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The aim of this book is to provide a systematic and rigorous access to the main topics of linear state-space system theory in both the continuous-time case and the discrete-time case; and the I/O description of linear systems. The main thrusts of the work are the analysis of system descriptions and derivations of their properties, LQ-optimal control, state feedback and state estimation, and MIMO unity-feedback systems.
The development of a controller performance evaluation (CPE) methodology for multiinput/multioutput digital control systems is described. The equations used to obtain the open-loop plant, controller transfer matrices, and return-difference matrices are given. Results of applying the CPE methodology to evaluate MIMO digital flutter suppression systems being tested on an active flexible wing wind-tunnel model are presented to demonstrate the CPE capability.
A discrete-time adaptive control law for stabilization, command following, and disturbance rejection that is effective for systems that are unstable, MIMO, and/or nonminimum phase. The adaptive control algorithm includes guidelines concerning the modeling information needed for implementation. This information includes the relative degree, the first nonzero Markov parameter, and the nonminimum-phase zeros. Except when the plant has nonminimum-phase zeros whose absolute value is less than the plant's spectral radius, the required zero information can be approximated by a sufficient number of Markov parameters. No additional information about the poles or zeros need be known. Numerical examples are presented to illustrate the algorithm's effectiveness in handling systems with errors in the required modeling data, unknown latency, sensor noise, and saturation.
Today’s Massive MIMO cellular operation is dominated by orthogonal frequency division multiplexing (OFDM) modulation. One of the advantages of OFDM is the flexibility to carve up the available spectrum into resource blocks (RBs) that can operate adjacent to one another. Massive MIMO adds spatial multiplexing layers on top of the RBs, enabling the simultaneous operation of dozens of UEs. Cyclic prefixed single carrier modulation (CP-SCM) is an alternative to OFDM that also benefits from massive MIMO and is useful as an OFDM alternative in specific scenarios. However, until recently, no resource allocation method has been proposed for CP-SCM. In this paper, we present a CP-SCM resource allocation scheme using virtual antennas in a massive MIMO time domain duplexed scenario. By creating several virtual antennas for each physical antenna, the benefits of massive MIMO are achieved with a smaller physical antenna count. Resources are quantized into data streams, and each user can be assigned a variable number of simultaneous streams. This paper presents a detailed development and analysis of multi-stream processing (MSP) for both uplink detection and downlink precoding. We also introduce heterogeneous MSP, where CP-SCM and OFDM signals can be processed in the same MSP framework.
In low earth orbit (LEO) satellite applications spacecraft power is provided by photovoltaic cells and batteries. To overcome battery shortcomings the University of Maryland, working in cooperation with NASA/GSFC and NASA/LeRC, has developed a magnetically suspended flywheel for energy storage applications. The system is referred to as an Open Core Composite Flywheel (OCCF) energy storage system. Successful application of flywheel energy storage requires integration of several technologies, viz. bearings, rotor design, motor/generator, power conditioning, and system control. In this paper we present a parameter design method which has been developed for analyzing the linear SISO model of the magnetic bearing controller for the OCCF. The objective of this continued research is to principally analyze the magnetic bearing system for nonlinear effects in order to increase the region of stability, as determined by high speed and large air gap control. This is achieved by four tasks: (1) physical modeling, design, prototyping, and testing of an improved magnetically suspended flywheel energy storage system, (2) identification of problems that limit performance and their corresponding solutions, (3) development of a design methodology for magnetic bearings, and (4) design of an optimal controller for future high speed applications. Both nonlinear SISO and MIMO models of the magnetic system were built to study limit cycle oscillations and power amplifier saturation phenomenon observed in experiments. The nonlinear models include the inductance of EM coils, the power amplifier saturation, and the physical limitation of the flywheel movement as discussed earlier. The control program EASY5 is used to study the nonlinear SISO and MIMO models. Our results have shown that the characteristics and frequency responses of the magnetic bearing system obtained from modeling are comparable to those obtained experimentally. Although magnetic saturation is shown in the bearings, there are good correlations between the theoretical model and experimental data. Both simulation and experiment confirm large variations of the magnetic bearing characteristics due to air gap growth. Therefore, the gap growth effect should be considered in the magnetic bearing system design. Additionally, the magnetic bearing control system will be compared to other design methods using not only parameter design but H-infinity optimal control and mu synthesis.
Described here is the development and implementation of on-line, near real time controller performance evaluation (CPE) methods capability. Briefly discussed are the structure of data flow, the signal processing methods used to process the data, and the software developed to generate the transfer functions. This methodology is generic in nature and can be used in any type of multi-input/multi-output (MIMO) digital controller application, including digital flight control systems, digitally controlled spacecraft structures, and actively controlled wind tunnel models. Results of applying the CPE methodology to evaluate (in near real time) MIMO digital flutter suppression systems being tested on the Rockwell Active Flexible Wing (AFW) wind tunnel model are presented to demonstrate the CPE capability.
This invention is a ground flutter testing system without a wind tunnel, called Dry Wind Tunnel (DWT) System. The DWT system consists of a Ground Vibration Test (GVT) hardware system, a multiple input multiple output (MIMO) force controller software, and a real-time unsteady aerodynamic force generation software, that is developed from an aerodynamic reduced order model (ROM). The ground flutter test using the DWT System operates on a real structural model, therefore no scaled-down structural model, which is required by the conventional wind tunnel flutter test, is involved. Furthermore, the impact of the structural nonlinearities on the aeroelastic stability can be included automatically. Moreover, the aeroservoelastic characteristics of the aircraft can be easily measured by simply including the flight control system in-the-loop. In addition, the unsteady aerodynamics generated computationally is interference-free from the wind tunnel walls. Finally, the DWT System can be conveniently and inexpensively carried out as a post GVT test with the same hardware, only with some possible rearrangement of the shakers and the inclusion of additional sensors.
FSO (Free-Space Optical)-based communication systems experience difficulty with receiving and separating signals arising from multiple transmitters, a capability that would facilitate implementation of MIMO (Multiple-In, Multiple-Out) systems. Current implementations require multiple, distinct optical antennas, each tracking a single user, which proves bulky and costly, especially if the transmitters are moving and must be tracked. A fiber-bundle receiver has the potential to use multiple pathways, corresponding to the individual fibers within the receiver, to capture different combinations of the incoming optical signals. If the bundle provides linear combining of the optical signals from both the individual fibers in the bundle and amongst the incoming optical signals, signal processing could extract the individual signals from the combinations. In this paper, we experimentally investigate whether the fiber-bundle receiver possesses sufficient linearity of operation to allow the separation of two signals by simple processing algorithms, for both turbulent and non-turbulent conditions. Data from two distinct sources enters a single-bundle, single field of view receiver, and a basis signal from one transmitter provides the reference for performing simple subtraction-based extraction of the unknown signal from the other transmitter. The experimental results show that the receiver does operate linearly, and that the linear operation remains sufficiently intact in the presence of turbulence to extract a recognizable copy of one signal from the other. The ability of the fiber bundle receiver to mitigate turbulence effects appears to assist in maintaining this sufficient level of linearity.
A MIMO linear time-invariant feedback system 1S(P,C) is considered which is assumed to be U-stable. The plant P is subjected to an additive perturbation Delta P which is proper but not necessarily stable. It is proved that the perturbed system is U-stable if and only if Delta P(I + Q x Delta P) exp -1 is U-stable.
The coordinate-free module-theoretic treatment of transmission zeros for MIMO transfer functions developed by Wyman and Sain (1981) is generalized to include noncontrollable and nonobservable linear dynamical systems. Rational, finitely-generated-modular, and torsion-divisible interpretations of the Rosenbrock system matrix are presented; Gamma-zero and Omega-zero modules are defined and shown to contain the output-decoupling and input-decoupling zero modules, respectively, as submodules; and the cases of left and right invertible transfer functions are considered.
The need to return high mass payloads is driving the development of a new class of vehicles, Deployable Entry Vehicles (DEV) for which feasible and optimized control architectures have not been developed. The Pterodactyl project, seeks to advance the current state-of-the-art for entry vehicles by developing a design, test, and build capability for DEVs that can be applied to various entry vehicle configurations. This paper details the efforts on the NASA-funded Pterodactyl project to investigate multiple control techniques for the Lifting Nano-ADEPT (LNA) DEV. We design and implement multiple control architectures on the LNA and evaluate their performance in achieving varying guidance commands during entry.First we present an overview of DEVs and the Lifting Nano-ADEPT (LNA), along with the physical LNA configuration that influences the different control designs. Existing state-of-the-art for entry vehicle control is primarily propulsive as reaction control systems (RCS) are widely employed. In this work, we analyze the feasibility of using both propulsive control systems such as RCS to generate moments, and non-propulsive control systems such as aerodynamic control surfaces and internal moving mass actuations to shift the LNA center of gravity and generate moments. For these diverse control systems, we design different multi-input multi-output (MIMO) state-feedback integral controllers based on linear quadratic regulator (LQR) optimal control methods. The control variables calculated by the controllers vary, depending on the control system being utilized and the outputs to track for the controller are either the (i) bank angle or the (ii) angle of attack and sideslip angle as determined by the desired guidance trajectory. The LQR control design technique allows the relative allocation of the control variables through the choice of the weighting matrices in the cost index. Thus, it is easy to (i) specify which and how much of a control variable to use, and (ii) utilize one control design for different control architectures by simply modifying the choice of the weighting matrices.By providing a comparative analysis of multiple control systems, configurations, and performance, this paper and the Pterodactyl project as a whole will help entry vehicle system designers and control systems engineers determine suitable control architectures for integration with DEVs and other entry vehicle types.
Modeling of power distribution system components that are valid for a wide range of frequencies are crucial for highly accurate modeling of electromagnetic transient (EMT) events. This has recently become of interest due to the improvements needed for the resilient operation of distribution systems. Vector fitting (VF) is a very popular and commonly used algorithm for wide band representations of power system components in EMT simulations. In this research, we present a new multi-input rational approximation algorithm (MIAAA) and illustrate its advantages with respect to VF using examples of approximations of admittance matrices discussed in the literature. We show that MIAAA not only outperforms VF in terms of achieving better accuracy using lesser number of poles, but also has no numerical issues achieving convergence. In contrast to VF, MIAAA is not sensitive to the location of input sample points and it does not require good estimates for the location of the desired approximation poles. The novelty of this research work is the use of recent mathematical results to solve existing challenges in distribution system modeling and to develop rational approximations for power system models that intend to be optimal in terms of accuracy and performance.
A method to provide active noise control to reduce noise and vibration in reverberant acoustic enclosures such as aircraft, vehicles, appliances, instruments, industrial equipment and the like is presented. A continuous-time multi-input multi-output (MIMO) state space mathematical model of the plant is obtained via analytical modeling and system identification. Compensation is designed to render the mathematical model passive in the sense of mathematical system theory. The compensated system is checked to ensure robustness of the passive property of the plant. The check ensures that the passivity is preserved if the mathematical model parameters are perturbed from nominal values. A passivity-based controller is designed and verified using numerical simulations and then tested. The controller is designed so that the resulting closed-loop response shows the desired noise reduction.
The Vibration Admittance Test (VET) was performed to measure the emitted disturbances of the Near Infrared Camera and Multi-Object Spectrometer (NICMOS) Cryogenic Cooler (NCC) in preparation for NCC installation onboard the Hubble Space Telescope (HST) during Servicing Mission 3B (SM3B). Details of the VET ground-test are described, including facility characteristics, sensor complement and configuration, NCC suspension, and background noise measurements. Kinematic equations used to compute NCC mass center displacements and accelerations from raw measurements are presented, and dynamic equations of motion for the NCC VET system are developed and verified using modal test data. A MIMO linear frequency-domain analysis method is used to compute NCC-induced loads and HST boresight jitter from VET measurements. These results are verified by a nonlinear time-domain analysis approach using a high-fidelity structural dynamics and pointing control simulation for HST. NCC emitted acceleration levels not exceeding 35 micro-g rms were measured in the VET and analysis methods herein predict 3.1 milli-areseconds rms jitter for HST on-orbit. Because the NCC is predicted to become the predominant disturbance source for HST, VET results indicate that HST will continue to meet the 7 milli-arcsecond pointing stability mission requirement in the post-SM3B era.
A method for adaptive identification of reduced-order models for continuous stable SISO and MIMO plants is presented. The method recursively finds a model whose transfer function (matrix) matches that of the plant on a set of frequencies chosen by the designer. The algorithm utilizes the Moving Discrete Fourier Transform (MDFT) to continuously monitor the frequency-domain profile of the system input and output signals. The MDFT is an efficient method of monitoring discrete points in the frequency domain of an evolving function of time. The model parameters are estimated from MDFT data using standard recursive parameter estimation techniques. The algorithm has been shown in simulations to be quite robust to additive noise in the inputs and outputs. A significant advantage of the method is that it enables a type of on-line model validation. This is accomplished by simultaneously identifying a number of models and comparing each with the plant in the frequency domain. Simulations of the method applied to an 8th-order SISO plant and a 10-state 2-input 2-output plant are presented. An example of on-line model validation applied to the SISO plant is also presented.
The computational requirements for obtaining the results summarized in the preceding section were very modest and were easily accomplished using computer-aided control system design software. Of special significance is the ability of the PDT to indicate a loop closure sequence for MIMO QFT designs that employ sequential loop closure. Although discussed as part of a 2 x 2 design, the PDT is obviously applicable to designs with a greater number of inputs and system responses.
Summary: Sensor selection approach for MIMO testing was defined and demonstrated on a model of a practical system. Laboratory response obtained using the approach matched the field response well. Information about how many control sensors, and where to locate sensors can be gleaned from the approach.
The output variance constraint controller design procedure is integrated with model reduction by modal cost analysis. A procedure is given for tuning MIMO controller designs to find the maximal rms performance of the actual system. Controller designs based on a finite-element model of the system are compared with controller designs based on an identified model (obtained using the Q-Markov Cover algorithm). The identified model and the finite-element model led to similar closed-loop performance, when tested in the Mini-Mast facility at NASA Langley.