Seung-Bok Choi Young-Min Han

A vibration control of a flexible beam is presented by the implementation of piezoceramic actuators associated with the quantitative feedback theory (QFT) control technique, in which system uncertainties such as non-linear hysteresis behavior of the piezoactuators are treated. Since piezoelectric materials possess anisotropic properties, their mechanical and electrical behavior is dependent on the direction of the external electric field relative to a set of axes fixed in the material.

FIGURE 1.1 The micromechanism of the piezoelectric effect. (a) No voltage and (b) poling voltage.

General Requirements for Control Devices

Based on the prescribed specifications, the appropriate smart material actuator or sensor combination is then determined. Most of the currently available sensors, such as the accelerometer, can be adapted to measure the dynamic responses of a control system coupled to piezoelectric actuators.

FIGURE 1.3 A typical control system featuring piezoelectric actuators.

PID Control

The control value u(t) is changed at a rate proportional to the actuating error signal e(t) using controller I. Using the action of controller I, the steady-state error of the control system can be effectively mitigated or eliminated .

LQ Control

But OS instability can occur when using very high feedback gains of kp. The matrices Q and R determine the relative importance of the error and the control energy consumption.

Sliding Mode Control

This implies that the initial system response is independent of system parameters on the sliding line (movement in sliding mode). In general, the sliding mode movement can be achieved by satisfying the following so-called sliding mode condition [3]:.

FIGURE 2.4 Invariance property of the SMC. (a) Saddle, (b) spiral source, and (c) with switching logic.

H ∞ Control

In the controller given by equation 2.22, k is the discrete control gain and sgn(·) is a sign function. The H∞ rates also have a physically meaningful interpretation that is the largest possible gain over all unity sinusoidal input frequencies.

Figure 2.6 shows a loop shaping design procedure (LSDP) using H ∞ synthesis for a left coprime factor perturbed plant given by [5,6]

QFT Control

From a plot of the open-loop frequency response G(jω), the values of Lm(M(jω)) and phase α(jω) can be found. The performance specifications consist of limitations on the magnitude of the closed-loop frequency responses.

FIGURE 2.7 Control block diagram of the QFT.

Inverse Model Control

Introduction
Dynamic Modeling
Controller Formulation

General Formulation
Application to the Structure

Control Results
Some Final Thoughts

This implies that the control ratio of the closed-loop transfer function can be changed by the prefi lter. Observing position (from fixed) 100 mm. the steady state error for the step reference input of the system.

FIGURE 2.8 Confi guration of the Preisach model. (a) Block diagram and (b) hysteresis relay on Preisach plane.

Vibration Control of Hull Structures

Introduction
Dynamic Modeling
Modal Analysis
Control Results

Piezoelectric Actuator FIGURE 3.13 Geometry of the end-coated hull structure with surface-bonded piezoelectric actuators. The fundamental mode shapes of the end-covered hull structure without piezoelectric actuators are the same, as shown in Figure 3.15.

FIGURE 3.11 Measured 1 Hz sinusoidal tracking responses up to 10,000 cycles. (a) Biased and (b) symmetric

Vibration Control Using Piezostack Mount

Introduction

A sliding mode controller is then designed to actively control unwanted vibration responses of the system due to the imposed excitations. The controller is experimentally implemented and vibration control performances such as acceleration and displacement of the beam structure are evaluated and presented in both frequency and time domains.

Mount Design

A is the cross-sectional area of the piezoelectric element l and δ(t) is the length and stroke of the piezoelectric actuator kp(= Ac/l) is the spring constant. The piezostack actuator is of the bipolar type and is connected to the rubber mount through the intermediate mass.

System Modeling and Analysis

In the above, qi(t) is the generalized modal coordinate, ϕi(x) is the mode shape function at position x, ωi is the natural frequency of the beam, ζi is the damping ratio of the beam, and Ii is the generalized mass of the i -the mode. Equation 3.38 can thus be rewritten to integrate with the hybrid container model.

FIGURE 3.22 Mechanical model of the beam structure supported by the hybrid and rubber mounts.

Controller Formulation

On the other hand, the weakening of dynamic movement of the intermediate mass implies the control of the transmitted power by the hybrid mount. The sliding mode controller satisfying the existence condition of the sliding mode motion in Equation 3.46 is obtained by.

FIGURE 3.23 Acceleration of the beam without control. (From Kim, S.H. et al., Int. J

Control Results

From the remarkable reduction of the force transfer to the base, it can be seen that the imposed vibration of the beam structure has been effectively isolated. One clearly observes significant reductions in the accelerations, displacements and forces transmitted by actuation.

Figure 3.25 presents the measured acceleration of the beam structure. a 1 , a 2 , and a 3 denote the accelerations at the positions ➀ , ➁ , and ➂ , respectively

Some Concluding Comments

Numerical modeling of distributed active vibration absorbers (DAVA) for control of plate-radiated noise. Active vibration control of frame structures with smart structures rising piezoelectric actuators (vibration control by control of bending moments of columns).

FIGURE 3.27 Force transmissibility of the beam structure with SMC. (From Kim, S.H.

Introduction

The adopted mount consists of one passive rubber element and two active piezostack actuators with additional mass; we call it "hybrid active carrier". Then, a vibration control system consisting of a hybrid active mount and a supported mass of 100 kg is set up to evaluate the effectiveness of vibration control.

Design and Modeling

After manufacturing the assembly, dynamic properties of the piezo stacks and the rubber element are experimentally identified. This is possible because the stiffness of the piezo stack is much higher than that of the rubber element.

FIGURE 4.1 Confi guration of the proposed hybrid active mount.

Controller Formulation

It should be noted that the stability of the system is ensured if the observer and the controller are well designed. The observer poles are designed to be fast enough that the estimated states quickly converge to the actual states using the pole placement technique.

Control Results

From the experimental results, it can be seen that when the controller is turned on, the vibration of the mass is attenuated from 0.114 to 0.014 m/s2, or equivalently, −18.4 dB more than in the uncontrolled case. It is noted that the stiffness of the piezo stack is much higher than that of the rubber element.

FIGURE 4.14 Block diagram of the control system.

Some Concluding Comments

At the low frequency, however, the vibration damping is not as good as at high frequencies. In the hybrid active holder, the operating force is mainly generated by the inertia force.

Three-Axis Active Mount

Introduction

The active mounting system consists of the rubber element and the inertia type piezoelectric actuator (piezo actuator for short). The vibration control performance of the 3-axis active holder is verified by computer simulation with significant practical applications.

Parameter Identifi cation

The Rubber Element
The Piezoelectric Actuator

These parameters will be used for the force and moment evaluation of the 3-axis active mount shown in Figure 4.24. It is the inherent characteristic of the inertia type actuator that is very effective for vibration control.

FIGURE 4.21 Frequency responses of a rubber mount. (a) z-Direction and (b) x,y-direction

Dynamic Modeling

Br is the distance from the origin {B} to the center of gravity of the rubber and joint. BX and BΩ are the linear and angular displacement, respectively, at the center of gravity of the active holder.

Figure 4.25 presents the confi guration of the experimental setup for the measure- measure-ment of the generated force and momeasure-ment of the 3-axis active mount

Controller Formulation and Results

From the mechanical model shown in Figure 4.30b, the governing equation of motion of the structural system can be derived as follows: 4.46) where Me and BÎs are the mass and moment of inertia of the structure respectively.

FIGURE 4.27 Generated force and moment of actuator 2. (From Choi, S.B. et al., SAGE, 19, 1053, 2008.)

Some Concluding Comments

From the results, it can be ensured that the inertial type of 3-axis piezoelectric beam is very effective for vibration control in the motion of a multi-degree-of-freedom structural system. Active vibration control of frame structures with smart structures using piezoelectric actuators (vibration control by control of column bending moments).

FIGURE 4.33 Control result in roll motion. (From Choi, S.B. et al., SAGE, 19, 1053, 2008.)–0.8

Introduction

Dynamic Modeling

The controller associated with the piezoceramic actuator is designed based on Lyapunov stability. M is the configuration-dependent system mass matrix K is the system stiffness matrix associated with the bond elasticity f is the nonlinear inertial effects (Coriolis force and centrifugal force) z is the generalized coordinate vector.

FIGURE 5.2 Cross section of the beam within the piezopatch.

Controller Formulation

Sliding Mode Controller
Constant Amplitude Controller

This satisfies Lyapunov's stability condition and thus guarantees the stability of the distributed system (5.8). In other words, the stability of the flexible manipulator system can be easily violated.

Control Responses

Climbing the tip mass reduces the first natural frequency of the elbow beam from 5.42 to 1.76 Hz. Figure 5.6b shows that a large swing occurs at the top of the elbow joint.

FIGURE 5.4 Schematic diagram of an experimental apparatus.

Some Final Thoughts

However, the implemented controllers work very well without oscillations by applying a feedback voltage to the piezoceramic actuators. Favorable tracking control performance in terms of tracking error without unwanted oscillation due to link flexibility was obtained.

Flexible Gantry Robot

Introduction
System Modeling

Bidirectional ER Clutch Actuator
Modeling of Flexible Gantry Robot

Control Responses

This constant is determined by the geometric and material properties of the flexible arm. The disturbance caused by the acceleration of the moving part affects the flexible arm to be oscillated.

FIGURE 5.8 The bidirectional ER clutch actuator. (a) Layout and (b) photograph.

Optical Pickup Device

Introduction
Modeling and Mechanism Design
Control Results
Some Concluding Comments

The objective lens attached to the tip of the piezoceramic bimorph can be considered as a concentrated mass m. This constant is determined by the geometric and the material properties of the piezoceramic bimorph.

FIGURE 6.1 The optical pickup using piezoceramic bimorph. (a) Schematic confi guration and (b) mathematical model (focusing only).

Dual-Servo Stage

Introduction

They designed the disturbance estimator and robust feedback control system to eliminate external disturbances, such as unwanted vibrations on the fine positioning system due to coarse movements of the robot arm. The ER clutch actuator is one of the most potential candidates for coarse motion control in dual-servo systems.

FIGURE 6.6 Position tracking responses for single sinusoidal trajectory. (a) y d = 100 sin(2 π × 8 × time): fi rst track and (b) y d = 100 sin(2 π × 4.3 × time): last track

Modeling and Mechanism Design

Coarse Motion Stage
Fine Motion Stage

A fine positioning stage consisting of the piezostack actuator and the displacement amplifier has been developed to achieve fast and accurate positioning. Therefore, it can be assumed that the function of the magnifying device cannot affect the gross movement.

FIGURE 6.9 The dual-servo stage system. (a) Confi guration and (b) photograph.

Controller Formulation

The Preisach model for describing the hysteresis behavior of the piezostack actuator-driven fine positioning stage can be expressed by [28]. It is noted that the reliability of the hysteresis output calculated by the Preisach model is entirely dependent on the accuracy of the experimentally obtained FOD data sets for the Preisach function, Y(αk, βk).

FIGURE 6.15 Construction of FOD data sets for the fi ne motion stage. (a) Measured FOD curves and (b) corresponding data mesh

Control Results

So, it is expected that the control accuracy of the dual servo system can be improved by adopting a high-performance DC drive motor. To investigate the control stability of the dual servo system, a mass of 3 kg is added to the coarse motion stage.

Figure 6.17 presents the measured regulating control response of the dual- dual-servo system

Some Concluding Comments

Development of a high-precision assembly robot with a fine motion mechanism (2nd report) - control of the fine mechanism taking into account the dynamic response and disturbances of the coarse mechanism. Dual servo stage position control with electrorheological fluid coupling and piezostack actuator.

FIGURE 6.20 Robustness investigation of smart dual-servo system (regulating). (a) Dual- Dual-servo and macro motion, (b) input for the coarse stage, (c) fi ne stage displacement, (d) input for the fi ne stage, (e) displacement after 2 s, and (f) error si

Introduction

Pump Design and Analysis

Pcrack is the minimum pressure to open the control valve Cq is the flow rate constant of the control valve. This is, of course, due to the reduction of the volume change in the room.

FIGURE 7.3 Photograph of the piezo pump.

Controller Formulation

ΔP is the pressure difference between the cylinder pressure from the piezo pump and the external pressure. By considering the cylinder force balance and adding a proportional damping, the governing equation of the cylinder system is derived from.

FIGURE 7.5 Output fl ow rate with respect to the voltage. (From Choi, S.B. et al., Mecha- Mecha-tronics, 15, 239, 2005

Control Results

The favorable agreement between simulation and measurement validates the control model of the piezo pump-driven cylinder system. Small tracking errors at the peaks can be caused by non-linear behavior of the diaphragm and cylinder friction.

FIGURE 7.8 An experimental apparatus for the cylinder position control.

Some Concluding Comments

The starting position of the cylinder rod is fixed to be 5 mm from the starting position. It has been demonstrated that both the regulation and tracking control performances of the piezo pump-based cylinder system are favorable.

Piezoactuator-Driven Jetting Dispenser

Introduction
Mechanism Design
Dynamic Modeling
Controller Formulation and Responses
Some Concluding Comments
Introduction
Shunt Circuit Design
Implementation and Analysis

Dynamic Characteristics of the
Admittance Analysis of the CD-ROM

Shunt Responses

The flow rate at the nozzle depends on the speed and position of the needle. Δj is the net deflection of hump j (a positive value of Δj reflects an extension of the spring).