A Recursive Pole Placement Method for Large Flexible Structures

1990 ◽  
Vol 112 (3) ◽  
pp. 407-410 ◽  
Author(s):  
H. Baruh
Keyword(s):  
Closed Loop ◽  
Flexible Structures ◽  
Open Loop ◽  
Pole Placement ◽  
Matrix Perturbation ◽  
Placement Method ◽  
Matrix Perturbation Theory ◽  
The Difference ◽  
Vibrating Systems ◽  
Uncontrolled System

This paper presents a recursive method to accomplish pole placement for control of large-order vibrating systems. The pole placement is based on matrix perturbation theory, where the controls are considered as a perturbation on the uncontrolled system. The difference between the open-loop poles and the desired closed-loop poles is divided into regions small enough to maintain validity of the perturbation assumption. Control gains are then calculated in each region, resulting in a stepwise design.

scholarly journals The usage of Lambert W function for identification and speed control of a DC motor

2019 ◽  
Vol 32 (4) ◽  
pp. 581-600
Author(s):  
Radmila Gerov ◽  
Zoran Jovanovic
Keyword(s):  
Closed Loop ◽  
Dc Motor ◽  
Pole Placement ◽  
Step Response ◽  
Lambert W Function ◽  
Placement Method ◽  
Speed Regulation ◽  
Measured Speed ◽  
Proportional Controller ◽  
Integral Gain

The paper proposes a new method of identifying the linear model of a DC motor. The parameter estimation is based on the closed-loop step response of the DC motor under a proportional controller. For the application of the method, a deliberate delay of the measured speed was introduced. The paper considers the speed regulation of the direct current motor with negligible inductance by applying 1-DOF and 2-DOF, proportional integral retarded controllers. The proportional and integral gain of the PI retarded controllers was received by using a pole placement method on the identified model. The Lambert W function was applied for the identification and in designing the controller with the purpose of finding the rightmost poles of the closed-loop as well as the boundary conditions for selecting the gain of the PI controller. The robustness of the calculated controllers was considered under the effect of an disturbance, uncertainty in each of the DC motor parameters as well as perturbations in time delay.

Self-Sensing Active Magnetic Dampers for Vibration Control

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Angelo Bonfitto ◽  
Xavier De Lépine ◽  
Mario Silvagni ◽  
Andrea Tonoli
Keyword(s):  
Vibration Control ◽  
Closed Loop ◽  
Flexible Structures ◽  
Open Loop ◽  
System Response ◽  
Model Parameters ◽  
Loop Model ◽  
Single Degree Of Freedom ◽  
Luenberger Observer ◽  
Model Response

The aim of this paper is to investigate the potential of a self-sensing strategy in the case of an electromagnetic damper for the vibration control of flexible structures and rotors. The study has been performed in the case of a single degree of freedom mechanical oscillator actuated by a couple of electromagnets. The self-sensing system is based on a Luenberger observer. Two sets of parameters have been used: nominal ones (based on simplifications on the actuator model) and identified ones. In the latter case, the parameters of the electromechanical model used in the observer are identified starting from the open-loop system response. The observed states are used to close a state-feedback loop with the objective of increasing the damping of the system. The results show that the damping performance are good in both cases, although much better in the second one. Furthermore, the good correlation between the closed-loop model response and the experimental results validates the modeling, the identification procedure, the control design, and its implementation. The paper concludes on a sensitivity analysis, in which the influence of the model parameters on the closed-loop response is shown.

Vibration Confinement by Minimum Modal Energy Eigenstructure Assignment

2007 ◽  
Author(s):  
Mohammad Rastgaar Aagaah ◽  
Mehdi Ahmadian ◽  
Steve C. Southward
Keyword(s):  
Closed Loop ◽  
Null Space ◽  
Flexible Structures ◽  
Output Feedback Control ◽  
Open Loop ◽  
Loop System ◽  
Eigenstructure Assignment ◽  
Open Loop System ◽  
The Matrix ◽  
Value Decomposition

A novel Eigenstructure Assignment (ESA) method for vibration confinement of flexible structures has been developed. This method is an output feedback control and determines the closed-loop systems that their eigenvectors are orthogonalized to the open-loop eigenvectors. This method is a numerical method and used Singular Value Decomposition (SVD) to find the null space of the closed-loop eigenvectors. The matrix that spans the null space can be used to regenerate the open-loop system as well as the systems that have orthogonal eigenvectors to the regenerated open-loop system. As a result the isolation of vibration is independent of the type of the disturbance. Also in this method, the energy of the closed-loop system is minimized. As an important outcome, the proposed method needs neither to specify the closed-loop eigenvalues nor to define a desired set of eigenvectors.

scholarly journals On PID Controller Design by Combining Pole Placement Technique with Symmetrical Optimum Criterion

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Viorel Nicolau
Keyword(s):  
Transfer Function ◽  
Closed Loop ◽  
Controller Design ◽  
Open Loop ◽  
Pole Placement ◽  
Loop Transfer Function ◽  
Heading Control ◽  
Pid Controller Design ◽  
Analytical Expressions ◽  
Placement Technique

In this paper, aspects of analytical design of PID controllers are studied, by combining pole placement technique with symmetrical optimum criterion. The proposed method is based on low-order plant model with pure integrator, and it can be used for both fast and slow processes. Starting from the desired closed-loop transfer function, which contains a second-order oscillating system and a lead-lag compensator, it is shown that the zero value depends on the real-pole value of closed-loop transfer function. In addition, there is only one pole value, which satisfies the assumptions of symmetrical optimum criterion imposed to open-loop transfer function. In these conditions, by combining the pole placement technique with symmetrical optimum criterion, the analytical expressions of the controller parameters can be simplified. For simulations, PID autopilot design for heading control problem of a conventional ship is considered.

Extended Pole Placement Method With Noncausal Reference Model for Digital Servo-Control

1995 ◽  
Vol 117 (4) ◽  
pp. 641-644 ◽  
Author(s):  
Chwan-Hsen Chen ◽  
Hendrik Van Brussel ◽  
Jan Swevers
Keyword(s):  
Reference Model ◽  
Phase Error ◽  
Flexible Structures ◽  
Servo Control ◽  
Pole Placement ◽  
Placement Method ◽  
Tracking Tasks ◽  
Servo Control System ◽  
Slide Show ◽  
Zero Phase

The extended pole placement (EPP) method extends the well-known pole placement method to digital servo-control with known control inputs. A servo-control system designed using the EPP method achieves an accurate command response through the use of a noncausal reference model and an accurate approximation of nonminimum-phase zeros. The phase error of the command response between the desired output and the actual output may be made arbitrarily small, while its gain extends uniformly to a selectable bandwidth. A selectable feedforward bandwidth is important in controlling flexible structures where unmodeled resonances might be excited by rough feedforward inputs. Experimental results on a machine tool slide show that a controller designed by the EPP method yields better servo performance for cornering and contour tracking tasks than an E-filter-enhanced zero phase error tracking controller.

Vibration Cancellation in a Plate Using Orthogonal Eigenstructure Control

2010 ◽  
Vol 77 (6) ◽  
Author(s):  
M. A. Rastgaar ◽  
M. Ahmadian ◽  
S. C. Southward
Keyword(s):  
Degrees Of Freedom ◽  
Closed Loop ◽  
Vibration Suppression ◽  
Control Method ◽  
Null Space ◽  
Flexible Structures ◽  
Element Model ◽  
Open Loop ◽  
Gain Matrix ◽  
Control Gain

Orthogonal eigenstructure control is a novel control method that can be used for vibration suppression in flexible structures. The method described in this study does not need defining the desired locations of the closed-loop poles or predetermining the closed-loop eigenvectors. The method, which is applicable to linear multi-input multi-output systems, determines an output feedback control gain matrix such that some of the closed-loop eigenvectors are orthogonal to the open-loop eigenvectors. Using this, the open-loop system’s eigenvectors as well as a group of orthogonal vectors are regenerated based on a matrix that spans the null space of the closed-loop eigenvectors. The gain matrix can be generated automatically; therefore, the method is neither a trial and error process nor an optimization of an index function. A finite element model of a plate is used to study the applicability of the method to systems with relatively large degrees of freedom. The example is also used to discuss the effect of operating eigenvalues on the process of orthogonal eigenstructure control. The importance of the operating eigenvalues and the criteria for selecting them for finding the closed-loop system are also investigated. It is shown that choosing the operating eigenvalues from the open-loop eigenvalues that are farthest from the origin results in convergence of the gain matrix for the admissible closed-loop systems. It is shown that the converged control gain matrix has diagonal elements that are two orders of magnitude larger than the off-diagonal elements, which implies a nearly decoupled control.

Adaptive control designs for control-based continuation in a class of uncertain discrete-time dynamical systems

2020 ◽  
Vol 26 (21-22) ◽  
pp. 2092-2109
Author(s):  
Yang Li ◽  
Harry Dankowicz
Keyword(s):  
Adaptive Control ◽  
Discrete Time ◽  
Closed Loop ◽  
Control Strategies ◽  
Open Loop ◽  
Numerical Continuation ◽  
Pole Placement ◽  
Control Input ◽  
Loop Dynamics ◽  
Reference Input

This article proposes a methodology for integrating adaptive control with the control-based continuation paradigm for a class of uncertain, linear, discrete-time systems. The proposed adaptive control strategies aim to stabilize the closed-loop dynamics with convergence toward a known reference input, such that the dynamics approach the open-loop fixed point if the reference input is chosen to make the steady-state control input equal 0. This enables the tracking of a parameterized branch of open-loop fixed points using methods of numerical continuation without specific knowledge about the system. We implement two different adaptive control strategies: model-reference adaptive control and pole-placement adaptive control. Both implementations achieve the desired objectives for the closed-loop dynamics and support parameter continuation. These properties, as well as the boundedness of system states and control inputs, are guaranteed provided that certain stability conditions are satisfied. Besides, the tuning effort is significantly reduced in the adaptive control schemes compared with traditional proportional–derivative controllers and linear state-space feedback controllers.

scholarly journals High-bandwidth nanopositioning via active control of system resonance

2021 ◽  
Author(s):  
Linlin Li ◽  
Sumeet S. Aphale ◽  
Limin Zhu
Keyword(s):  
Resonant Frequency ◽  
Closed Loop ◽  
Performance Enhancement ◽  
Open Loop ◽  
Pole Placement ◽  
Loop Control ◽  
Damping Control ◽  
Significant Performance ◽  
High Bandwidth ◽  
Almost All

AbstractTypically, the achievable positioning bandwidth for piezo-actuated nanopositioners is severely limited by the first, lightly-damped resonance. To overcome this issue, a variety of open- and closed-loop control techniques that commonly combine damping and tracking actions, have been reported in literature. However, in almost all these cases, the achievable closed-loop bandwidth is still limited by the original open-loop resonant frequency of the respective positioning axis. Shifting this resonance to a higher frequency would undoubtedly result in a wider bandwidth. However, such a shift typically entails a major mechanical redesign of the nanopositioner. The integral resonant control (IRC) has been reported earlier to demonstrate the significant performance enhancement, robustness to parameter uncertainty, guaranteed stability and design flexibility it affords. To further exploit the IRC scheme’s capabilities, this paper presents a method of actively shifting the resonant frequency of a nanopositioner’s axis, thereby delivering a wider closed-loop positioning bandwidth when controlled with the IRC scheme. The IRC damping control is augmented with a standard integral tracking controller to improve positioning accuracy. And both damping and tracking control parameters are analytically optimized to result in a Butterworth Filter mimicking pole-placement—maximally flat passband response. Experiments are conducted on a nanopositioner’s axis with an open-loop resonance at 508 Hz. It is shown that by employing the active resonance shifting, the closed-loop positioning bandwidth is increased from 73 to 576 Hz. Consequently, the root-mean-square tracking errors for a 100 Hz triangular trajectory are reduced by 93%.

An optimal sensor/actuator placement method for flexible structures considering spatially varying disturbances

2021 ◽  
pp. 107754632110358
Author(s):  
Runze Ding ◽  
Ding Chenyang ◽  
Xu Yunlang ◽  
Xiaofeng Yang
Keyword(s):  
Genetic Algorithm ◽  
Closed Loop ◽  
Flexible Structures ◽  
Optimization Criterion ◽  
Control Performance ◽  
Optimization Framework ◽  
Sensor Actuator ◽  
Placement Method ◽  
Spatially Varying ◽  
Actuator Placement

Disturbances acting on flexible structures at spatially varying locations instead of fixed points may lead to deteriorated vibration control performance. To tackle this problem, this article presents an optimal sensor/actuator placement method, in which the closed-loop spatial [Formula: see text] norm is employed as the optimization criterion. In addition, a new way to calculate the spatial [Formula: see text] norm is proposed, which is independent of the modal orthogonality assumption in previous research. An optimization framework is established to optimize sensor/actuator placement by minimizing the closed-loop spatial [Formula: see text] norm using the genetic algorithm. Comprehensive numerical simulations are implemented on a fixed-fixed plate to validate the proposed method. Results show that magnitude of vibrations is reduced and decays faster after the optimization, which indicates that the proposed method markedly improves control performance when spatially varying disturbances exist.

scholarly journals Modelling And Control Of Automated Polishing/Deburring Process

2021 ◽  
Author(s):  
Liang Liao
Keyword(s):  
Feedback Linearization ◽  
Closed Loop ◽  
Control Method ◽  
Minimum Degree ◽  
Open Loop ◽  
Pole Placement ◽  
Control Performance ◽  
Nonlinear Controller ◽  
Loop Control ◽  
And Control

In this thesis, a new approach is presented for the modelling and control of an automated polishing/deburring process that utilizes a dual-purpose complaint toolhead mounted on a parallel tripod robot. This toolhead has a pneumatic spindle that can be extended and retracted by three pneumatic actuators to provide tool compliance. By integrating a pressure sensor and a linear encoder, this toolhead can be used for polishing and deburring. For the polishing open-loop control, the desired tool pressure is pre-planned based on the given part geometry. To improve control performance, a closed-loop controller is applied for pressure tracking through pressure sensing. For the deburring control, another closed-loop controller is applied to regulate the tool length through tool extension sensing. The two control methods have been tested and implemented on a polishing/deburring robot, and the experiment results demonstrate the effectiveness of the presented methods. To future improve the control performance, an adaptive controller is developed to deal with the uncertainties in the compliant tool. This control method combines the adaptive control theory with the constant stress theory of the contact model. A recursive last squares (RLS) estimator is developed to estimate the pneumatic plant model, and then a minimum-degree pole placement (MDPP) is applied to design a self-tuning controller. Afterwards, the simulation and experiment results of the proposed controller are presented and discussed. Finally, a nonlinear model of the pneumatic plant is developed. The nonlinear controller developed by using feedback linearization method is applied on the nonlinear pneumatic system of the compliant toolhead. The simulation is carried out to test the effectiveness of the pressure tracking for the polishing process.

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