Active control of sound and vibration has gained significant interest in recent years due to advances in digital signal processing hardware, the application of adaptive signal processing in the control of sound and vibration, and the development of new transduction devices for what have been frequently termed ''adaptive'', ''smart'', or ''intelligent'' structures. The application of adaptive control approaches, based largely upon the LMS algorithm and its derivatives, has proceeded in parallel with efforts in the controls community devoted to the design of fixed-gain, robust compensators [1]. Advantages of hybrid (adaptive feedforward and feedback) control has been discussed in recent years [2-4]; however, there has been very little effort devoted to the interpretation of the two control strategies from a common terminology base.
Within the control literature, the ''standard problem'' is frequently used as the basis for control system design and synthesis [5][6]. This standard problem essentially involves the development of a state variable model, obtained from analysis or experimental system identification, with a convenient structure. The block diagram describing the standard problem has been termed the two-input, two-output (TITO) model. A schematic diagram of this system is presented in Figure 1. As illustrated, there are two vector inputs, w(s) and u(s), and two vector outputs, z(s) and y(s). The two vector inputs are the disturbance and control respectively while the two vector outputs are the error and measurement respectively. The generalized plant, G(s), is divided into separate matrix transfer functions between each vector input and vector output. The performance path is defined between the disturbance input, w(s), and the error output, z(s), and this path essentially defines the cost function. The control path is defined between the control input, u(s), and the measured output, y(s), and is used to implement the controller, K(s). The reference path defines the relationship between the disturbance and the measured output and the secondary path defines the relationship between the control and error output.
The generalized plant shown in Figure 1 contains the dynamics of the system to be controlled as well as any additional frequency weighted filters that describe physical processes or penalties imposed by the designer. For example, in the structural acoustic control problem, measurements are obtained and control inputs are applied through the dynamic structure (beam, plate, shell, etc.); however, a model of the fluid-structure interaction must be constructed such that the controller is designed to minimize sound radiation as opposed to vibration. This fully coupled model describes the generalized plant, G(s). In general, the designer's knowledge of the application physics is conveyed in the model of the generalized plant.