reference adaptive control (MRAC) or adaptive sliding mode control can provide robustness in the presence of uncertainties and measurement noise.

Nonlinear Control:

Utilizing nonlinear control strategies such as feedback linearization or backstepping control to handle the nonlinearities in the system dynamics. Nonlinear controllers can provide improved performance and stability in systems with complex oscillatory behavior.

Decentralized Control:

Implementing decentralized control strategies that distribute the control actions across multiple actuators and sensors in the system. Decentralized control can overcome the limitations of non-collocated systems by allowing for independent control of different system components.

Optimal Control:

Exploring optimal control techniques like model predictive control (MPC) or LQR control to optimize the system's performance while considering constraints and uncertainties. Optimal control strategies can provide a systematic approach to designing controllers for non-collocated oscillatory systems.

Robust Control:

Implementing robust control methods such as H-infinity control or sliding mode control to ensure stability and performance in the presence of disturbances and uncertainties. Robust controllers can enhance the system's resilience to external perturbations and modeling errors.

By exploring these alternative control strategies, the practical limitations of observer-based state-feedback control for non-collocated oscillatory systems can be effectively addressed, leading to improved control performance and stability.

What potential applications beyond the mechanical system studied in this work could benefit from the adaptive time delay-based control approach, and how would the implementation differ in those domains?

The adaptive time delay-based control approach proposed in this work can be beneficial for various applications beyond the mechanical system studied. Some potential domains that could benefit from this control approach include:

Power Systems:

Implementing adaptive time delay-based control in power systems to regulate voltage and frequency fluctuations. The control approach can help in stabilizing the grid and improving the overall system performance.

Biomedical Systems:

Applying adaptive time delay-based control in biomedical systems for patient monitoring and drug delivery. The control approach can be used to adjust treatment parameters in real-time based on patient responses.

Aerospace Systems:

Utilizing adaptive time delay-based control in aerospace systems for aircraft stability and control. The control approach can enhance flight performance and response to external disturbances.

Renewable Energy Systems:

Implementing adaptive time delay-based control in renewable energy systems like wind turbines and solar panels. The control approach can optimize energy generation and improve system efficiency.

In these domains, the implementation of adaptive time delay-based control may differ based on the specific system requirements and dynamics. For example:

In power systems, the control approach may focus on frequency regulation and grid stability.
In biomedical systems, the control parameters may be tailored to patient-specific conditions and treatment protocols.
In aerospace systems, the control strategy may prioritize aircraft maneuverability and response time.
In renewable energy systems, the control approach may aim to maximize energy output and minimize fluctuations.
Overall, the adaptive time delay-based control approach can be versatile and adaptable to a wide range of applications, offering enhanced performance and robustness in diverse system settings.