Property:Abstract
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N
Nonlinear Control of Rotating Stall and Surge with Axisymmetric Bleed and Air Injection on Axial Flow Compressors +
The study of compressor instabilities in gas turbine engines has received
much attention in recent years. In particular, rotating stall and surge
are major causes of problems ranging from component stress and lifespan
reduction to engine explosion. In this thesis, modeling and control of
rotating stall and surge using bleed valve and air injection is studied and
validated on a low speed, single stage, axial compressor at Caltech.
<p>
Bleed valve control of stall is achieved only when the compressor
characteristic is actuated, due to the fast growth rate of the stall cell
compared to the rate limit of the valve. Furthermore, experimental results
show that the actuator rate requirement for stall control is reduced by a
factor of fourteen via compressor characteristic actuation. Analytical
expressions based on low order models (2--3 states) and a high fidelity
simulation (37 states) tool are developed to estimate the minimum rate
requirement of a bleed valve for control of stall. A comparison of the
tools to experiments show a good qualitative agreement, with increasing
quantitative accuracy as the complexity of the underlying model increases.
<p>
Air injection control of stall and surge is also investigated.
Simultaneous control of stall and surge is achieved using axisymmetric air
injection. Three cases with different injector back pressure are studied.
Surge control via binary air injection is achieved in all three cases.
Simultaneous stall and surge control is achieved for two of the cases, but
is not achieved for the lowest authority case. This is consistent with
previous results for control of stall with axisymmetric air injection
without a plenum attached.
<p>
Non--axisymmetric air injection control of stall and surge is also studied.
Three existing control algorithms found in literature are modeled and
analyzed. A three--state model is obtained for each algorithm. For two
cases, conditions for linear stability and bifurcation criticality on
control of rotating stall are derived and expressed in terms of
implementation--oriented variables such as number of injectors. For the
third case, bifurcation criticality conditions are not obtained due to
complexity, though linear stability property is derived. A theoretical
comparison between the three algorithms is made, via the use of low--order
models, to investigate pros and cons of the algorithms in the context of
operability.
<p>
The effects of static distortion on the compressor facility at Caltech is
characterized experimentally. Results consistent with literature are
obtained. Simulations via a high fidelity model (34 states) are also
performed and show good qualitative as well as quantitative agreement to
experiments. A non--axisymmetric pulsed air injection controller for stall
is shown to be robust to static distortion.
T
The synthesis of controllers guaranteeing linear temporal logic specifications on partially observable Markov decision processes (POMDP) via their belief models causes computational issues due to the continuous spaces. In this work, we construct a finite-state abstraction on which a control policy is synthesized and refined back to the original belief model. We introduce a new notion of label- based approximate stochastic simulation to quantify the deviation between belief models. We develop a robust synthesis methodology that yields a lower bound on the satisfaction probability, by compensating for deviations a priori, and that utilizes a less conservative control refinement. +
R
Real-time trajectory generation for constrained nonlinear dynamical systems using non-uniform rational B-spline basis functions +
The thesis describes a new method for obtaining minimizers for optimal control problems whose minima serve as control policies for guiding nonlinear dynamical systems to achieve prescribed goals under imposed trajectory and actuator constraints. One of the major contributions of the present work resides in the approximation of such minimizers by piecewise polynomial functions expressed in terms of a linear combination of non-uniform rational B-spline (NURBS) basis functions and the judicious exploitation of the properties of the resulting NURBS curves to improve the computational effort often associated with solving optimal control problems for constrained dynamical systems. In particular, by exploiting the two structures combined in a NURBS curve, NURBS basis functions and an associated union of overlapping polytopes constructed from the coefficients of the linear combination, we are able to separate an optimal control problem into two subproblems +
C
There is a growing interest in building autonomous systems that interact with complex environments. The difficulty associated with obtaining an accurate model for such environments poses a challenge to the task of assessing and guaranteeing the system’s performance. We present a data-driven solution that allows for a system to be evaluated for specification conformance without an accurate model of the environment. Our approach involves learning a conservative reactive bound of the environment’s behavior using data and specification of the system’s desired behavior. First, the approach begins by learning a conservative reactive bound on the environment’s actions that captures its possible behaviors with high probability. This bound is then used to assist verification, and if the verification fails under this bound, the algorithm returns counter-examples to show how failure occurs and then uses these to refine the bound. We demonstrate the applicability of the approach through two case-studies: i) verifying controllers for a toy multi-robot system, and ii) verifying an instance of human-robot interaction during a lane-change maneuver given real-world human driving data. +
M
Thin film deposition is a manufacturing process in which tolerances may approach
the size of individual atoms. The final film is highly sensitive to the processing
conditions, which can be intentionally manipulated to control film properties. A
lattice model of surface evolution during thin film growth captures many important
features, including the nucleation and growth of clusters of atoms and the
propagation of atomic-height steps. The dimension of this probabilistic master
equation is too large to directly simulate for any physically realistic domain, and
instead stochastic realizations of the lattice model are obtained with kinetic Monte
Carlo simulations.
<p>
In this thesis simpler representations of the master equation are developed for
use in analysis and control. The static map between macroscopic process conditions
and microscopic transition rates is first analyzed. In the limit of fast periodic
process parameters, the surface responds only to the mean transition rates, and,
since the map between process parameters and transition rates is nonlinear, new
effective combinations of transition rates may be generated. These effective rates
are the convex hull of the set of instantaneous rates.
<p>
The map between transition rates and expected film properties is also studied.
The dimension of a master equation can be reduced by eliminating or grouping
configurations, yielding a reduced-order master equation that approximates the
original one. A linear method for identifying the coefficients in a master equation
is then developed, using only simulation data. These concepts are extended to
generate low-order master equations that approximate the dynamic behavior seen
in large Monte Carlo simulations. The models are then used to compute optimal
time-varying process parameters.
<p>
The thesis concludes with an experimental and modeling study of germanium
film growth, using molecular beam epitaxy and reflection high-energy electron
diffraction. Growth under continuous and pulsed flux is compared in experiment,
and physical parameters for the lattice model are extracted. The pulsing accessible
in the experiment does not trigger a change in growth mode, which is consistent
with the Monte Carlo simulations. The simulations are then used to suggest other
growth strategies to produce rougher or smoother surfaces.
R
Thin film deposition encompasses a variety of physical processes,
which occur over a wide range of length and time scales. A major challenge in modeling and simulating thin film deposition is this disparity
in scales. In this study we focus on an atomic-scale lattice model of
surface processes. Kinetic Monte Carlo simulations provide stochastic
realizations of the surface evolution, which may then inform a reacting flow or heat transfer model. Unfortunately, these simulations are
extremely computationally intensive, particularly for design and optimization studies in which many cases are considered.
<p>
We develop reduced-order models of thin film growth using two techniques: balanced truncation and eigensystem realization. After identifying the underlying structure of the lattice model as a linear differential
equation, we apply the reduction techniques to obtain reduced-order
models of root-mean-square roughness and step edge density. Three
modes are needed for a very small model system, while only five modes
capture the evolution of a 200x200-site system over a range of growth
modes, from stochastic roughening to island nucleation and coalescence. +
E
Thin film deposition is an industrially-important process that is highly dependent on the process
conditions. Most films are grown under constant conditions, but a few studies show that modified
properties may be obtained with periodic inputs. However, assessing the effects of modulation
experimentally becomes impractical with increasing material complexity. Here we consider periodic
conditions in which the period is short relative to the time-scales of growth. We analyze a stochastic
model of thin film growth, computing effective transition rates associated with rapid periodic
process parameters. Combinations of effective rates may exist which are not attainable under
steady conditions, potentially enabling new film properties. An algorithm is presented to construct
the periodic input for a desired set of effective transition rates. These ideas are first illustrated
by two simple examples using kinetic Monte Carlo simulations and are then compared to existing
deposition techniques. +
M
Modeling and Control of Thin Film Morphology Using Unsteady Processing Parameters: Problem Formulation and Initial Results +
Thin film deposition is an industrially-important process to which control theory has not historically been applied. The need for control is growing as the size of integrated
circuits shrinks, requiring increasingly tighter tolerances in the manufacture of thin films. Our contributions in this study are two-fold: we formulate a model of thin film
growth as a control system and we examine the effects of fast periodic forcing.
<p>
We choose a lattice formulation of crystal growth as our physical model, which captures atomic length scale effects at a time scale compatible with film growth. We focus on the control of film morphology, or surface height profile. Although the system
dimension is high, the structure is simple: the dynamics and the output are linear in the state. We consider the process conditions as inputs, which alter the transition rate
functions. In the evolution equation, each of these nonlinear functions is multiplied by a linear vector field, yielding a system with a structure similar to a bilinear system.
<p>
The process conditions in some deposition methods are inherently unsteady, which
produces films with altered morphology. We use the model developed in this study to analyze the effects of fast periodic forcing on thin film evolution. With the method of
averaging we develop new effective transition rates which may produce film properties
unattainable with constant inputs. We show that these effective rates are the convex
hull of the set of rates associated with constant inputs. We present conditions on
the convex hull for which the finite-time and infinite-time reachability sets cannot be
expanded with fast periodic forcing. An example in which this forcing increases the
reachability set and produces more desirable morphology is also presented. +
F
This paper deals with fault-tolerant controller design for linear time-invariant (LTI) systems with multiple actuators. Given some critical subsets of the actuators, it is assumed that every combination of actuators can fail as long as the set of the remaining actuators includes one of these subsets. Motivated by electric power systems and biological systems, the goal is to design a controller so that the closed-loop system satisfies two properties: (i) stability under all permissible sets of faults and (ii) better performance after clearing every subset of the existing faults in the system. It is shown that a state-feedback controller satisfying these properties exists if and only if a linear matrix inequality (LMI) problem is feasible. This LMI condition is then transformed into an optimal-control condition, which has a useful interpretation. The results are also generalized to output-feedback and decentralized control cases. The efficacy of this work is demonstrated by designing fault-tolerant speed governors for a power system. The results developed here can be extended to more general types of faults, where each fault can possibly affect all state-space matrices of the system. +
C
This article focuses on extending, disseminating and interpreting the findings of an IEEE Control Systems Society working group looking at the role of control theory and engineering in solving some of the many current and future societal challenges. The findings are interpreted in a manner designed to give focus and direction to both future education and research work in the general control theory and engineering arena, interpreted in the broadest sense. The paper is intended to promote discussion in the community and also provide a useful starting point for colleagues wishing to re-imagine the design and delivery of control-related topics in our education systems, especially at the tertiary level and beyond. +
S
This article provides a review of control protocol synthesis techniques that incorporate methodologies from formal methods and control theory to provide correctness guarantee for different types of autonomous systems, including those with discrete and continuous state space. The correctness of the system is defined with respect to a given specification expressed as a formula in linear temporal logic to precisely describe the desired properties of the system. The formalism presented in this article admits non-determinism, allowing uncertainties in the system to be captured. A particular emphasis is on alleviating some of the difficulties, e.g., heterogeneity in the underlying dynamics and computational complexity, that naturally arise in the construction of control protocols for autonomous systems. +
R
This dissertation addresses the problem of control and kinematic
planning for constrained robot systems. An example of a system of
this type is a multifingered robot hand grasping an object. The
individual fingers act as robot manipulators and are constrained by
their contact with the object. If the contacts allow rolling between
the object and the fingertips, it is possible for the constraints to
be nonholonomic. That is, the constraints may not restrict the
reachable configurations of the system, but rather, constrain only the
allowable velocities of the system.
<p>
Using the multifingered hand as a motivating example, this
dissertation presents a detailed analysis of the kinematics, dynamics,
and control of robot systems with contact constraints. In particular,
it presents a unified derivation of the dynamics of robot manipulators
with Pfaffian velocity constraints, including the nonholonomic case.
This derivation allows control laws to be specified which are provably
stable for an entire class of systems, including unconstrained robots,
robot hands, and other systems of multiple robots performing a
coordinated task. A method for building complex controllers which
respects this class of constraints is also developed using a set of
simple primitives which allow hierarchical control structures to be
created in an organized fashion.
<p>
Finally, the nonholonomic motion planning problem is introduced and
discussed in detail. Using tools from differential geometric control
theory, it is possible to classify and analyze systems with
nonholonomic constraints. A brief review of the necessary tools along
with a review of the current literature is presented. A practical
method for steering nonholonomic systems using sinusoids is derived
and applied to several kinematic systems with contact constraints. +
E
This dissertation lays the foundation for practical exponential
stabilization of driftless control systems. Driftless systems have
the form $$\dot x = X_1(x)u_1+\cdots +X_m(x)u_m, \quad x\in\real^n$$.
Such systems arise when modeling mechanical systems with nonholonomic
constraints. In engineering applications it is often required to
maintain the mechanical system around a desired configuration. This
task is treated as a stabilization problem where the desired
configuration is made an asymptotically stable equilibrium point. The
control design is carried out on an approximate system. The
approximation process yields a nilpotent set of input vector fields
which, in a special coordinate system, are homogeneous with respect to
a non-standard dilation. Even though the approximation can be given a
coordinate-free interpretation, the homogeneous structure is useful to
exploit: the feedbacks are required to be homogeneous functions and
thus preserve the homogeneous structure in the closed-loop system.
The stability achieved is called {\em $\rho$-exponential stability}.
The closed-loop system is stable and the equilibrium point is
exponentially attractive. This extended notion of exponential
stability is required since the feedback, and hence the closed-loop
system, is not Lipschitz. However, it is shown that the convergence
rate of a Lipschitz closed-loop driftless system cannot be bounded by
an exponential envelope.
<p>
The synthesis methods generate feedbacks which are smooth on
\rminus. The solutions of the closed-loop system are proven to be
unique in this case. In addition, the control inputs for many
driftless systems are velocities. For this class of systems it is
more appropriate for the control law to specify actuator forces
instead of velocities. We have extended the kinematic velocity
controllers to controllers which command forces and still
$\rho$-exponentially stabilize the system.
<p>
Perhaps the ultimate justification of the methods proposed in this
thesis are the experimental results. The experiments demonstrate the
superior convergence performance of the $\rho$-exponential stabilizers
versus traditional smooth feedbacks. The experiments also highlight
the importance of transformation conditioning in the feedbacks. Other
design issues, such as scaling the measured states to eliminate
hunting, are discussed. The methods in this thesis bring the
practical control of strongly nonlinear systems one step closer.
<p>
M
This paper applies some previously studied extended
Kalman filter techniques for planar road geometry
estimation to the domain of autonomous navigation of offhighway
vehicles. In this work, a clothoid model of the road
geometry is constructed and estimated recursively based on
road features extracted from single-axis LADAR range measurements.
We present a method for feature extraction of the
road centerline in the image plane, and describe its application
to recursive estimation of the road geometry. We analyze
the performance of our method against simulated motion of
varied road geometries and against recorded data from previous
autonomous navigation runs. Our method accomodates full 6
DOF motion of the vehicle as it navigates, constructs consistent
estimates of the road geometry with respect to a fixed global
reference frame, and requires an estimate of the sensor pose
for each range measurement. +
R
This paper bridges the advances in computer science and control to allow automatic synthesis of complex dynamical systems which are guaranteed, by construction, to satisfy the desired properties even in the presence of adversary. The desired properties are expressed in the language of temporal logic. With its expressive power, a wider class of properties than safety and stability can be specified. The resulting system consists of a discrete planner which plans, in the abstracted discrete domain, a set of transitions of the system to ensure the correct behaviors and a continuous controller which continuously implements the plan. For a system with certain structure, we present an approach, based on a receding horizon scheme, to overcome computational difficulties in the synthesis of a discrete planner and allow more complex problems to be solved. +
E
Exponential Stabilization of Driftless Nonlinear Control Systems via Time-varying, Homogeneous Feedback +
This paper brings together results from a number of different areas in
control theory to provide an algorithm for the synthesis of locally
exponentially stabilizing control laws for a large class of driftless
nonlinear control systems. The exponential stabilization relies on the
use of feedbacks which render the closed loop vector field homogeneous
with respect to a dilation. These feedbacks are generated from a
modification of Pomet's algorithm for smooth feedbacks. Converse
Liapunov theorems for time-periodic homogeneous vector fields
guarantee that local exponential stability is maintained in the
presence of higher order (with respect to the dilation) perturbing
terms.
<p> +
R
This paper concerns the average consensus problem with the constraint of quantized communication between nodes. A broad class of algorithms is analyzed, in which the transmission strategy, which decides what value to communicate to the neighbors, can include various kinds of rounding, probabilistic quantization, and bounded noise. The arbitrariness of the transmission strategy is compensated by a feedback mechanism which can be interpreted as a self-inhibitory action. The result is that the average of the nodes state is not conserved across iterations, and the nodes do not converge to a consensus; however, we show that both errors can be made as small as desired. Bounds on these quantities involve the spectral properties of the graph and can be proved by employing elementary techniques of LTI systems analysis. +
D
This paper considers a group of agents that aim to reach an agreement on individually measured time-varying signals by local communication. In contrast to static network averaging problem, the consensus we mean in this paper is reached in a dynamic sense. A discrete-time dynamic average consensus protocol can be designed to allow all the agents tracking the average of their reference inputs asymptotically. We propose a minimal-time dynamic consensus algorithm, which only utilises minimal number of local observations of randomly picked node in a network to compute the final consensus signal. Our results illustrate that with memory and computational ability, the running time of distributed averaging algorithms can be indeed improved dramatically using local information as suggested by Olshevsky and Tsitsiklis. +
S
This paper considers distributed control of interconnected multi-agent systems. The dynamics of the individual agents are not required to be homogeneous and the interaction topology is described by an arbitrary directed graph. We derive the sensitivity transfer functions between every pair of agents and we analyze stability and performance of non-homogeneous systems, showing that the low frequency behavior is influenced not only by topology, but also by static gain and poles of the agents. +
O
This paper considers how a team of mobile sensors
should cooperatively move so as to optimally categorize a
single moving target from their noisy sensor readings. The
cooperative control procedure is based on the development of
a cost function that quantifies the teamâs classification error.
The robotsâ motions are then chosen to minimize this function.
We particularly investigate the case where the sensor noise and
class distributions are Gaussian. In this case, we can derive a
duality principle which states that optimal classification will be
realized when the covariance of the target estimate is minimized.
That is, in this case, optimal estimation leads naturally to
optimal classification. We extend previous work to develop a
distributed discrete-gradient search algorithm that guides the
teamâs location motions for purposes of optimal estimation and
classification. The concepts developed are validated through
numerical studies. +
