Chapter 1 Introduction
Vibration control is a major problem in many mechanical systems. Continuous mild vibrations may interfere with the system’s performance and/or cause a rapid weathering of physical elements. Intensive vibrations may even cause immediate damage to the system. A promising approach for dealing with such unwanted dynamic phenomena in civil structures, has attracted growing attention over the last decades. This upcoming field, known as structural control, suggests the use of approac hes and to ols from control theory for analyzing and/or improving structures dynamic behavior, with emphasis on suppressing seismic and wind responses of structures [89]. Its goal is to keep the structures strains, stresses, accelerations, displacements, etc., which are caused by a dynamic excitation, below a given bound [49].
Generally speaking, physical realization of structural control is done by applying forces to the vibrating structure in real time. The required forces are generated by mechanical devices, called actuators, which take commands (control signals) from a controller. Control implementation consists of two main stages. First, a law, which defines what are the suitable control signals at each moment, should be formulated. Next, this law is embedded into some electronic controller that calculates these signals in real-time and translates them into electric signals. These electric signals are sent to the actuators, which turn them into real forces that are applied to the structure. Various types of actuators, have been developed for that purpose. Each type of device is based on different physical phenomenon and possesses its advantages and limitations. This led to the definition of four main structural control classes: passive, active, semi-active, and hybrid [49].
In active control systems, the actuators need external energy source in order to generate control forces. The actuators are distributed in the structure and can be used to add or dissipate mechanical energy from it. Although this strategy is known to be highly effective, the need for a significant energy source makes active control vulnerable to power failure, which is very likely to occur during strong excitations, i.e., earthquakes. This disadvantage brings into question the effectiveness of active control for improving structural response to extreme loadings [49].
Passive control is a well known solution for structural vibration problems. An important feature of a passive control system is that it can generate the required control forces without any external power. Instead, the structural motion itself is utilized to generate the forces in dampers by forcing motion on the damper’s anchors. Essentially, passive control has four main advantages: (1) it is usually relatively inexpensive, (2) it consumes no external energy, (3) it is inherently stable and (4) it works even during strong excitations [49]. However, a major drawback of passive methods is that they are unable to adapt to changes in structural properties, usage patterns and loading conditions. For example, structures that used passive base isolation in one region of Los Angeles and survived the 1994 Northridge earthquake, may have been damaged severely if they were located elsewhere in the region. Yet, its relative simplicity and reliability makes passive control a worthy alternative in many structural control problems.
Semi-active control strategy is sometimes referred to as a class of active control. Similar to an active one, a semi-active control system can alter its properties in real-time, however, it can do this by a very small amount of external power, compared to an active control system [49]. An important group of semi-active devices are semi-active dampers. The forces in such dampers can only resist the structural motion in the damper’s anchors but the device’s resistance properties can be changed by a very small amount of external power [49]. Semi-active systems provide an attractive alternative to active ones for structural vibration reduction. They offer the reliability of passive devices and maintain the versatility of fully active systems without the need for a large power sources. However, at the same time semi-active dampers set restrictions on the control forces, which significantly complicate the use of optimal control theory for controller design. A hybrid control system is a combination of different control schemes. In many cases, the only essential difference between active and hybrid control is the amount of external power used for control implementation. A side benefit is that in case of power failure the system still provides a certain protection to the structure.
The present book deals with several optimal control design problems, which are related to passive and semi-active controlled structures, and with their solutions. First, the problems are form ulated while taking into consideration constraints and excitations which are common in structural control. Next, optimal control theories are used in order to solve these problems rigorously. Chapter 2 analyzes models that are commonly used for civil structures and control actuators. The analysis is performed by modern theoretical concepts, such as systems dissipativity and passivit y, and hints to novel models and approaches for optimal control solutions. Chapter 3 describes optimal control theories that are suitable to the addressed problems. Chapter 4 introduces successive methods that are used later for solving optimal control problems, related to control law design. Chapters 5 and 6 present new results that correspond to optimal passive and semi-active control of structures, respectively. Chapter 7 presents an approach for effectively placing dampers in structures with seismic excitation.
