# ESA GNC Conference Papers Repository

**Title:**

##### System Identification for Control System Design and Demonstration by Flexlab

**Authors:**

**Presented at:**

**Abstract:**

In order to design high performance feedback control systems for complex systems such as large flexible, space-based structures or aero-elastic aircraft, accurate mathematical models are required. The applications of large flexible space structures include space-based telescopes, robotic systems, the space station, and any space-based platform using deployables, such as solar panels or antennae. A common problem with all of these applications is the structures are highly flexible because of their low mass and large size. As a consequence, vibration and accurate attitude control are challenging problems to solve. The National Aeronautics and Space Administration (NASA) in conjunction with the United States Air Force Research Laboratories (AFRL) and Boeing Phantom Works have recently been exploring ways to use flexible structures to their advantage at Dryden Flight Research Center in Edwards, California [1]. Active Aeroelastic Wing Flight Research was the topic of a research project that began in 1996 and was completed in 2005. The project goal was to use the aerodynamic forces acting on the control surfaces of an aircraft to bend a flexible wing to provide better roll maneuvering. Data was collected to combine control surface techniques and flexible wing structures to use in designing a more flexible, lighter weight wing for current aircraft [1]. In the Journal of Sound and Vibration, Yan-Ru Hu, and Charles Ng [2] of the Directorate of Spacecraft Engineering in the Canadian Space Agency, Saint Hubert, Quebec, Canada, wrote an article entitled Active robust vibration control of flexible structures, in which they developed an active vibration control technique with piezoelectric actuators. Their test bed was a flexible circular plate and their experiments showed that this control method suppressed structural vibrations adequately. The design of control system for complex systems as described above requires a model that accurately portrays the dynamics of the system. The most widely used control engineering analysis and design techniques require accurate linear, time-invariant (LTI) models; therefore, developing LTI models of physical systems is crucial. An accurate model provides the engineer with information regarding the response of the system in its practical operational frequency range [3]. Based on this model the engineer can make accurate predictions as to how the system will behave, as well as, produce good closed loop designs to achieve the specified dynamic performance requirements. It is essential to use models that accurately describe the relationship among system variables in terms of mathematical expressions, such as difference equations or differential equations [1]. Three approaches to developing mathematical models of dynamical systems are: (1) equations developed from the physics of the system (first principles); (2) equations developed from finite element methods; and (3) equations developed from system identification. For complex flexible structures, the first two methods often do not produce adequate models to design high performance control systems for such applications as pointing and vibration suppression. System identification is the process of extracting or inferring information about a mathematical model by numerical processing experimental data or data derived from experimentally collected data, e.g., frequency response data obtained by using time domain data that has been processed using signal processing techniques. One approach to System ID is to collect data in a laboratory environment for estimating key parameters to fine-tune models developed from dynamics and kinematics or finite element techniques. A typical scenario in this case would involve a test article that is instrumented with many sensors and then excited by tapping with a calibrated hammer at various locations while data is collected. Then the data is processed to get estimates of model frequencies, damping values, mode shapes, etc. The thrust of this paper system is system ID that is performed using the actuators and sensors that will be used to form feedback loops for proper operation after the system has been deployed. This is called System ID for Control System Design and is depicted as shown in the following figure. The implications are that the digital computer, that will be used to implement a feedback control law, is used to generate a random discrete signal as shown by the us in Figure 1. The digital sequence from the computer is converted to an analog signal that provides commands for the control system actuators (assumed to be integrated with the plant). Sensors (also assumed to be integrated with the plant) that will used to form feedback loops for control measure the effects of input excitations on the system outputs. The sensor outputs are converted to digital signals with A/Ds. The digital input and output data is processed through system ID algorithms to produce linear discrete models between the inputs to the D/As and outputs from the A/Ds. The models are difference equations, z-domain transfer functions, or discrete state space. The advantages of the system ID for control system design are as follows: (1) the dynamics of the actuators, and sensors are assumed to be part of the plant and, hence, are naturally included in the derived model; (2) by exciting the system with digital signals and collecting data at the same rate at which a digital controller will be used, the effects of D/A and A/D processes are inherently included in the model; (3) sampled-data models, needed to perform digital controller designs, are produced; (4) if need be, this type of system ID can be performed after the system has been deployed. The downside of system ID for control system design is that placement of actuators and sensors must be pre-determined. There basically are three approaches for performing system ID for control system design: (1) time domain least squares system ID; (2) frequency domain least squares system ID; and (3) time domain state space system ID. Time domain least squares system ID uses weighted least squares curve fitting to determine the coefficients of linear difference equation model(s) of a single-input, single-output (SISO) or singleinput, multiple-output (SIMO) systems, given timesamples of input and output data [3]. Frequency domain least squares system ID (also known as the transfer function determination code or TFDC) determines linear models of SISO or SIMO systems, given frequency response data [4], [5]. The Eigensystem Realization Algorithm (ERA), an extension of the Ho-Kalman realization algorithm, determines a time domain state space realization given impulse response data between each input and each output [3], [6]. ERA is useful in obtaining multiple-input, multiple-output models (MIMO) as well as SISO models, even though the data must be obtained experimentally via multiple SIMO tests.