Technology of Semiactive Devices and Applications in Vibration Mitigation
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The main steps are presented, even if in a schematic way, to allow coding of the described control laws in C or Fortran. Chapter 5 is devoted to a description of the implementation of the semiactive control strategies. Once the general control frame has been described, the developed semiactive control software is presented in detail. The next chapter, Chapter 6, describes the testing procedures developed at ELSA to verify the structural control devices experimentally by using the on-line testing method with substructuring.
Finally, in Chapter 7, the theoretical aspects of stability are revisited before the conclusions and further future developments are presented. This is a critical aspect when dealing with semiactive control systems which are usually designed to increase the structural damping. In writing this book, the authors had mainly in mind its potential end users, namely: 1. Civil engineers active in the areas of bridges, high-rise buildings, railways, aseismic structures.
Automotive engineers. Mechanical engineers working on vibration problems. Post graduate students. On the one hand earthquakes and hurricanes were considered completely unpredictable, in both occurrence and intensity, while, on the other hand, there were no suitable techniques to reduce the risk of collapse. The Code of Hammurabi is a collection of laws written in 51 columns on a stele discovered at the beginning of the twentieth century and now held at the Louvre Museum in Paris. It consists of a prologue and an epilogue celebrative of the king and of articles regarding various aspects of the civil, penal and commercial law.
The question is: how far has human society moved after 37 centuries? A quick, nearly blasphemous, answer might be: we are slowly coming back to the starting point! This prevailing framework is generally promoted by those designers who want to preserve their identity, role and responsibilities, rather than being replaced by sophisticated software able to navigate across prescriptions better than any human being.
But the reader must have noted that the border between predictable and unpredictable events in the previous scheme is rather fuzzy. Are we still there after 37 centuries? Success and failure are situations characterized by their probability of occurrence; it is the society which decides the target to be pursued for ultimate limit states.
Serviceability limit states are ruled by the desiderata of the contractor, as well as the relevant probability of failure. In any case the designer cannot conceive structural architectures which result in weakness to accidental events. They can be introduced as likely events, without the chance of associating a probability of occurrence to them. In other words, they can be conceived, but not assessed on a statistical basis. The structure remains elastic for the major part of its life under ordinary loads , but it will enter the plastic state under exceptional lateral loads; in this way the input energy should be dissipated.
Even if there might be permanent damage to the structural members, the building is designed in such a way that it should not collapse, so no loss of life should result. This capacity design approach also has another drawback: it is not able to mitigate vibrations that do not induce damage in the structure. This means that comfort aspects cannot be considered with this technique. So the problem of swaying of tall buildings caused by not very intense winds, for example, is not resolvable.
This means that the structure is regarded as a dynamic system in which some properties, typically the stiffness or the damping, can be adjusted in such a way that the dynamic effect of the load on the building decreases to an acceptable level. The natural frequency of the structure, its natural shape and the corresponding damping values are changed in such a way that the dynamic forces from the environmental loads are reduced. This can be done using a large variety of techniques that can be collected in four classes: passive, active, hybrid and semiactive. Active control techniques have been studied extensively from a theoretical, numerical and, more recently, an experimental point of view.
They are surely the most effective ones, but they also show some disadvantages for example, the need for a lot of power to operate that have lead to a low number of implementations. Their application is still limited, even if some tuned mass dampers equipped with a little active mass driver were patented and installed in some buildings in Japan. Semiactive techniques are, at present, the most studied solution, from theoretical, numerical and experimental points of view, because of their excellent characteristics intermediate between those of active and passive techniques. These forces can be used either to add or dissipate energy in the structure.
Active control makes use of a wide variety of actuators, including active mass dampers, hybrid mass dampers and active tendons, which may employ hydraulic, pneumatic, electromagnetic or motor-driven ball—screw actuation. An essential feature of the active control system is that external power is used to effect the control action.
This makes such systems vulnerable to power failure, which is always very likely during a strong environmental event. Passive control devices impart forces that are generated by the mutual displacement of the two connection points of the device inside the protected structure. Passive control may depend on the initial design of the structure, on the addition of viscoelastic material to the structure, on the use of impact dampers, or on the use of tuned mass dampers. The energy of a passively controlled structural system cannot be increased by the passive controller devices.
Though seldom as effective as active control, passive control has three main advantages: 1. It is usually relatively inexpensive. It consumes no external energy. It is inherently stable. A hybrid control system may use active control to supplement and improve the performance of a passive control scheme. Alternatively, passive control may be added to an active control scheme to decrease its energy requirements. For example, as a structure equipped with distributed viscoelastic damping supplemented with an active mass damper on the top of the structure, or a base-isolated structure with actuators actively controlled to enhance performance.
It should be noted that the only essential difference between an active and a hybrid control scheme is, in many cases, the amount of external energy used to implement control. Hybrid control schemes alleviate some of the limitations that exist for either a passive or an active control acting alone, thus leading to an improved solution.
For this reason, usually the semiactive control system energy requirements are orders of magnitude smaller than typical active control systems. Indeed, the system overall energy can be increased by adding a passive system! This depends on the external excitation. In this case much more energy than in the unprotected case will go into the system. This means that bad performances can be obtained if passive or even semiactive systems are improperly tuned. Passive or semiactive devices can even be dangerous because they allow the external excitation to feed a system that would be partially isolated otherwise.
Semiactive control devices are often viewed as controllable passive devices. Details are provided in Chapter 3. A powerful technique for analysing such systems is the state-space approach, based on the concept of state. Furthermore the state-space approach is very general and can be applied to both linear and nonlinear systems and to both time-invariant and time-variant systems.
Damping Technologies for Tall Buildings: New Trends in Comfort and Safety
This state-space representation is commonly used in structural control engineering. These forces can be generated by external excitations such as seismic disturbance or wind load. By calling the displacement vector x1 and the velocity vector x2 , the system represented by 1. It expresses the link between output and input Laplace transforms. It must be recalled that this representation is not applicable to nonlinear systems. The stiffness and the damping are completely due to columns, walls, non-structural vertical elements.
In this case, the three matrices M, C and K can be obtained as follows. The forces acting on each storey are depicted in Figure 1. On both the lower and the upper side of the mass there are two forces: the viscous and the elastic forces. These forces are related to the inter-storey displacement and the inter-storey velocity. One favourable choice is to use the identity matrix in order to have direct access to the states of the system: in this case each output is directly related with a state variable.
In this simple case the function of the vibration isolator is to reduce the amplitude of force transmitted from the vibratory mass to its foundation or to reduce the magnitude of motion transmitted from a vibratory foundation to the mass. The transmissibility of this system is a measure of the reduction of transmitted force or motion provided by the isolator. If the source of vibration excitation force is attached to the mass, transmissibility is the ratio of the force amplitude transmitted to the foundation to the amplitude of the exciting force.
If the source of vibration is a vibratory motion of the foundation excitation motion , transmissibility is the ratio of the vibration amplitude of the mass to the vibration amplitude of the foundation. Figure 1. This means that the insertion of passive dissipation devices into a structure can sometimes lead to unwanted effects, especially during transient response Pinkaew and Fujino Usually an augmented level of damping also induces a higher level of forces at some structural connection. With a semiactive device it is possible to adjust the damping in the most proper manner, for example using an on—off control law that switches the damping value from a high value to a low one.
In the example of Figure 1. The hatched region between the active and passive response curves is the theoretically possible working area of a semiactive system for more details on the transfer function of semiactive systems see also Pinkaew and Fujino The forces that are present at the various storeys of the structure, the inter-storey drifts and the accelerations must also be attentively considered. It is usually necessary to obtain a balance among all these constrains. Nevertheless, such a high availability level is not required if the target is no longer safety against ultimate limit states, but serviceability or robustness.
Such important features, however, do not justify the high costs of active control realizations. In fact the outputs of the measurement devices and the inputs of the actuators are voltages which are proportional to the physical quantities of interest. So normalization constants are inserted all along the formulation. The transfer function of the system 1. Unconditional stability is nevertheless preserved.
It can be shown that 2. This means that actuators and sensors must still have the same supports, even if it is possible to control an actuator using the input coming from a sensor placed in the location of another actuator. In practice, time delays that are much smaller than the system dynamics can be neglected see Chapter 7.
So, the hypothesis that no time delay occurs in the measurement and command chain should be present in civil engineering controlled structures. This confusion comes from the fact that a collocated system is likely to be also a non-centralized system and a non-collocated system a centralized system. But this is not always the case. For example, one could conceive of a collocated system in which the control is performed by a central computer, or structures controlled by several sets of non-collocated control systems. This last situation can be used to avoid problems related to the failure of a portion of the whole control system.
Linear systems in which the equations describing their dynamic behaviour are linear. Non-linear systems in which the equations are no longer linear. In civil engineering applications, especially in earthquake engineering, non-linear behaviour is very common as a consequence of inelastic deformations and damage Barroso This is especially true if no protection is added to the structure. If a control system is designed to help the structure to resist environment loads, it can be designed in order to maintain the structure in a linear range.
In the next sections of this chapter, the concept of transfer function is used, which is strictly related to the linearity of the system. It shows its matrix nature there. Truncating the modal expansion of the transfer function without introducing a residual mode can lead to substantial errors in the calculation of the openloop zeros and, as a result, of the performance of the control system. With this in mind, consider the diagonal kth term in Equation 2.
This means that the function must always be increasing. In the case of little damping a very common case when unacceptable vibrations are observed , the poles and zeros still alternate near the imaginary axis of the left-half complex plane. This observation will be very useful for studying the stability. This means that, at anti-resonance frequency, the structure behaves as if an additional restraint has been added to that point.
Only the lowest and most meaningful frequencies are then taken into consideration. The numerical model often called the reduced model will deal with the few dominant low-frequency modes. This can lead to a destabilization of the reduced model. This phenomenon is called spillover. It is also proved that, if observation spillover is absent, control spillover itself cannot destabilize the system. In this case, control spillover causes unwanted excitation of the residual modes that can degrade the system response but cannot destabilize the system.
The same conclusions are achieved in Meirovitch It is observed that, because the term given by control spillover has no effect on the eigenvalues of the close-loop system, it can be concluded that control spillover cannot destabilize the system, although it can cause some degradation in the system performance.
So, only observation spillover is really dangerous. Some solutions for reducing observation spillover are also proposed in the same book Meirovitch As a rule of thumb, it can be greatly reduced by using a large number of sensors. However, this last solution is not as simple as it seems, because one must know in advance which are the uncontrolled modes. Direct output feedback control is proposed to avoid spillover, but in this proposal one does not consider that time delay can occur and can still generate instability.
Since the control law design is based on this reduced order system, spillover is always possible. For spillover reduction, it should be better to locate controllers and sensors at or very near the zeros of the affected modes, but this is usually quite impossible. Because the controller is designed taking into consideration only the lowest modes, a method that penalizes the highest and unmodelled modes should be preferred.
Clearly this method can be effective only for spillover due to the second step of discretization, because the designer must know in advance which modes not to consider. The contamination of observation spillover in Equation 2. These interactions are shown graphically in Figure 2. It can be shown that spillovers can reduce the stability margins of the actual structure and are at the heart of the control problem based on the reduced order models. It is also a function of the controller and sensor locations and their effects on the residual modes.
A force actuator is placed under a simple supported beam and is controlled via an active controller. The input signal to the control algorithm is given by a position sensor in this case a laser transducer sensor placed somewhere on the beam but not in the same position as the actuator. So the beam is controlled at a point measuring the displacement at a different point this is the typical non-collocated architecture. The controller will execute the algorithm instantaneously and communication times among the parts will be zero.
Even in this case, however, instability can occur because of the spillover phenomenon. The controlled beam, in fact, has its internal dynamics: this means that the waves generated by the actuator will propagates along the beam. This means that there will surely be some modes that the control strategy has not been designed for. If the sensor is placed at a distance that is a multiple of the half wavelength of the displacement travelling wave of an uncontrolled beam mode, the resulting signal could be a displacement with an inverted sign with respect to the displacement at the location of the force actuator.
This mode has not been properly taken into account in the design process of the non-collocated control law, so it may happen that the algorithm commands the actuator to generate forces that excite the beam instead of stopping it. Obviously, in the controller process design it is not realistic to consider more than a few modes, usually just the modes associated with the lower frequencies.
This means that the controller can give improper command signals to the actuator due to the lack of the highest modes. If there is no observation spillover, however, control spillover cannot destabilize the system, even if it can induce cyclic oscillations, as emphasized in Section 2. It is important to note that no best solutions can be taken a priori, because the right choice depends on the particular needs and on the control systems for that particular case. Constraints are different from one situation to another and they must be evaluated by the control designer.
In this case it was shown that the transfer function has poles and zeros alternating on the left side of the imaginary axis and the root locus gives a trajectory always included in the left part of the complex plane. This means that any chosen gain of the control system ensures stability, the remaining question being to choose the optimal gain value. In conclusion, collocated systems can be considered inherently robust. A non-collocated control system is always subject to spillover problems, regarding either observation spillover or control spillover, as mentioned earlier.
This problem is inherent in the non-collocated control system itself, where a model of the structure to be controlled is needed and, even in the best situation, it is a discretization of a continuous structure. Moreover, one must consider that the root locus of a non-collocated system can pass from the left part of the complex plane to the right one and vice versa , so the control system can be very sensitive to any distortion from the nominal design situation. Another important question is: what happens if a sensor or an actuator fails?
In a collocated control system the corresponding actuator could be switched off, while in the non-collocated control strategy a new control algorithm avoiding that signal can be adopted. But a system must remain robust, i. One strategy for strengthening robustness could be the use of redundancy measurements Noltingk which is common practice in nuclear power plants, for example in order to accept that some sensors can give wrong values.
Three measures can be taken for each quantity and the mode value can be assumed as the right one. With three sensors it is also possible to control the failure of any sensor: if the mean value of two sensors is quite close to the value of the third, all is going well; on the contrary, one or more sensors have surely failed. An alternative approach is illustrated in Faravelli and Rossi From a theoretical point of view, however, they cannot reach the high performances of non-collocated systems.
Since a very large number of variables are involved, no preference can be given a priori to a collocated or non collocated strategy from the point of view of practical realization. A collocated system is generally easier to implement. For programming the controller, in fact, it is not necessary to have a complete model of the structural system, but just a rough idea about the interesting frequencies involved. With a non-collocated control strategy, both actuators and sensors must be put in communication with one or more computers where the control law is implemented.
It may be a problem to install the transmission cables inside the structure, because proper locations must be found in order to avoid vandalism or weather damages. Wireless solutions are currently being pursued Casciati et al. In this case there is no longer a need for cable connections and the mounting phase consists only of some mechanical operations, but no electronic connections must be arranged. The required implementation time makes a difference. As already explained, usually non-collocated systems need a deeper design, so they should be more expensive.
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Moreover the production of collocated systems can be easily industrialized, so the unit price should decrease. However, at the moment, only a few standard products are available on the market oriented to civil engineering applications. If one uses very precise sensors and actuators, in fact, one can achieve better results, but at a higher cost.
However, the precision of sensors must be compatible with the accuracy of the actuators and vice versa. The core of this comparison is to answer the following questions: 1. Which approach has the best performance for example, comparing the resulting transfer function?
Which is the most robust approach for example, when any sensor fails? Which is likely to be the best compromise between these two possibilities? As will be shown, even in the simple case of a storey building with an equal distribution of masses, stiffnesses and dampings, a general answer to these questions cannot be given.
The structure taken into consideration is the n-storey building of Figure 1. Only the case of decentralized control is considered, so that each actuator works on its own. Even in the case when there is an actuator at each storey, they work independently of each other.
In the following A1 denotes the actuator placed at storey 1, A2 the actuator placed at storey 2, and so on. Given in Table 2. It can be seen from Table 2. Incidentally, some of these possibilities are feasible but, in practical applications, not useful. The last step was to consider the fact that more than one actuator can simultaneously be present on the structure. Table 2. These three possibilities are quite realistic, because to use only one sensor for each storey is the cheapest way to achieve control and, in the meantime, is the case in which the sensors are collocated, one by one, with the actuators.
The case of an actuator using the sensor placed on its own storey and the sensors immediately on the upper and lower ones is a straight generalization of the previous case. In this study these sensors are supposed to measure velocity and displacement, but the generalization to acceleration sensors is straightforward. This assumption was considered because a linear quadratic regulator LQR controller was designed and for this type of controller full state knowledge is necessary.
The three matrices of Section 1. The important thing to bear in mind is that the weighting function in the three cases must have a physical meaning in order to compare these different controlling schemes. Here the meaning of assuming the Q matrix equal to the total energy of the considered storey is to show that, if the energy of a larger number of storeys is taken into consideration, the results can be much improved. The results are shown in Figure 2. The dotted line represents the uncontrolled structure. The dashed dot and the dashed lines represent respectively the controlled structure in which each actuator uses one or three sensors.
It is clear that the behaviour of the controlled Bode Diagram —10 Magnitude dB —20 —30 Uncontrolled Controlled — 1 sensor Controlled — 3 sensors Controlled — all sensors —40 —50 —60 —70 —80 —90 0 —45 Phase deg —90 — — — — — 10 0 10 1 Frequency Hz Figure 2. The solid line represents the case in which each actuator has full information. This fact suggests that the information coming from storeys far away from the actuator is not important, so it may not be useful to have full state feedback.
The comparison in the frequency domain is very useful if a linear behaviour is expected from both the building and the actuating system. Force: this is the external force acting upon the storey. It can be an external force coming from wind, earthquakes or other environmental loads or a control force caused by an actuator or the resultant of the sum of the two.
Displacement up: this is the displacement of the upper storey. This signal, subtracted from the actual value of the displacement in the considered storey and multiplied by the stiffness value of the columns connecting the actual storey with the upper one, enters in the force balance 3.
Displacement down: this is the displacement of the lower storey. Speed up: this is the velocity of the upper storey. Speed down: this is the velocity of the lower storey. The two outputs are: 1. Displacement: this is the actual displacement of the storey. Speed: this is the actual velocity of the storey.
The resulting signal is the inertial force of the storey. The acceleration is then integrated once to obtain velocity and twice to obtain displacement. As a result of the conducted time analysis Marazzi , the failure of one sensor is critical if it refers to the controlled storey, while the performance is not so badly affected if the failure refers to a sensor far away. This means that passive and active devices will not be mentioned here, even if some of the described devices can be seen as an adaptation of passive or active solutions.
It is worth noting that, from the semiactive control point of view, it does not make sense to speak of actuators as in active control , because semiactive devices can only generate forces in a passive way, but they are unable to provide any force. The force that the semiactive devices generates is always related to the relative velocity and displacement of their ends.
As mentioned in Section 1. This requires a minimum amount of energy to turn the mechanical component devoted to the changing behaviour of the system a valve, for example, or a bolt friction connection. The main advantage is to join the simplicity and reliability of a passive device to the adaptability of the active systems. They had automotive applications in mind, so their target was to obtain a better isolation of the vehicle from the roughness of the road.
In that work the concept of semiactive control was extended to civil buildings, proposing a tuned mass damper that was connected to the main structure with a semiactive viscous damper. Karnopp et al. In the case of ABS braking, the main concern is the avoidance of sticking in a frictional interface while, in the case of semiactive damping, the main aim is to dissipate energy as quickly as possible. The two objectives are different but they are very much interconnected because both deal with the problem of allowing a relative movement of two parts.
A sticking interface cannot dissipate energy, in fact. The optimal friction value is not constant, so the best device can adapt itself to these changes. Since that time, many studies have been conducted from the point of view of both control strategies and implemented devices. New hardware and software capabilities allow the design of more sophisticated control laws, while, in addition, new materials such as magnetorheological liquids are now available to permit proper device design.
In the next chapter the main control strategies present in the literature will be described, while the most promising devices are illustrated in the remainder of this chapter. The valve enable such a device to deliver a wide range of damping level. As a result, the force— velocity relation in the damper is a variable function that can be controlled in real time.
Technology of Semiactive Devices and Applications in Vibration Mitigation
Variable-friction dampers dissipate vibrational energy in a structural system by utilizing forces generated by surface friction. The ability of such devices to reduce drifts within high-storey buildings that are seismically excited has been successfully investigated. Furthermore friction-controllable systems are commonly employed in conjunction with seismic isolation systems. These adjustable tuned liquid dampers are based on passive tuned sloshing dampers and tuned liquid column dampers. Finally, one of the most promising classes of semiactive control devices is the magnetorheological MR damper.
This type of actuator is shown in Figure 3. The reader is referred to Karnopp et al. F t v t Cadapt Figure 3. These types of devices are usually simpler than the continuous ones, but they have a lower performance. This kind of device will be discussed later in the section devoted to magnetorheological devices. Kmin and Kmax are the minimum and the maximum stiffness that the device can induce in a portion of the structure. One of the most common schemes for these devices consists in bracing that can vary its stiffness accordingly to a control law.
This is usually achieved by means of hydraulic devices that can clamp the bracing to the structure. In this case the semiactive stiffness device is coupled to a semiactive damping device: the result is a varying viscoelastic device. Another interesting way for varying stiffness is the adapted tuned mass damper scheme Figure 3.
In , W. This phenomenon is reversible, very fast response time of the order of a millisecond and consumes very little energy. Iron particles have the highest saturation magnetization. In Table 3. However, the actual behaviour is more complicated and includes striction and hysteresis. Figure 3. The valve mode is the normal operating mode of MR dampers and shock absorbers; the direct shear mode is that of clutches and brakes.
This happens because the excitation covers a broad frequency band, and there is limited scope for adjusting the mass or stiffness properties of a structure in order to shift the resonance frequencies.
Integrated Design of Structural and Semi-active Control Systems: Inverse Lyapunov Approach
The problem is how to insert damping into the structure. With low joint clamping pressures, sliding on a macro scale takes place. If the joint clamping pressure is increased, mutual embedding of the surfaces starts to occur. Sliding on a macro scale is reduced and micro slip is initiated, which involves very small displacements of an asperity relative to its opposite surface. A further increase in the joint clamping pressure will cause greater penetration of the asperities. The pressure on the contact areas will be the yield stress of the softer material.
Relative motion causes further plastic deformation of the asperities. In most joints he studied, the previously described mechanisms were working. Many joints have to carry great pressures to satisfy structural criteria, such as high static stiffness. An improvement in the quality of the surfaces in contact will also facilitate the slipping. With the macro slip mechanism, the dissipated energy is proportional to the product of an interface shear force function and the relative slip.
In order to set and maintain the normal force, a clamping arrangement more elaborate than simple bolts or rivets may be necessary, although this may only mean the addition of an active washer. A piezoelectric stack disc is used as a washer to control in real time the normal force in the friction interface based on feedback from sensor outputs.
If a voltage is applied to the piezoelectric washer, the stack disc tries to expand, which results in increasing the normal force. This idea of semiactive friction damping in joint connections has been patented by Gaul Gaul and Nitsche ; Gaul and Lenz For example, as shown in Figure 3.
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The system can be a passive sliding isolation system as long as the pressure of the bearing chamber, and thus the friction, is kept at a constant value. This has the great advantage that the device can become operative also at a low excitation level while maintaining high performance for stronger excitations. One important point concerns the time response of the system: for practical application a very fast control algorithm should be used together with a good pumping system in order to avoid excessive delays.
More recent efforts are described in Dowdell and Cherry The other advantage of this device with respect to a passive one is that it can become operational also for small forces that is, small earthquakes or winds but maintain good performances also for stronger solicitations. A frustum—conical TLD was also proposed as an alternative to the traditional rectangular, cylindrical or annular tank.
A linear model can interpret TLD behaviour for small excitations. For larger amplitudes, strong non-linearities occur and the linear model is no longer predictive. The most practical way of addressing the non-linearity of a physical model is by substituting the real TLD system with an equivalent ideal TMD with parameters mass, frequency and damping varying with the excitation amplitude besides depending on the geometry of the tank. In Casciati et al. Actually, as far as a linear behaviour is concerned, one of the most favourable aspects of conical TLDs, compared with cylindrical ones, is the greater percentage of the mobile mass to the total mass of liquid, which allows smaller total masses for an identical level of performance.
In each case, in fact, the mass has been assumed identical to the total mass of liquid in the tank. This fact is responsible for the decrement of the frequency response for the normalized force, but should not be looked upon as an unfavourable property. Such a device can be easily made into a semiactive device.
The interesting feature is that the behaviour of this class of devices can be studied by simply investigating the response of an electric motor controlled to have zero speed Figures 3.
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The response behaviour is practically independent of the external temperature because the device operating temperature is always higher than the air temperature and it is reached in few seconds. Then pulses of relatively short duration from suitable nozzles, each of them requiring a relatively low amount of energy, could be used to control the structures. The paper by Brambilla et al. This is the case with structures belonging to the offshore drilling technology. They are commonly adopted for the realization of passive devices, while the different and long reaction times to cooling and heating prevented their adoption in semiactive devices.
In areas different from civil engineering, however, SMAs were conveniently incorporated into suitable devices and the reader is referred to Kohl for a review of the main ideas. Future adaptations for civil engineering purposes can be easily foreseen. With a semiactive control device, the energy can only be dissipated and so removed from the system. These kinds of devices could be seen as passive dampers with changing characteristics to be adjusted on-line. The control law is set a priori and no knowledge of the state variables is necessary. The damping characteristic of the devices can vary continuously or by steps, depending on the operating conditions.
Typically, the variable dampers work in a bi-state on—off manner. This is the simplest and cheapest way to implement a control law and can be used very usefully for vibration isolation of rotating machines. Such a technique is used, for example, for washing machines: one value of damping high is used when the drum is at low speed that is, during acceleration or deceleration , while a lower damping value is used for high speed Figure 4. This type of control is useful when the system to be damped has very well-known dynamic characteristics and loading conditions.
In some cases the different level of damping is chosen by the user, as in the case of the semiactive suspension of vehicles. This control law was developed in order to obtain the lower vibration amplitude of the body mass the upper one, see Figure 4. Illustrated in Figure 4. The choice between a damper adjusted to its high state or low state is made using the following control law.
Depending on the product of the relative velocity vrel across the damper Figure 4. If the product is positive or zero, the damping value cs of the damping device is adjusted to its high state; otherwise, cs is set to the low state. The logic of the on—off skyhook control policy is as follows.
When the relative velocity of the damper is positive, the force of the damper acts to pull on the system body mass; when the relative velocity is negative, the force of the damper pushes the body mass. Thus, when the absolute velocity of the body mass is negative, it is travelling to the left and the maximum high-state value of damping is required to push the body mass, while the minimum low-state value of damping is required to continue pulling on the body mass. However, if the absolute velocity of the body mass is positive and the body mass is travelling to the right, the maximum high-state damping value is required to pull the body mass, while the minimum low-state damping value is required to push the mass further to the right Figure 4.
It can also be observed that vrel 0 the two masses are going away from each other. The following four cases can therefore be found: 1. The two masses are moving away from each other and the mt is moving to the right product is positive : high damping is required in order to try to keep the body mass left. If the damping is high, the body mass would move to the left faster, in this case. The two masses are approaching each other and mt is moving to the left product is positive : high damping is required in order to keep the two masses as far apart as possible.
The two masses are approaching each other and mt is moving to the right product is negative : low damping is required. In conclusion, a high damping value is used only when needed; the lowest possible damping value is used when damping is not needed. However, now, the damping values are not limited to these two states alone; they may exist at any value within the two states. As illustrated in Figure 4. Contrary to the skyhook control strategy, this control law was developed in order to have the lower vibration amplitude on mt.
However, when the absolute velocity of mt is negative, it is travelling to the left and the maximum high-state value of damping is required to pull mt , while the minimum low-state value of damping is required to continue pushing on mt. But, if the absolute velocity of mt is positive and so mt is travelling to the right, the maximum high-state value of damping is required to push mt , while the minimum low-state value of damping is required to pull mt further to the right. The continuous groundhook control strategy can be derived directly from the continuous skyhook control simply by changing the chosen condition on the damping value, so it will be omitted.
Their common characteristic is the fact that these laws have a two-stage architecture, that is the controller design can be divided into two parts. The second step involves the design of a clipping controller allowing the semiactive damper to develop the force that the active device would have removed from the structure. To clip the active control law to a semiactive one the following rule is usually used: when the magnitude of the force Fd produced by the damper that is, the control force f in this case is smaller than the required target force fc , and the two forces have the same sign, the voltage applied to the current driver is increased to the maximum level, so as to match the required control force; otherwise, the command voltage is set to zero.
Figure 4. The output of the controller determined by the fuzzy logic may exist anywhere between the high and low damper states. Fuzzy logic is used in a number of controllers because it does not require an accurate model of the system to be controlled. Fuzzy logic 2 In the case of a linear system with state matrix A, see also 1. These rules are typically created through the intuition or knowledge of the designer regarding the operation of the system being controlled.
No matter what the system is, there are three basic steps that are characteristic of all fuzzy logic controllers. This step is accomplished through the construction of a membership function for each of the inputs. Once the membership functions are chosen, the input, read as a crisp value, is transformed into a fuzzy value by intersecting each component of the membership function with this value.
This must be done for all inputs of the controller. To give an example, the weighted average method is described in Section 4. These three steps must be repeated for each input point to obtain continuous outputs. In this approach, at every occurrence of local extremes in the deformation of the device that is, when the relative velocity between the ends of the semiactive device is zero , the normal force applied to the frictional interface is updated to a new value.
There is often no need to check if the force is greater than the static friction, because some semiactive devices have no static friction. A force feedback loop is used to induce the semiactive damper to produce approximately the frictional force corresponding to the required normal force. An appropriate choice of gn will keep the force fc within the operating envelope of the semiactive damper most of the time, allowing the device force closely to approximate the required force.
It provides a simple and yet often effective approach. In this way it works as a brake, thus allowing the dissipation of energy. On the other hand, when the relative displacement and the relative velocity of the ends of the device are in opposite directions, this control law decreases the friction forces to a minimum in order to make the device movement as easy as possible.
The control parameter umax should be at the optimal value, that is a value which provides the maximum energy dissipation. The normalized friction force f indirectly represents the amount of response acceleration and also serves as a measure of the transfer of induced force to the structure. They indicate the relative importance in the control objectives of relative displacement, response acceleration and control signal, respectively.
The basic objective of the control is to provide a device that dissipates the biggest amount of energy within an acceptable range and at the same time minimizes the transferred force. Without entering into details, an explicit Newmark method can be used for implementation to solve the involved equations numerically. In the case of a washing machine, for example, the control law can be implemented following these steps: 1. When the machine begins to spin-dry, the damping value is set to the maximum one and a time counter is reset to zero.
It is immediately evident that to implement this control strategy is very simple: it needs only to measure two quantities drel and dabs and then to act on some device switching the dissipator from one state to another. The only change that the control law can induce into the device is to switch from one value to another. The quantity t is the time step of acquisition. The algorithm checks at the beginning that the needed parameters are meaningful, then executes the procedure. This can consume energy and can also lead to damage of the device. It must be noted that, as in Figure 4.
The continuous skyhook algorithm implementation is much more complex than the on—off one at least for three main reasons: 1. The last point means that only special kinds of devices can perform this control strategy, such as the MR devices, because the response time is only some milliseconds. In the case of mechanical arrangements, it is much easier to switch between two values for example, clamped and unclamped than to pass through all the intermediate states.
It looks very similar to Figure 4. The clipping control can be viewed, in fact, as a control strategy in which the actuator can operate only resisting forces and not act directly on the structure. So the active control law applies when the device is subjected to forces and turns into a constant value when it should act. For the shaded region in Figure 4. The control must be designed in this case to manage saturation on the semiactive device: too high a value of command voltage to the magnetic coil can lead to damage.
A general criticism of this class of methods, however, is that there is no way of assessing if a good active control law can also give good results when turned into a clipped one. Because of the inherent non-linearity, the clipping strategy cannot be assessed with a frequency domain technique, but time domain analysis must always be performed with several types of excitations and at different intensity levels.
The Heaviside step function is implemented in algorithm 5. The real task for implementing the direct Lyapunov control method is then to obtain all the values that must be fed into the Heaviside step function. This may result in a long calculation time, so researchers have placed great emphasis on the design of a dedicated chip for fast on-line calculation Faravelli and Rossi In Figure 4.
An example of a rule table is shown in Table 4. The main advantage of fuzzy control, that is the fact that it is based on verbal rules and so very close to common sense practice , is also its main drawback. In fact it is impossible to obtain the optimal solution automatically or to check mathematically if the elaborated solution is stable or not. The main difference here is that the required control force is not calculated with an active control algorithm, but with Equation 4. Algorithm 7 describes in more detail what is shown in Figure 4.
Furthermore the control architecture can be oriented towards the realization of a centralized or non-centralized system, as illustrated in Chapter 2. In the development of their medium- and large-scale testing facilities the authors were confronted by many implementation problems regarding the hardware and software needed to realize prototype testing set-ups. An alternative choice is possible by selecting standard PC components and building, around an open architecture, the proper hardware and software.
The master processor board. One or several slave processor boards. The communication bus connection Figure 5. It collects data from the slaves, runs the centralized control algorithm and provides the target displacements or forces to the slaves. It consists of three main components, all based on the PC bus architecture: 1. A processing unit card.
A dual-port memory card enabling high-speed access and easy sharing of data between the local PC bus and the ISA bus connected to the master. Figure 5. These modular computers master Figure 5. This architecture was selected for three main reasons: 1. Active devices, while providing significant reductions in structural motion, typically require large and often multiply-redundant power sources, and thereby raise concerns about stability.
Passive devices are fixed and cannot be modified based on information of excitation or structural response. Semiactive devices on the other hand can provide significant vibration reductions comparable to those of active devices but with substantially reduced power requirements and in a stable manner. Connecting structural dynamics with control, this book: Provides a history of semiactive control and a bibliographic review of the most common semiactive control strategies.
Presents state-of-the-art semiactive control systems and illustrates several case studies showing their implementation and effectiveness to mitigate vibration. Illustrates applications related to noise attenuation, wind vibration damping and earthquake effects mitigation amongst others. Offers a detailed comparison between collocated and non-collocated systems. Formulates the design concepts and control algorithms in simple and readable language.