The well known frequency-domain observability range space extraction (FORSE) algorithm provides a powerful multivariable system-identification tool with inherent flexibility, to create state-space models from frequency-response data (FRD). This paper presents a method of using FORSE to create “context models” of a lightly damped system, from which models of individual resonant modes can be extracted. Further, it shows how to combine the extracted models of many individual modes into one large state-space model. Using this method, the author has created very high-order state-space models that accurately match measured FRD over very broad bandwidths, i.e., resonant peaks spread across five orders-of-magnitude of frequency bandwidth.
KEYWORDS: Systems modeling, Data modeling, Actuators, System identification, Device simulation, Structural design, Sensors, Matrices, Process modeling, Control systems
This paper describes a multivariable controller design procedure that uses mixed-sensitivity H-infinity control theory. The design procedure is based on the assumption that structural noise can be modeled as entering a state-space system through a random input matrix. The design process starts with a full-order flexible state-space model that undergoes a frequency-weighted balanced truncation to obtain a reduced-order model with excellent low frequency matching.
Weighting functions are then created to specify the desired frequency range for disturbance rejection and controller bandwidth. A structural noise input matrix is also designed to identify system modes where maximal damping is desired. An augmented plant is then assembled using the reduced-order model, weighting functions and structural noise input matrix to create a mixed-sensitivity configuration. A state-space controller is then realized using an H-infinity design algorithm.
A two-input, three-output, doubly cantilevered beam system provides a design example. A 174th-order, discrete-time, state-space model of the cantilevered beam system was used to generate a reduced 40th- order model. A 55th-order Hinfinity controller was then designed with a controller bandwidth of approximately 300 Hz. This non-square modern
controller uses feedback signals from two piezoelectric sensors, each collocated with one of two piezoelectric actuators, and one highly non-collocated accelerometer. The two piezoelectric actuators provide the control actuation. Frequency analysis and time-domain simulations are utilized to demonstrate the damping performance.
We present a multivariable controller architecture that is a hybrid combination of a classically designed controller and an observer-based controller. The design process starts with a classical multivariable feedback controller, designed by any convenient method, such as sequential SISO loop closing. After designing the classical controller, an observer-based modern controller is designed to be stable in parallel combination with the classical controller. The hybrid configuration is realized by introducing an additional feedback path between the two feedback controllers, to subtract the effects of the classical controller from the observer-state estimate. All of the controller gains are re-tuned to improve a variety of performance measures. The additional feedback path does not increase the number of states in the controller but allows significantly higher gains to be used in the observer-based controller, resulting in better isolation from input disturbances. A six-input, nine-output lightweight space structure (LSS) provides a working example. The classical controller was implemented as six 40th-order SISO feedback controllers, at a sample rate of 20 kHz, closed in parallel around the six main mount struts, achieving very good isolation across the struts. A 240th-order observer-based modern controller, also at a 20 kHz sample rate, was designed to work with the classical closed loops and has been implemented in the hybrid configuration described. This non-square modern controller uses feedback signals from three non-collocated sensors, in addition to the six used by the classical SISO controllers, and improves isolation by about 5 dB in the most critical regions of the controller bandwidth.
KEYWORDS: Sensors, Actuators, Semiconducting wafers, Mathematical modeling, 3D modeling, Systems modeling, Data modeling, Performance modeling, Control systems, Mathematics
Presented below is a summary of the results obtained to date on the verification of a novel state space model identification technique called PLID (pseudo linear identification), given in Hopkins et al. This technique has several unique features that include: (1) optimal joint parameter and state estimation (that gives rise to its nonlinearities); (2) provisions for sensor, actuator, and state noise; (3) and it converges almost surely to the true plant parameters provided that the plant is linear, completely controllable/observable, strictly proper, time invariant, and all noise sources are zero mean white Gaussian (ZMWG). Experiments carried out on a flexible, modally dense 3-D truss structure standing 4 feet tall have shown PLID to be a robust technique capable of managing significant deviations from the assumptions made to prove strict optimality. Using the 3 actuators and 3 sensors attached to the structure, models varying in size from 24 to 64 states have been used to approximate this infinite dimensional testbed in the frequency range between 50 to 500 Hz. Sensor signals with rms levels of approximately 2 volts have been predicted by PLID to within 0.01 volts rms.
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