Design of Low-Order Controllers using Optimization Techniques

In many applications, especially in the process industry, low-level controllers are the workhorses of the automated production lines. The aim of this study has been to provide simple tuning procedures, either optimization-based methods or tuning rules, for design of low-order controllers. The first part of this thesis deals with PID tuning. Design methods or both SISO and MIMO PID controllers based on convex optimization are presented. The methods consist of solving a nonconvex optimization problem by deriving convex approximations of the original problem and solving these iteratively until convergence. The algorithms are fast because of the convex approximations. The controllers obtained minimize low-frequency sensitivity subject to constraints that ensure robustness to process variations and limitations of control signal effort. The second part of this thesis deals with tuning of feedforward controllers. Tuning rules that minimize the integrated-squared-error arising from measurable step disturbances are derived for a controller that can be interpreted as a filtered and possibly time-delayed PD controller. Using a controller structure that decouples the effects of the feedforward and feedback controllers, the controller is optimal both in open and closed loop settings. To improve the high-frequency noise behavior of the feedforward controller, it is proposed that the optimal controller is augmented with a second-order filter. Several aspects on the tuning of this filter are discussed. For systems with PID controllers, the response to step changes in the reference can be improved by introducing set-point weighting. This can be interpreted as feedforward from the reference signal to the control signal. It is shown how these weights can be found by solving a convex optimization problem. Proportional set-point weight that minimizes the integrated-absolute-error was obtained for a batch of over 130 different processes. From these weights, simple tuning rules were derived and the performance was evaluated on all processes in the batch using five different feedback controller tuning methods. The proposed tuning rules could improve the performance by up to 45% with a modest increase in actuation

1992 NASA Life Support Systems Analysis workshop

The 1992 Life Support Systems Analysis Workshop was sponsored by NASA's Office of Aeronautics and Space Technology (OAST) to integrate the inputs from, disseminate information to, and foster communication among NASA, industry, and academic specialists. The workshop continued discussion and definition of key issues identified in the 1991 workshop, including: (1) modeling and experimental validation; (2) definition of systems analysis evaluation criteria; (3) integration of modeling at multiple levels; and (4) assessment of process control modeling approaches. Through both the 1991 and 1992 workshops, NASA has continued to seek input from industry and university chemical process modeling and analysis experts, and to introduce and apply new systems analysis approaches to life support systems. The workshop included technical presentations, discussions, and interactive planning, with sufficient time allocated for discussion of both technology status and technology development recommendations. Key personnel currently involved with life support technology developments from NASA, industry, and academia provided input to the status and priorities of current and future systems analysis methods and requirements

A state space approach to the design of globally optimal FIR energy compaction filters

We introduce a new approach for the least squared optimization of a weighted FIR filter of arbitrary order N under the constraint that its magnitude squared response be Nyquist(M). Although the new formulation is general enough to cover a wide variety of applications, the focus of the paper is on optimal energy compaction filters. The optimization of such filters has received considerable attention in the past due to the fact that they are the main building blocks in the design of principal component filter banks (PCFBs). The newly proposed method finds the optimum product filter Fopt(z)=Hopt(Z)Hopt (z^-1) corresponding to the compaction filter Hopt (z). By expressing F(z) in the form D(z)+D(z^-1), we show that the compaction problem can be completely parameterized in terms of the state-space realization of the causal function D(z). For a given input power spectrum, the resulting filter Fopt(z) is guaranteed to be a global optimum solution due to the convexity of the new formulation. The new algorithm is universal in the sense that it works for any M, arbitrary filter length N, and any given input power spectrum. Furthermore, additional linear constraints such as wavelets regularity constraints can be incorporated into the design problem. Finally, obtaining Hopt(z) from Fopt(z) does not require an additional spectral factorization step. The minimum-phase spectral factor Hmin(z) can be obtained automatically by relating the state space realization of Dopt(z) to that of H opt(z

A new computational approach to the synthesis of fixed order controllers

The research described in this dissertation deals with an open problem concerning the synthesis of controllers of xed order and structure. This problem is encountered in a variety of applications. Simply put, the problem may be put as the determination of the set, S of controller parameter vectors, K = (k1; k2; : : : ; kl), that render Hurwitz a family (indexed by F) of complex polynomials of the form fP0(s; ) + Pl i=1 Pi(s; )ki; 2 Fg, where the polynomials Pj(s; ); j = 0; : : : ; l are given data. They are specied by the plant to be controlled, the structure of the controller desired and the performance that the controllers are expected to achieve. Simple examples indicate that the set S can be non-convex and even be disconnected. While the determination of the non-emptiness of S is decidable and amenable to methods such as the quantier elimination scheme, such methods have not been computationally tractable and more importantly, do not provide a reasonable approximation for the set of controllers. Practical applications require the construction of a set of controllers that will enable a control engineer to check the satisfaction of performance criteria that may not be mathematically well characterized. The transient performance criteria often fall into this category. From the practical viewpoint of the construction of approximations for S, this dissertation is dierent from earlier work in the literature on this problem. A novel feature of the proposed algorithm is the exploitation of the interlacing property of Hurwitz polynomials to provide arbitrarily tight outer and inner approximation to S. The approximation is given in terms of the union of polyhedral sets which are constructed systematically using the Hermite-Biehler theorem and the generalizations of the Descartes' rule of signs

Nonlinear system identification using wavelet based SDP models

System identification has played an increasingly dominant role in a wide range of engineering applications. While linear system's theory is mature, nonlinear system identification remains an open research area in recent years. This thesis develops a new, efficient and systematic approach to the identification of nonlinear dynamic systems using wavelet based State Dependent Parameter (SDP) models, from structure determination to parameter estimation. In this approach, the system's nonlinearities are analysed and effectively represented by a SDP model structure in the form of wavelets. This provides a computationally efficient tool to open up the `black-box', offering valuable insights into the system's dynamics. In this thesis, 1-dimensional (1-D) approach is first developed based on a conventional SDP model structure which relies on a single state variable dependency. It is then extended into a multi-dimensional approach in order to solve the identification problem of systems with significant multi-variable dependence nonlinear dynamics. Here, parametrically efficient nonlinear model is obtained by the application of an effective model structure selection algorithm based on the Predicted Residual Sums of Squares (PRESS) criterion in conjunction with Orthogonal Decomposition (OD) to avoid any ill-conditioning problems associated with the parameter estimation. This thesis also investigates the aspects of noise, stability and other engineering application of the proposed approaches. More specifically, this includes: (1) nonlinear identification in the presence of noise, (2) development of bounded characteristics of the estimated models and (3) application studies where the developed approaches have been used in various engineering applications. Particularly, the modelling and forecast of daily peak power demand in the state of Victoria, Australia have been effectively studied using the proposed approaches. This strongly motivates a great deal of potential future research to be carried out in the area of power system modelling

Extremum-Seeking Guidance and Conic-Sector-Based Control of Aerospace Systems

This dissertation studies guidance and control of aerospace systems. Guidance algorithms are used to determine desired trajectories of systems, and in particular, this dissertation examines constrained extremum-seeking guidance. This type of guidance is part of a class of algorithms that drives a system to the maximum or minimum of a performance function, where the exact relation between the function's input and output is unknown. This dissertation abstracts the problem of extremum-seeking to constrained matrix manifolds. Working with a constrained matrix manifold necessitates mathematics other than the familiar tools of linear systems. The performance function is optimized on the manifold by estimating a gradient using a Kalman filter, which can be modified to accommodate a wide variety of constraints and can filter measurement noise. A gradient-based optimization technique is then used to determine the extremum of the performance function. The developed algorithms are applied to aircraft and spacecraft. Control algorithms determine which system inputs are required to drive the systems outputs to follow the trajectory given by guidance. Aerospace systems are typically nonlinear, which makes control more challenging. One approach to control nonlinear systems is linear parameter varying (LPV) control, where well-established linear control techniques are extended to nonlinear systems. Although LPV control techniques work quite well, they require an LPV model of a system. This model is often an approximation of the real nonlinear system to be controlled, and any stability and performance guarantees that are derived using the system approximation are usually void on the real system. A solution to this problem can be found using the Passivity Theorem and the Conic Sector Theorem, two input-output stability theories, to synthesize LPV controllers. These controllers guarantee closed-loop stability even in the presence of system approximation. Several control techniques are derived and implemented in simulation and experimentation, where it is shown that these new controllers are robust to plant uncertainty.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143993/1/aexwalsh_1.pd

Design and Analysis of an adaptive λ-Tracking Controller for powered Gearshifts in automatic Transmissions

To meet the continuously increasing goals in vehicle fuel efficiency, a number of measures are taken in automotive powertrain engineering, such as the combination of electric drives and conventional combustion engines in hybrid vehicles or the increase in gear ratios. This development leads to more complex powertrain systems, such as automatic transmissions. At the same time, the need for complex control systems is increased to achieve this desired functionality. Automatic transmissions are controlled by an electro-hydraulic control unit that governs all operations such as gear shifting and starting. Since most of the control software is designed in the form of open-loop control, most of the operations have to be calibrated manually. Thus, there exists a large number of calibration parameters in the control software that have to be tuned individually for each combination of engine, transmission and vehicle model. This process is therefore time-consuming and costly. Hence, it would be advantageous to reduce the need for calibration and in the end shorten the development process for automatic transmissions by reducing software complexity while maintaining functionality and performance. The goal of this thesis is to replace parts of the control software responsible for conducting the gearshifts that require extensive tuning by implementing control systems that have no need for calibration: adaptive high-gain λ-tracking controllers. In order to obtain the control parameters, i.e., the feedback gains, without calibration, an adaption law is implemented that continuously computes these parameters during operation of the controller. Thus, calibration is no longer needed. Since the system has to be high-gain-stabilizable, an extensive system analysis is conducted to determine whether an adaptive λ-tracking controller can be implemented. A nonlinear model of the clutch system dynamics is formulated and investigated. As a result, high-gain stability is proven for the system class and validated in simulation. Following the stability analysis, the devised adaptive controller is implemented into the control software running on the series production transmission control unit. Extensive simulations with a comprehensive vehicle model running the extended transmission software are conducted to design and to test the adaptive controllers and their underlying parameters during transmission operation in order to evaluate the control performance. The control software containing the adaptive controller is then implemented in two distinct vehicles with different automatic transmissions equipped with series production control hardware for the purpose of hardware experiments and validation. The resulting reduction of calibration efforts is discussed

Mission Control Center (MCC) System Specification for the Shuttle Orbital Flight Test (OFT) Timeframe

System specifications to be used by the mission control center (MCC) for the shuttle orbital flight test (OFT) time frame were described. The three support systems discussed are the communication interface system (CIS), the data computation complex (DCC), and the display and control system (DCS), all of which may interfere with, and share processing facilities with other applications processing supporting current MCC programs. The MCC shall provide centralized control of the space shuttle OFT from launch through orbital flight, entry, and landing until the Orbiter comes to a stop on the runway. This control shall include the functions of vehicle management in the area of hardware configuration (verification), flight planning, communication and instrumentation configuration management, trajectory, software and consumables, payloads management, flight safety, and verification of test conditions/environment