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- Member of: ASU Electronic Theses and Dissertations
Description
This study focuses on state estimation of nonlinear discrete time systems with constraints. Physical processes have inherent in them, constraints on inputs, outputs, states and disturbances. These constraints can provide additional information to the estimator in estimating states from the measured output. Recursive filters such as Kalman Filters or Extended Kalman Filters are commonly used in state estimation; however, they do not allow inclusion of constraints in their formulation. On the other hand, computational complexity of full information estimation (using all measurements) grows with iteration and becomes intractable. One way of formulating the recursive state estimation problem with constraints is the Moving Horizon Estimation (MHE) approximation. Estimates of states are calculated from the solution of a constrained optimization problem of fixed size. Detailed formulation of this strategy is studied and properties of this estimation algorithm are discussed in this work. The problem with the MHE formulation is solving an optimization problem in each iteration which is computationally intensive. State estimation with constraints can be formulated as Extended Kalman Filter (EKF) with a projection applied to estimates. The states are estimated from the measurements using standard Extended Kalman Filter (EKF) algorithm and the estimated states are projected on to a constrained set. Detailed formulation of this estimation strategy is studied and the properties associated with this algorithm are discussed. Both these state estimation strategies (MHE and EKF with projection) are tested with examples from the literature. The average estimation time and the sum of square estimation error are used to compare performance of these estimators. Results of the case studies are analyzed and trade-offs are discussed.
ContributorsJoshi, Rakesh (Author) / Tsakalis, Konstantinos (Thesis advisor) / Rodriguez, Armando (Committee member) / Si, Jennie (Committee member) / Arizona State University (Publisher)
Created2013
Description
The problem of systematically designing a control system continues to remain a subject of intense research. In this thesis, a very powerful control system design environment for Linear Time-Invariant (LTI) Multiple-Input Multiple-Output (MIMO) plants is presented. The environment has been designed to address a broad set of closed loop metrics and constraints; e.g. weighted H-infinity closed loop performance subject to closed loop frequency and/or time domain constraints (e.g. peak frequency response, peak overshoot, peak controls, etc.). The general problem considered - a generalized weighted mixed-sensitivity problem subject to constraints - permits designers to directly address and tradeoff multivariable properties at distinct loop breaking points; e.g. at plant outputs and at plant inputs. As such, the environment is particularly powerful for (poorly conditioned) multivariable plants. The Youla parameterization is used to parameterize the set of all stabilizing LTI proper controllers. This is used to convexify the general problem being addressed. Several bases are used to turn the resulting infinite-dimensional problem into a finite-dimensional problem for which there exist many efficient convex optimization algorithms. A simple cutting plane algorithm is used within the environment. Academic and physical examples are presented to illustrate the utility of the environment.
ContributorsPuttannaiah, Karan (Author) / Rodriguez, Armando A (Thesis advisor) / Tsakalis, Konstantinos S (Committee member) / Si, Jennie (Committee member) / Arizona State University (Publisher)
Created2013
Description
Increasing interest in individualized treatment strategies for prevention and treatment of health disorders has created a new application domain for dynamic modeling and control. Standard population-level clinical trials, while useful, are not the most suitable vehicle for understanding the dynamics of dosage changes to patient response. A secondary analysis of intensive longitudinal data from a naltrexone intervention for fibromyalgia examined in this dissertation shows the promise of system identification and control. This includes datacentric identification methods such as Model-on-Demand, which are attractive techniques for estimating nonlinear dynamical systems from noisy data. These methods rely on generating a local function approximation using a database of regressors at the current operating point, with this process repeated at every new operating condition. This dissertation examines generating input signals for data-centric system identification by developing a novel framework of geometric distribution of regressors and time-indexed output points, in the finite dimensional space, to generate sufficient support for the estimator. The input signals are generated while imposing “patient-friendly” constraints on the design as a means to operationalize single-subject clinical trials. These optimization-based problem formulations are examined for linear time-invariant systems and block-structured Hammerstein systems, and the results are contrasted with alternative designs based on Weyl's criterion. Numerical solution to the resulting nonconvex optimization problems is proposed through semidefinite programming approaches for polynomial optimization and nonlinear programming methods. It is shown that useful bounds on the objective function can be calculated through relaxation procedures, and that the data-centric formulations are amenable to sparse polynomial optimization. In addition, input design formulations are formulated for achieving a desired output and specified input spectrum. Numerical examples illustrate the benefits of the input signal design formulations including an example of a hypothetical clinical trial using the drug gabapentin. In the final part of the dissertation, the mixed logical dynamical framework for hybrid model predictive control is extended to incorporate a switching time strategy, where decisions are made at some integer multiple of the sample time, and manipulation of only one input at a given sample time among multiple inputs. These are considerations important for clinical use of the algorithm.
ContributorsDeśapāṇḍe, Sunīla (Author) / Rivera, Daniel E. (Thesis advisor) / Peet, Matthew M. (Committee member) / Si, Jennie (Committee member) / Tsakalis, Konstantinos S. (Committee member) / Arizona State University (Publisher)
Created2014
Description
There is increasing interest in the medical and behavioral health communities towards developing effective strategies for the treatment of chronic diseases. Among these lie adaptive interventions, which consider adjusting treatment dosages over time based on participant response. Control engineering offers a broad-based solution framework for optimizing the effectiveness of such interventions. In this thesis, an approach is proposed to develop dynamical models and subsequently, hybrid model predictive control schemes for assigning optimal dosages of naltrexone, an opioid antagonist, as treatment for a chronic pain condition known as fibromyalgia. System identification techniques are employed to model the dynamics from the daily diary reports completed by participants of a blind naltrexone intervention trial. These self-reports include assessments of outcomes of interest (e.g., general pain symptoms, sleep quality) and additional external variables (disturbances) that affect these outcomes (e.g., stress, anxiety, and mood). Using prediction-error methods, a multi-input model describing the effect of drug, placebo and other disturbances on outcomes of interest is developed. This discrete time model is approximated by a continuous second order model with zero, which was found to be adequate to capture the dynamics of this intervention. Data from 40 participants in two clinical trials were analyzed and participants were classified as responders and non-responders based on the models obtained from system identification. The dynamical models can be used by a model predictive controller for automated dosage selection of naltrexone using feedback/feedforward control actions in the presence of external disturbances. The clinical requirement for categorical (i.e., discrete-valued) drug dosage levels creates a need for hybrid model predictive control (HMPC). The controller features a multiple degree-of-freedom formulation that enables the user to adjust the speed of setpoint tracking, measured disturbance rejection and unmeasured disturbance rejection independently in the closed loop system. The nominal and robust performance of the proposed control scheme is examined via simulation using system identification models from a representative participant in the naltrexone intervention trial. The controller evaluation described in this thesis gives credibility to the promise and applicability of control engineering principles for optimizing adaptive interventions.
ContributorsDeśapāṇḍe, Sunīla (Author) / Rivera, Daniel E. (Thesis advisor) / Si, Jennie (Committee member) / Tsakalis, Konstantinos (Committee member) / Arizona State University (Publisher)
Created2011
Description
This thesis presents a multi-modal motion tracking system for stroke patient rehabilitation. This system deploys two sensor modules: marker-based motion capture system and inertial measurement unit (IMU). The integrated system provides real-time measurement of the right arm and trunk movement, even in the presence of marker occlusion. The information from the two sensors is fused through quaternion-based recursive filters to promise robust detection of torso compensation (undesired body motion). Since this algorithm allows flexible sensor configurations, it presents a framework for fusing the IMU data and vision data that can adapt to various sensor selection scenarios. The proposed system consequently has the potential to improve both the robustness and flexibility of the sensing process. Through comparison between the complementary filter, the extended Kalman filter (EKF), the unscented Kalman filter (UKF) and the particle filter (PF), the experimental part evaluated the performance of the quaternion-based complementary filter for 10 sensor combination scenarios. Experimental results demonstrate the favorable performance of the proposed system in case of occlusion. Such investigation also provides valuable information for filtering algorithm and strategy selection in specific sensor applications.
ContributorsLiu, Yangzi (Author) / Qian, Gang (Thesis advisor) / Olson, Loren (Committee member) / Si, Jennie (Committee member) / Arizona State University (Publisher)
Created2010
Description
This dissertation examines modeling, design and control challenges associatedwith two classes of power converters: a direct current-direct current (DC-DC) step-down (buck)
regulator and a 3-phase (3-ϕ) 4-wire direct current-alternating current
(DC-AC) inverter. These are widely used for power transfer in a variety of industrial
and personal applications. This motivates the precise quantification of conditions
under which existing modeling and design methods yield satisfactory designs, and
the study of alternatives when they don’t. This dissertation describes a method
utilizing Fourier components of the input square wave and the inductor-capacitor (LC)
filter transfer function, which doesn’t require the small ripple approximation. Then,
trade-offs associated with the choice of the filter order are analyzed for integrated buck
converters with a constraint on their chip area. Design specifications which would
justify using a fourth or sixth order filter instead of the widely used second order
one are examined. Next, sampled-data (SD) control of a buck converter is analyzed.
Three methods for the digital controller design are studied: analog design followed
by discretization, direct digital design of a discretized plant, and a “lifting” based
method wherein the sampling time is incorporated in the design process by lifting
the continuous-time design plant before doing the controller design. Specifically,
controller performance is quantified by studying the induced-L2 norm of the closed
loop system for a range of switching/sampling frequencies. In the final segment of
this dissertation, the inner-outer control loop, employed in inverters with an
inductor-capacitor-inductor (LCL) output filter, is studied. Closed loop sensitivities for the
loop broken at the error and the control are examined, demonstrating that traditional
methods only address these properties for one loop-breaking point. New controllers
are then provided for improving both sets of properties.
ContributorsSarkar, Aratrik (Author) / Rodriguez, Armando A (Thesis advisor) / Si, Jennie (Committee member) / Mittelmann, Hans D (Committee member) / Tsakalis, Konstantinos (Committee member) / Arizona State University (Publisher)
Created2021
Description
The Inverted Pendulum on a Cart is a classical control theory problem that helps understand the importance of feedback control systems for a coupled plant. In this study, a custom built pendulum system is coupled with a linearly actuated cart and a control system is designed to show the stability of the pendulum. The three major objectives of this control system are to swing up the pendulum, balance the pendulum in the inverted position (i.e. $180^\circ$), and maintain the position of the cart. The input to this system is the translational force applied to the cart using the rotation of the tires. The main objective of this thesis is to design a control system that will help in balancing the pendulum while maintaining the position of the cart and implement it in a robot. The pendulum is made free rotating with the help of ball bearings and the angle of the pendulum is measured using an Inertial Measurement Unit (IMU) sensor. The cart is actuated by two Direct Current (DC) motors and the position of the cart is measured using encoders that generate pulse signals based on the wheel rotation. The control is implemented in a cascade format where an inner loop controller is used to stabilize and balance the pendulum in the inverted position and an outer loop controller is used to control the position of the cart. Both the inner loop and outer loop controllers follow the Proportional-Integral-Derivative (PID) control scheme with some modifications for the inner loop. The system is first mathematically modeled using the Newton-Euler first principles method and based on this model, a controller is designed for specific closed-loop parameters. All of this is implemented on hardware with the help of an Arduino Due microcontroller which serves as the main processing unit for the system.
ContributorsNamasivayam, Vignesh (Author) / Tsakalis, Konstantinos (Thesis advisor) / Rodriguez, Armando (Committee member) / Si, Jennie (Committee member) / Shafique, Md. Ashfaque Bin (Committee member) / Arizona State University (Publisher)
Created2021