System Level Synthesis

This article surveys the System Level Synthesis framework, which presents a novel perspective on constrained robust and optimal controller synthesis for linear systems. We show how SLS shifts the controller synthesis task from the design of a controller to the design of the entire closed loop system, and highlight the benefits of this approach in terms of scalability and transparency. We emphasize two particular applications of SLS, namely large-scale distributed optimal control and robust control. In the case of distributed control, we show how SLS allows for localized controllers to be computed, extending robust and optimal control methods to large-scale systems under practical and realistic assumptions. In the case of robust control, we show how SLS allows for novel design methodologies that, for the first time, quantify the degradation in performance of a robust controller due to model uncertainty -- such transparency is key in allowing robust control methods to interact, in a principled way, with modern techniques from machine learning and statistical inference. Throughout, we emphasize practical and efficient computational solutions, and demonstrate our methods on easy to understand case studies.Comment: To appear in Annual Reviews in Contro

System level synthesis

This article surveys the System Level Synthesis framework, which presents a novel perspective on constrained robust and optimal controller synthesis for linear systems. We show how SLS shifts the controller synthesis task from the design of a controller to the design of the entire closed loop system, and highlight the benefits of this approach in terms of scalability and transparency. We emphasize two particular applications of SLS, namely large-scale distributed optimal control and robust control. In the case of distributed control, we show how SLS allows for localized controllers to be computed, extending robust and optimal control methods to large-scale systems under practical and realistic assumptions. In the case of robust control, we show how SLS allows for novel design methodologies that, for the first time, quantify the degradation in performance of a robust controller due to model uncertainty – such transparency is key in allowing robust control methods to interact, in a principled way, with modern techniques from machine learning and statistical inference. Throughout, we emphasize practical and efficient computational solutions, and demonstrate our methods on easy to understand case studies

Adaptive time-integration for goal-oriented and coupled problems

We consider efficient methods for the partitioned time-integration of multiphysics problems, which commonly exhibit a multiscale behavior, requiring independent time-grids. Examples are fluid structure interaction in e.g., the simulation of blood-flow or cooling of rocket engines, or ocean-atmosphere-vegetation interaction. The ideal method for solving these problems allows independent and adaptive time-grids, higher order time-discretizations, is fast and robust, and allows the coupling of existing subsolvers, executed in parallel. We consider Waveform relaxation (WR) methods, which can have all of these properties. WR methods iterate on continuous-in-time interface functions, obtained via suitable interpolation. The difficulty is to find suitable convergence acceleration, which is required for the iteration converge quickly. We develop a fast and highly robust, second order in time, adaptive WR method for unsteady thermal fluid structure interaction (FSI), modelled by heterogeneous coupled linear heat equations. We use a Dirichlet-Neumann coupling at the interface and an analytical optimal relaxation parameter derived for the fully-discrete scheme. While this method is sequential, it is notably faster and more robust than similar parallel methods.We further develop a novel, parallel WR method, using asynchronous communication techniques during time-integration to accelerate convergence. Instead of exchanging interpolated time-dependent functions at the end of each time-window or iteration, we exchange time-point data immediately after each timestep. The analytical description and convergence results of this method generalize existing WR theory.Since WR methods allow coupling of problems in a relative black-box manner, we developed adapters to PDE-subsolvers implemented using DUNE and FEniCS. We demonstrate this coupling in a thermal FSI test case.Lastly, we consider adaptive time-integration for goal-oriented problems, where one is interested in a quantity of interest (QoI), which is a functional of the solution. The state-of-the-art method is the dual-weighted residual (DWR) method, which is extremely costly in both computation and implementation. We develop a goal oriented adaptive method based on local error estimates, which is considerably cheaper in computation. We prove convergence of the error in the QoI for tolerance to zero under a controllability assumption. By analyzing global error propagation with respect to the QoI, we can identify possible issues and make performance predictions. Numerical results verify these results and show our method to be more efficient than the DWR method

Cycle-to-cycle control of multiple input-multiple output manufacturing processes

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2005."June 2005."Includes bibliographical references (leaves 199-200).In-process closed-loop control of many manufacturing processes is impractical owing to the impossibility or the prohibitively high cost of placing sensors and actuators necessary for in-process control. Such processes are usually left to statistical process control methods, which only identify problems without specifying solutions. In this thesis, we look at a particular kind of manufacturing process control, cycle-to-cycle control. This type of control is similar to the better known run-by-run control. However, it is developed from a different point of view allowing easy analysis of the process' transient closed-loop behavior due to changes in the target value or to output disturbances. Both types are methods for using feedback to improve product quality for processes that are inaccessible within a single processing cycle but can be changed between cycles. Through rigorous redevelopment of the control equations, we show these methods are identical in their response to output disturbances, but different in their response to changes in the target specification. Next, we extend these SISO results to multiple input-multiple output processes. Gain selection, stability, and process variance amplification results are developed. Then, the limitation of imperfect knowledge of the plant model is imposed. This is consistent with manufacturing environments that require minimal cost and number of tests in determining a valid process model. The effects of this limitation on system performance and stability are discussed. To minimize the number of pre-production experiments, a generic, easily calibrated model is developed for processes with a regional-type coupling between the inputs and outputs, in which one input affects a region of outputs.(cont.) This model can be calibrated in just two experiments and is shown to be a good predictor of the output. However, it is determined that models for this class of process are ill- conditioned for even moderate numbers of inputs and outputs. Therefore, controller design methods that do not rely on direct plant gain inversion are sought and a representative set is selected: LQR, LQG, and H-infinity. Robust stability bounds are computed for each design and all results are experimentally verified on a 110 input- 10 output discrete-die sheet metal forming process, showing good agreement.by Adam Kamil Rzepniewski.Ph.D

Reduced Order Model Inspired Robotic Bipedal Walking: A Step-to-step Dynamics Approximation based Approach

Controlling bipedal robotic walking is a challenging task. The dynamics is hybrid, nonlinear, high-dimensional, and typically underactuated. Complex physical constraints have to be satisfied in the walking generation. The stability in terms of not-falling is also hard to be encoded in the walking synthesis. Canonical approaches for enabling robotic walking typically rely on large-scale trajectory optimizations for generating optimal periodic behaviors on the full-dimensional model of the system; then the stabilities of the controlled behaviors are analyzed through the numerically derived Poincaré maps. This full-dimensional periodic behavior based synthesis, despite being theoretically rigorous, suffers from several disadvantages. The trajectory optimization problem is computationally challenging to solve. Non-trivial expert-tuning is required on the cost, constraints, and initial conditions to avoid infeasibilities and local optimality. It is cumbersome for realizing non-periodical behaviors, and the synthesized walking can be sensitive to model uncertainties. In this thesis, we propose an alternative approach of walking synthesis that is based on reduced order modeling and dynamics approximation. We formulate a discrete step-to-step (S2S) dynamics of walking, where the step size is treated as the control input to stabilize the pre-impact horizontal center of mass (COM) state of the robot. Stepping planning thus is converted into a feedback control problem. To effectively and efficiently solve this feedback stepping planning problem, an underactuated Hybrid Linear Inverted Pendulum (H-LIP) model is proposed to approximate the dynamics of underactuated bipedal walking; the linear S2S dynamics of the H-LIP then approximates the robot S2S dynamics. The H-LIP based stepping controller is hence utilized to plan the desired step sizes on the robot to control its pre-impact horizontal COM state. Stable walking behaviors are consequently generating by realizing the desired step size in the output construction and stabilizing the output via optimization-based controllers. We evaluate this approach successfully on several bipedal walking systems with an increase in the system complexity: a planar five-linkage walker AMBER, an actuated version of the Spring Loaded Inverted Pendulum (aSLIP) in both 2D and 3D, and finally the 3D underactuated robot Cassie. The generated dynamic walking behaviors on these systems are shown to be highly versatile and robust. Furthermore, we show that this approach can be effectively extended to realizing more complex walking tasks such as global trajectory tracking and walking on rough terrain.</p

Automated visual inspection for the quality control of pad printing

Pad printing is used to decorate consumer goods largely because of its unique ability to apply graphics to doubly curved surfaces. The Intelpadrint project was conceived to develop a better understanding of the process and new printing pads, inks and printers. The thesis deals primarily with the research of a printer control system including machine vision. At present printing is manually controlled. Operator knowledge was gathered for use by an expert system to control the process. A novel local corner- matching algorithm was conceived to effect image segmentation, and neuro-fuzzy techniques were used to recognise patterns in printing errors. Non-linear Finite Element Analysis of the rubber printing-pad led to a method for pre-distorting artwork so that it would print undistorted on a curved product. A flexible, more automated printer was developed that achieves a higher printing rate. Ultraviolet-cured inks with improved printability were developed. The image normalisation/ error-signalling stage in inspection was proven in isolation, as was the pattern recognition system

A Scalable Safety Critical Control Framework for Nonlinear Systems

There are two main approaches to safety-critical control. The first one relies on computation of control invariant sets and is presented in the first part of this work. The second approach draws from the topic of optimal control and relies on the ability to realize Model-Predictive-Controllers online to guarantee the safety of a system. In the second approach, safety is ensured at a planning stage by solving the control problem subject for some explicitly defined constraints on the state and control input. Both approaches have distinct advantages but also major drawbacks that hinder their practical effectiveness, namely scalability for the first one and computational complexity for the second. We therefore present an approach that draws from the advantages of both approaches to deliver efficient and scalable methods of ensuring safety for nonlinear dynamical systems. In particular, we show that identifying a backup control law that stabilizes the system is in fact sufficient to exploit some of the set-invariance conditions presented in the first part of this work. Indeed, one only needs to be able to numerically integrate the closed-loop dynamics of the system over a finite horizon under this backup law to compute all the information necessary for evaluating the regulation map and enforcing safety. The effect of relaxing the stabilization requirements of the backup law is also studied, and weaker but more practical safety guarantees are brought forward. We then explore the relationship between the optimality of the backup law and how conservative the resulting safety filter is. Finally, methods of selecting a safe input with varying levels of trade-off between conservatism and computational complexity are proposed and illustrated on multiple robotic systems, namely: a two-wheeled inverted pendulum (Segway), an industrial manipulator, a quadrotor, and a lower body exoskeleton

Compensation of distributed delays in integrated communication and control systems

The concept, analysis, implementation, and verification of a method for compensating delays that are distributed between the sensors, controller, and actuators within a control loop are discussed. With the objective of mitigating the detrimental effects of these network induced delays, a predictor-controller algorithm was formulated and analyzed. Robustness of the delay compensation algorithm was investigated relative to parametric uncertainties in plant modeling. The delay compensator was experimentally verified on an IEEE 802.4 network testbed for velocity control of a DC servomotor