Hybrid Control of Smart Structures

In this Keynote Lecture, first a novel wavelet-hybrid feedback least mean square (LMS) algorithm is presented for robust control of civil structures through adroit integration of a feedback control algorithm such as the LQR or LQG algorithm, the filtered-x LMS algorithm, and wavelets. Next, a new hybrid control system is presented through judicious integration of a passive supplementary damping system with a semi-active tuned liquid column damper (TLCD) system. The new hybrid control system utilizes the advantages of both passive and semi-active control systems, thereby improving the overall performance and reliability of the control system. It is shown that the new hybrid control model is effective in significantly reducing the response of structures under various seismic excitations. Further, it provides increased reliability and maximum operability during normal operations as well as a power or computer failure. Passive, Active, Semi-Active, and Hybrid Control of Structures Passive control refers to systems that do not require an external power source. It includes base isolation, supplementary damper, and tuned mass damper (TMD) systems. A base isolation system attempts to reduce the response of structures subjected to seismic ground excitations by isolating the structure from the external seismic excitations. As an alternative to the base isolation system, the supplementary damper system has been widely used for the vibrations suppression in general. In this system mechanical devices increase the existing inherent damping of the structure and help dissipate the energy of the external excitation. The mechanical dampers in buildings are usually installed as part of its bracing system, such as diagonal or Chevron bracings. A TMD system relies on the damping forces introduced through the inertia force of a secondary system attached to the main structure by spring and dashpot in order to reduce the response of the main structure. A properly designed TMD system can alter the dynamic characteristics of the structure and reduce its response effectively. A TMD system is usually placed on the top of the structure. The tuned liquid column damper (TLCD) system was introduced to civil engineers by Sakai et al. (1989) as another type of passive damping system. As a special type of TMD system, the TLCD system provides performance similar to a TMD system but offers a number of advantages over the traditional TMD system, to be discussed later. As an alternative to passive control systems, active control systems have been proposed where sensors measure the motions of the structure and actuators and a feedback control strategy exert counteracting forces to compensate for the effect of external excitations (Adeli and Saleh, 1997, 1999). Adeli and Saleh (1997) present a computational model for active control of large structures subjected to various types of dynamic loadings such as impact, wind, and earthquake loadings. The authors also present robust and efficient parallel-vector algorithms (Saleh and Adeli 1997) for solution of the Riccati equations encountered in the structural control problems on shared-memory multiprocessor machines using the eigenvector approach and exploiting the architecture of shared memory supercomputers (Adeli, 1992a&1992b; Adeli and Kamal, 1993; Adeli and Soegiarso, 1999). The computational model and parallel vector algorithms have been applied to both steel bridge and multistory space frame structures subjected to various types of dynamic loadings such as impulsive traffic, wind, and earthquake loadings. Further, they present algorithms for simultaneous optimization of control and structural systems (Adeli and Saleh, 1999). The primary conclusion of that work is that through adroit use of active controllers the weight of the minimum weight structure can be reduced substantially. The result would be a substantially lighter structure for both bridge and building structures. A shortcoming of active control of structures is its dependency on a large power requirement for the control system. An active control system will not operate when a strong earthquake causes the failure of the electric power system unless there is a large properly operating backup battery system. Semi-active control strategies have been proposed by researchers to increase the overall reliability and efficacy of the controlled system (Housner et al., 1997). Semiactive control systems are physically similar to passive control systems but computationally similar to active control systems. Developed from passive control devices, semi-active control devices are designed to operate with a very small power (e.g. a battery) thus eliminating to need for a large external electric power source. They control the response of the structure by actively changing the properties of controllers when power is supplied, but behave like passive control systems when the power source is cut off or when there is a computer system failure. As such, semi-active control systems provide a more reliable and stable way of controlling structures compared with active control systems. There is another strategy to overcome the vulnerability of active control systems, called hybrid control, where two distinct systems are employed together. Traditionally, an active control system is used in conjunction with a passive control system (Soong and Reinhorn, 1993, Lee-Glauser et al., 1997). When there is power (normally electric power) the two systems work simultaneously. When the external power fails the passive control system still works, thus reducing the response of the structure at least to some extent even after the active control system stops functioning. The shortcoming of this approach is that in the event of power failure during a catastrophic or maximum probable earthquake only one half of the earthquake resistant system is available and safety of the structural system is not guaranteed. A goal of the authors' research has been to devise a hybrid control system with increased reliability and maximum operability during power failure. In this lecture, a new hybrid control system is presented through judicious integration of a passive supplementary damping system with a semi-active TLCD system. The new hybrid control system utilizes the advantages of both passive and semi-active control systems, thereby improving the overall performance and reliability of the control system. Novel Wavelet-Based Algorithms for Control of Structures Classical feedback control algorithms such as the Linear Quadratic Regulator (LQR) and Linear Quadratic Gaussian (LQG) algorithms (Stein and Athans, 1987; Soong, 1990; Dorato et al., 1995; Lewis and Syrmos, 1995; Adeli and Saleh, 1999) have been used for structural control problems over the past three decades. These algorithms are among the most popular optimal feedback control algorithms mainly due to their simplicity and ease of implementation. Even though they can be used to reduce vibrations, they suffer from a number of fundamental shortcomings such as being susceptible to parameter uncertainty and modeling error (Prakah-Asante and Craig, 1994) and failing to suppress the vibrations when frequency of the external disturbance differs even slightly from the natural frequencies of the structure. The authors have developed novel control algorithms to overcome the limitations of classical feedback control algorithms. A hybrid feedback-LMS algorithm has been developed for control of structures through integration of a feedback control algorithm such as the LQR or LQG algorithm and the filtered-x Least Mean Square (LMS) algorithm. It is shown that the hybrid feedback-LMS algorithm minimizes vibrations over the entire frequency range and thus is less susceptible to modeling error and inherently more stable (Kim and Adeli, 2004). Wavelet analysis is a transformation method in which the original signal is transformed into and represented in a different domain that is more amenable to analysis and processing (Mallat, 1989, 1998; Daubechies, 1992; Farge et al., 1993; Wickerhauser, 1994; Jameson et al., 1996; Ruskai et al., 1992; Vetterli and Kovacevic, 1995; Burrus et al., 1998). In recent years, the senior author and his associates have advanced the applications of wavelets in various engineering fields such as transportation engineering(Adeli and Samant 2000, Samant and Adeli 2000, 2001, Adeli and Karim 2000, Karim and Adeli 2002a&b), earthquake engineering (Zhou and Adeli 2003a&b, Sirca and Adeli 2004), structural engineering (Kim and Adeli, 2004, 2005), and biomedical engineering (Adeli et al. 2003). Low-pass filtering of dynamic environmental disturbance signals due to winds and earthquakes is required when the hybrid feedback-LMS algorithm is used for control of civil structures, because the frequency bandwidths of such environmental signals are much wider than those of common structural systems. It is shown that the wavelet transform can be used as an effective filtering scheme for control problems. A new wavelet-hybrid feedback LMS algorithm has been developed for robust control of civil structures through adroit integration of a feedback control algorithm such as the LQR or LQG algorithm, the filtered-x Least Mean Square (LMS) algorithm, and wavelets. (Adeli and Kim, 1994). The new control model • has the ability to suppress vibrations over a range of input frequencies, • is less susceptible to structural modeling approximations and errors, • is effective for control of both steady-state and transient vibrations, and • includes the external excitation term. Simulation results demonstrate that the proposed model is effective for control of both steady and transient vibrations without any significant additional computational burden, and can be used readily to enhance the performance of existing feedback control algorithms. Hybrid Control of Smart Structures A TLCD system provides the same level of vibration suppression as a conventional tuned mass damper system but with following advantages (Kim and Adeli, 2005): • The required level of damping can be readily achieved and controlled through the orifice/valve, making it suitable not only for passive control systems but also for semi-active control systems • When there are changes in the dynamic characteristics of the main structure after construction is completed or after the occurrence of an earthquake, the TLCD parameters (frequency and mass) can be easily tuned by adjusting the height of the liquid in the tube. • The liquid in the system is easily mobilized at all levels of the structural motion, thereby eliminating the activation mechanism required in the conventional TMD system where a certain level of threshold excitation must be set. • Water contained in the tube can be utilized as a secondary water source for an emergency such as fire. • It provides configuration and space flexibilities as one can design one large tube or a group of smaller tubes. By optimally adjusting the head loss coefficient, the semi-active TLCD system can achieve a significant improvement over passive TLCD system (Kim and Adeli 2005). However, performance of either semi-active or passive TLCD system is bounded by mass and tuning ratios of liquid tube. Even though a TLCD system with a larger mass ratio may yield more effective response reductions, the larger mass ratio may increase the stiffness requirement of the primary structure in order to support the larger mass at the top. This may result in an uneconomical design. Also, values of the mass and tuning ratios are limited by the space and length available for the TLCD system. A hybrid control system has been developed through judicious combination of a passive supplementary damping system with a semi-active TLCD system. The semi-active TLCD system is integrated with viscous fluid passive damper devices in order to overcome the shortcomings of the semi-active TLCD system and enhance its reliability and vibration reduction capability. Viscous fluid dampers are used because they do not introduce any additional stiffness and can provide any desired damping force. Moreover, a passive damper system is inherently reliable because it does not depend on an external electric power source. The entire hybrid TLCD-damper control system can operate on very small power, e.g. a battery, without having to rely on a large external electric power. This elimination of the need for a large power requirement makes the proposed hybrid control system more reliable than other hybrid control systems where active and passive systems are combined. The new model utilizes the advantages of both passive and semi-active control systems, thereby improving the overall performance, reliability, operability of the control system during normal operations as well as a power or computer failure. The novel wavelethybrid feedback LMS control algorithm is employed for solution of the resulting control problem. The effectiveness and robustness of the hybrid damper-TLCD system in reducing the vibrations under various seismic excitations are evaluated through numerical simulations performed for an 8-story frame using three different simulated earthquake ground accelerations. It is shown that the new hybrid control model is effective in significantly reducing the response of structures under various seismic excitations. The hybrid control system provides increased reliability and maximum operability during normal operations as well as a power or computer failure. The proposed system eliminates the need for a large power requirement, unlike other proposed hybrid control systems where active and passive systems are combined.