From Model-Based to Data-Driven Discrete-Time Iterative Learning Control

This dissertation presents a series of new results of iterative learning control (ILC) that progresses from model-based ILC algorithms to data-driven ILC algorithms. ILC is a type of trial-and-error algorithm to learn by repetitions in practice to follow a pre-defined finite-time maneuver with high tracking accuracy. Mathematically ILC constructs a contraction mapping between the tracking errors of successive iterations, and aims to converge to a tracking accuracy approaching the reproducibility level of the hardware. It produces feedforward commands based on measurements from previous iterations to eliminates tracking errors from the bandwidth limitation of these feedback controllers, transient responses, model inaccuracies, unknown repeating disturbance, etc. Generally, ILC uses an a priori model to form the contraction mapping that guarantees monotonic decay of the tracking error. However, un-modeled high frequency dynamics may destabilize the control system. The existing infinite impulse response filtering techniques to stop the learning at such frequencies, have initial condition issues that can cause an otherwise stable ILC law to become unstable. A circulant form of zero-phase filtering for finite-time trajectories is proposed here to avoid such issues. This work addresses the problem of possible lack of stability robustness when ILC uses an imperfect a prior model. Besides the computation of feedforward commands, measurements from previous iterations can also be used to update the dynamic model. In other words, as the learning progresses, an iterative data-driven model development is made. This leads to adaptive ILC methods. An indirect adaptive linear ILC method to speed up the desired maneuver is presented here. The updates of the system model are realized by embedding an observer in ILC to estimate the system Markov parameters. This method can be used to increase the productivity or to produce high tracking accuracy when the desired trajectory is too fast for feedback control to be effective. When it comes to nonlinear ILC, data is used to update a progression of models along a homotopy, i.e., the ILC method presented in this thesis uses data to repeatedly create bilinear models in a homotopy approaching the desired trajectory. The improvement here makes use of Carleman bilinearized models to capture more nonlinear dynamics, with the potential for faster convergence when compared to existing methods based on linearized models. The last work presented here finally uses model-free reinforcement learning (RL) to eliminate the need for an a priori model. It is analogous to direct adaptive control using data to directly produce the gains in the ILC law without use of a model. An off-policy RL method is first developed by extending a model-free model predictive control method and then applied in the trial domain for ILC. Adjustments of the ILC learning law and the RL recursion equation for state-value function updates allow the collection of enough data while improving the tracking accuracy without much safety concerns. This algorithm can be seen as the first step to bridge ILC and RL aiming to address nonlinear systems

Frequency domain descriptions of linear systems

This thesis begins by applying Lagrange interpolation to linear systems theory. More specifically, a stable, discrete time linear system, with transfer function G(z), is interpolated with an FIR transfer function at n equally spaced points around the unit circle. The L∞ error between the original system and the interpolation is bounded, the bound going to zero exponentially fast as n -> ∞. A similar result applies to unstable systems except that the interpolating function is a non-causal FIR transfer function . The thesis then considers Hilbert transforms from interpolation data. Given the real part of a stable transfer function evaluated at n equally spaced points around the unit circle, the Hilbert transform from interpolation data reconstructs the complete frequency response, real and imaginary parts, at all frequencies, to within a bounded L∞ error. The error bound goes to zero exponentially fast as n -> ∞. Also considered is the gain-phase problem from interpolation data. This is the same as the Hilbert transform from interpolation data, except that magnitude interpolation data instead of real part interpolation data is given. Two constructions for the gain phase problem from interpolation data are given , and L∞ error bounds derived . In both cases, the error bounds go to zero exponentially fast as n -> ∞. Application of Kalman filters to short-time Fourier analysis then follows. This contains a new method in Kalman filtering called covariance setting. The filters derived from covariance setting generalize the discrete Fourier transform. They offer a design trade-off between noise smoothing and transient response time, are recursive, and are of similar computational complexity to the discrete Fourier transform. Combining the Kalman filters for short-time Fourier analysis and Lagrange interpolation gives a new method of adaptive frequency response identification. A feature of this method is the L∞ error bound between the original system and the identified model. Using recent analysis on the inherent frequency weighting in identification algorithms shows the superiority of this new method over previous adaptive frequency response identification schemes. Finally, model reduction for unstable systems is considered. Given an unstable rational function of high McMillan degree, an approximation of lower McMillan degree, but with the same number of unstable poles, is constructed. An L∞ error bound between the original transfer function and approximation is derived. Such an approximation has application to control systems

Real Time Estimation, Quantization, And Remote Control Of Permanent Magnet Dc Motors

Establishing real-time models for electric motors is of importance for capturing authentic dynamic behavior of the motors to improve control performance, enhance robustness, and support diagnosis. Quantized sensors are less expensive and remote controlled motors mandate signal quantization. Such limitations on observations introduce challenging issues in motor parameter estimation. This dissertation develops estimators for model parameters of permanent magnet direct current motors (PMDC) using quantized speed measurements. A typical linearized model structure of PMDC motors is used as a benchmark platform to demonstrate the technology, its key properties, and benefits. Convergence properties are established. Simulations and experimental studies are performed to illustrate potential applications of the technology. Remotely-controlled Permanent Magnet DC (PMDC) motors must transmit speed measurements and receive control commands via communication channels. Sampling, quantization, data transfer, and signal reconstruction are mandatory in such networked systems, and introduce additional dynamic subsystems that substantially affect feedback stability and performance. The intimate interaction among sampling periods, signal estimation step sizes, and feedback dynamics entails careful design considerations in such systems. This dissertation investigates the impact of these factors on PMDC motor performance, by rigorous analysis, simulation case studies, and design trade-off examination. The findings of this dissertation will be of importance in providing design guidelines for networked mobile systems, such as autonomous vehicles, mobile sensors, unmanned aerial vehicles which often use electric motors as main engines

Singular Switched Systems in Discrete Time: Solvability, Observability, and Reachability Notions

Discrete-time singular (switched) systems, also known as(switched) difference-algebraic equations and discrete-time (switched)descriptor systems, have in general three solvability issues:inconsistent initial values, nonexistence ornonuniqueness of solutions, and noncausalities, which are generallynot desired in applications. To deal with those issues, newsolvability notions are proposed in the study, and the correspondingnecessary and sufficient conditions have been derived with the help of(strictly) index-1 notions. Furthermore, surrogate (switched)systems--ordinary (switched) systems that have equivalentbehavior--have also been established for solvable systems. Byutilizing those surrogate systems, fundamental analysis includingobservability, determinability, reachability, and controllability has also beencharacterized for singular linear (switched) systems. The solvabilitystudy has been extended to singular nonlinear (switched) systems, andmoreover, Lyapunov and incremental stability analyses have beenderived via single and switched Lyapunov function approaches

H-infinity output-feedback control based on an FIR-type quasi-deadbeat observer

This technical note proposes a novel output-feedback control law based on a finite impulse response (FIR)-type quasi-deadbeat observer for linear systems. For nominal systems without disturbances, this technical note first establishes the deadbeat condition that reduces the state estimation error to zero within a finite time and verifies that all the hidden poles of the closed-loop system under the quasi-deadbeat observer-based control law are zero and that the separation principle holds true. In order to enhance the disturbance rejection capability for systems with random-work disturbances, on the structural merit of the FIR-type observer, we have proposed the conditions for an H-infinity quasi-deadbeat observer and an H-infinity stabilizer based on the predetermined observer, respectively.X1122sciescopu

Microgrids/Nanogrids Implementation, Planning, and Operation

Today’s power system is facing the challenges of increasing global demand for electricity, high-reliability requirements, the need for clean energy and environmental protection, and planning restrictions. To move towards a green and smart electric power system, centralized generation facilities are being transformed into smaller and more distributed ones. As a result, the microgrid concept is emerging, where a microgrid can operate as a single controllable system and can be viewed as a group of distributed energy loads and resources, which can include many renewable energy sources and energy storage systems. The energy management of a large number of distributed energy resources is required for the reliable operation of the microgrid. Microgrids and nanogrids can allow for better integration of distributed energy storage capacity and renewable energy sources into the power grid, therefore increasing its efficiency and resilience to natural and technical disruptive events. Microgrid networking with optimal energy management will lead to a sort of smart grid with numerous benefits such as reduced cost and enhanced reliability and resiliency. They include small-scale renewable energy harvesters and fixed energy storage units typically installed in commercial and residential buildings. In this challenging context, the objective of this book is to address and disseminate state-of-the-art research and development results on the implementation, planning, and operation of microgrids/nanogrids, where energy management is one of the core issues

Active vibration control of civil engineering structures

This thesis is in the area of active vibration control of Civil Engineering structures subject to earthquake loading. Existing structural control methods and technologies including passive, active, semi-active and hybrid control are first introduced. An extensive analysis of a frame-pendulum model is developed and analysed to investigate under what conditions effective energy dissipation is achieved in Tuned Mass Damper systems and the limitation of these devices under stiffness degradation when the structure enters the inelastic region. Linear Quadratic Gaussian and H-infinity active control schemes are designed, simulated and assessed for buildings, modelled as lumped parameter systems, including base and actuator dynamics. Various aspects of the designs are extensively evaluated using multiple criteria and loading conditions and validated in large-scale benchmark problems under practical limitations and implementation constraints. A novel design method is proposed for minimising peak responses of regulated signals via a deadbeat parametrisation of all stabilising controllers in discrete-time. The method incorporates constraints on the magnitude and rate of the control signal and is solved via efficient Linear Programming methods. It is argued that this type of optimisation is more relevant for structural control, as failure occurs when maximum member displacements are exceeded. The problem of stiffness matrix estimation from experimental data is formulated as an optimisation problem and solved under various conditions (positive definiteness, tridiagonal structure) via an alternating convex projection scheme. Both static and dynamic loading is considered. The method is finally incorporated in an adaptive control scheme involving the redesign in real-time of an LQR (Linear Quadratic Regulator) active vibration controller. It is shown that the method is successful in recovering the stability and performance properties of the nominal design under conditions of significant uncertainty in the stiffness parameters