scholarly journals Active vibration suppression of non-linear beams using optimal dynamic inversion

2009 ◽  
Vol 223 (5) ◽  
pp. 657-672 ◽  
Author(s):  
Sk F Ali ◽  
R Padhi
Keyword(s):  
Vibration Suppression ◽  
Control Variable ◽  
Linear Partial Differential Equation ◽  
Spatial Domain ◽  
Dynamic Inversion ◽  
Control Force ◽  
Control Approach ◽  
Closed Form Solutions ◽  
Non Linear ◽  
Optimal Dynamic

Euler-Bernoulli beams are distributed parameter systems that are governed by a non-linear partial differential equation (PDE) of motion. This paper presents a vibration control approach for such beams that directly utilizes the non-linear PDE of motion, and hence, it is free from approximation errors (such as model reduction, linearization etc.). Two state feedback controllers are presented based on a newly developed optimal dynamic inversion technique which leads to closed-form solutions for the control variable. In one formulation a continuous controller structure is assumed in the spatial domain, whereas in the other approach it is assumed that the control force is applied through a finite number of discrete actuators located at predefined discrete locations in the spatial domain. An implicit finite difference technique with unconditional stability has been used to solve the PDE with control actions. Numerical simulation studies show that the beam vibration can effectively be decreased using either of the two formulations.

scholarly journals Modified LQG/LTR Control Methodology in Active Structural Control

2003 ◽  
Vol 22 (2) ◽  
pp. 97-108 ◽  
Author(s):  
Yan Sheng ◽  
Chao Wang ◽  
Ying Pan ◽  
Xinhua Zhang
Keyword(s):  
Structural Control ◽  
Signal To Noise Ratio ◽  
Open Loop ◽  
Control Force ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Control Approach ◽  
Active Structural Control ◽  
Loop Transfer Recovery ◽  
Control Methodology

This paper presents a new active structural control design methodology comparing the conventional linear-quadratic-Gaussian synthesis with a loop-transfer-recovery (LQG/LTR) control approach for structures subjected to ground excitations. It results in an open-loop stable controller. Also the closed-loop stability can be guaranteed. More importantly, the value of the controller's gain required for a given degree of LTR is orders of magnitude less than what is required in the conventional LQG/LTR approach. Additionally, for the same value of gain, the proposed controller achieves a much better degree of recovery than the LQG/LTR-based controller. Once this controller is obtained, the problems of control force saturation are either eliminated or at least dampened, and the controller band-width is reduced and consequently the control signal to noise ratio at the input point of the dynamic system is increased. Finally, numerical examples illustrate the above advantages.

scholarly journals Influence of Time Delay on Controlling the Non-Linear Oscillations of a Rotating Blade

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 85
Author(s):  
Yasser Salah Hamed ◽  
Ali Kandil
Keyword(s):  
Time Delay ◽  
Natural Frequency ◽  
Multiple Scales ◽  
Control Process ◽  
Control Force ◽  
Specific Level ◽  
Loop Control ◽  
Positive Displacement ◽  
Non Linear ◽  
Linear Vibrations

Time delay is an obstacle in the way of actively controlling non-linear vibrations. In this paper, a rotating blade’s non-linear oscillations are reduced via a time-delayed non-linear saturation controller (NSC). This controller is excited by a positive displacement signal measured from the sensors on the blade, and its output is the suitable control force applied onto the actuators on the blade driving it to the desired minimum vibratory level. Based on the saturation phenomenon, the blade vibrations can be saturated at a specific level while the rest of the energy is transferred to the controller. This can be done by adjusting the controller natural frequency to be one half of the blade natural frequency. The whole behavior is governed by a system of first-order differential equations gained by the method of multiple scales. Different responses are included to show the influences of time delay on the closed-loop control process. Also, a good agreement can be noticed between the analytical curves and the numerically simulated ones.

Active Vibration Absorption Using Delayed Resonator With Relative Position Measurement

1995 ◽  
Author(s):  
Nejat Olgac ◽  
Martin Hosek
Keyword(s):  
Relative Position ◽  
Primary Structure ◽  
Vibration Suppression ◽  
Control Force ◽  
Range Analysis ◽  
Position Measurement ◽  
Harmonic Force ◽  
Stability Range ◽  
Vibration Absorption ◽  
Active Vibration

Abstract A novel active vibration absorption technique, the Delayed Resonator, has been introduced recently as a unique way of suppressing undesired oscillations. It suggests a control force on a mass-spring-damper absorber in the form of a proportional position feedback with a time delay. Its strengths consist of extremely simple implementation of the control algorithm, total vibration suppression of the primary structure against a harmonic force excitation and full effectiveness of the absorber in a semi-infinite range of disturbance frequency, achieved by real-time tuning. All this development work was done using the absolute displacements of the absorber in the feedback. These displacement measurements may be difficult to obtain and for some applications impossible. This paper deals with a substitute and easier measurement: the relative motion of the absorber with respect to the primary structure. Theoretical foundations for the Delayed Resonator (DR) are briefly recapitulated and its implementation on a single-degree-of-freedom primary structure disturbed by a harmonic force is introduced utilizing both absolute and relative position measurement of absorber mass. Methods for stability range analysis and transient behavior are presented. Properties acquired for the same system with these two different feedback are compared. Relative position measurement case is found to be more advantageous in most applications of the Delayed Resonator method.

Active Damping of a Large Flexible Manipulator With a Short-Reach Robot

1996 ◽  
Vol 118 (4) ◽  
pp. 704-713 ◽  
Author(s):  
I. Sharf
Keyword(s):  
Vibration Suppression ◽  
Controller Design ◽  
Reaction Force ◽  
Control Variable ◽  
Active Damping ◽  
Flexible Manipulator ◽  
Design Problems ◽  
Flexible Arm ◽  
Six Degree Of Freedom ◽  
Small Robot

This paper deals with manipulator systems comprising a long-reach manipulator (LRM) with a short-reach dextrous manipulator (SRM) attached to its end. The former, due to its size, is assumed to have significant structural flexibility, while the latter is modeled as a rigid robot. The particular problem addressed is that of active damping, or vibration suppression, of the LRM by using SRM specifically for that purpose Such a scenario is envisioned for operations where the large manipulator is used to deploy the small robot and it is necessary to damp out vibrations in LRM prior to operating SRM. The proposed solution to the problem uses the reaction force from SRM to LRM as a control variable which allows to effectively decouple the controller design problems for the two manipulators. A two-stage controller is presented that involves first, determining the trajectory of the short manipulator required to achieve a desired damping wrench to the supporting flexible arm and subsequently, brings the small manipulator to rest. Performance of the active damping algorithm developed is illustrated with a six-degree-of-freedom rigid manipulator on a flexible mast. Comparison to an independent derivative joint controller is included. The paper also discusses how the proposed methodology can be extended to address other issues related to operation of long-reach manipulator systems.

A tube-based robust MPC for duty-cycled rotation needle steering systems with bounded disturbances

2021 ◽  
pp. 014233122110430
Author(s):  
Zhi Qi ◽  
Qianyue Luo ◽  
Hui Zhang
Keyword(s):  
Model Predictive Control ◽  
Linear Model ◽  
Predictive Control ◽  
Control Method ◽  
Controller Design ◽  
Control Approach ◽  
Bounded State ◽  
Non Linear ◽  
System States ◽  
Trajectory Tracking Controller

In this paper, we aim to design the trajectory tracking controller for variable curvature duty-cycled rotation flexible needles with a tube-based model predictive control approach. A non-linear model is adopted according to the kinematic characteristics of the flexible needle and a bicycle method. The modeling error is assumed to be an unknown but bounded disturbance. The non-linear model is transformed to a discrete time form for the benefit of predictive controller design. From the application perspective, the flexible needle system states and control inputs are bounded within a robust invariant set when subject to disturbance. Then, the tube-based model predictive control is designed for the system with bounded state vector and inputs. Finally, the simulation experiments are carried out with tube-based model predictive control and proportional integral derivative controller based on the particle swarm optimisation method. The simulation results show that the tube-based model predictive control method is more robust and it leads to much smaller tracking errors in different scenarios.

Sign in / Sign up

Export Citation Format

Share Document