Mathematical models of physical systems aid in understanding and predicting their behavior. They also allow control system development and design improvements. Simulation is an important tool in most of CSA's work, from finite element modeling and magnetic circuit design to adaptive optics modeling and digital filter response prediction. Modeling and simulation can be applied at the device level to produce a mathematical description of linear or nonlinear response. Simulation can also be applied to a complete system, and that capability in particular is one of CSA's strengths. CSA's experience in control design covers a variety of methods, including several different feedback and feedforward algorithms.

Feedback Control

CSA's background in control systems begins with feedback control. We often consider our passive vibration suppression solutions in the feedback context. With the aid of sophisticated design tools and the use of fast DSP controllers, we create and implement feedback controllers for a variety of physical systems. Both classical and modern methods, and single input single output and multiple input multiple output architectures are employed. Algorithms include servo designs for process and motion control, and specialized designs for vibration isolation and suppression. In a typical project, frequency and time responses of the closed loop systems are modeled and compared with measured data.

Feedforward Control

Over the last several years, CSA has developed capabilities in feedforward control. The algorithms that originated in the signal processing world are often well suited to control of acoustic noise and other physical phenomena. CSA applies these algorithms to adaptive control systems, taking advantage of the processing power of digital signal processors (DSPs). We have used feedforward methods to create semi-autonomous and autonomous control for narrowband and broadband disturbances.

Dynamic Systems

CSA has always been concerned with the dynamic behavior of high technology structures and systems; our core capabilities were developed in the area of structural dynamics. Combining knowledge of fundamental physics with advanced modeling tools, we model structural dynamic response and other physical responses to generate predictable, reliable engineering solutions to difficult problems. Models are developed from physical principles or from measured data. These same models are exercised in control system development. Matlab is an important software tool in nearly all the ongoing modeling efforts at CSA.

Integrated Models

One of CSA's strengths is the ability to develop and integrate models of a variety of physical phenomena. Beginning with structures and controls, and vibration and acoustics, CSA has increased its capabilities over time to include coupled electromechanical systems and combined models of control systems that include precision optics. Electromechanical models are used to predict and optimize combined performance of actuators and amplifiers, or sensors and conditioners.

Matlab Tools

Matlab, a product of The MathWorks, continues to be one of CSA's most valuable tools. CSA personnel have been using Matlab for over a decade to analyze data, model physical systems, and design and evaluate controllers. We have developed custom Matlab code to export information to various DSP systems for rapid development of real-time code. More recently, we have taken advantage of new data acquisition capabilities within Matlab. For nonlinear systems, control involving saturation, and other situations, CSA employs Simulink and other Matlab-related tools.