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

High-order volterra model predictive control and its application to a nonlinear polymerisation process

Model Predictive Control (MPC) has recently found wide acceptance in the process industry, but the existing design and implementation methods are restricted to linear process models. A chemical process involves, however, severe nonlinearity which cannot be ignored in practice. This paper aims to solve this nonlinear control problem by extending MPC to nonlinear models. It develops an analytical framework for nonlinear model predictive control (NMPC), and also offers a third-order Volterra series based nonparametric nonlinear modelling technique for NMPC design which relieves practising engineers from the need for first deriving a physical-principles based model. An on-line realisation technique for implementing the NMPC is also developed. The NMPC is then applied to a Mitsubishi Chemicals polymerisation reaction process. The results show that this nonlinear MPC technique is feasible and very effective. It considerably outperforms linear and low-order Volterra model based methods. The advantages of the approach developed lie not only in control performance superior to existing NMPC methods, but also in relieving practising engineers from the need for deriving an analytical model and then converting it to a Volterra model through which the model can only be obtained up to the second order

Synthesis of Minimal Error Control Software

Software implementations of controllers for physical systems are at the core of many embedded systems. The design of controllers uses the theory of dynamical systems to construct a mathematical control law that ensures that the controlled system has certain properties, such as asymptotic convergence to an equilibrium point, while optimizing some performance criteria. However, owing to quantization errors arising from the use of fixed-point arithmetic, the implementation of this control law can only guarantee practical stability: under the actions of the implementation, the trajectories of the controlled system converge to a bounded set around the equilibrium point, and the size of the bounded set is proportional to the error in the implementation. The problem of verifying whether a controller implementation achieves practical stability for a given bounded set has been studied before. In this paper, we change the emphasis from verification to automatic synthesis. Using synthesis, the need for formal verification can be considerably reduced thereby reducing the design time as well as design cost of embedded control software. We give a methodology and a tool to synthesize embedded control software that is Pareto optimal w.r.t. both performance criteria and practical stability regions. Our technique is a combination of static analysis to estimate quantization errors for specific controller implementations and stochastic local search over the space of possible controllers using particle swarm optimization. The effectiveness of our technique is illustrated using examples of various standard control systems: in most examples, we achieve controllers with close LQR-LQG performance but with implementation errors, hence regions of practical stability, several times as small.Comment: 18 pages, 2 figure

Improved branch and bound method for control structure screening

The main aim of this paper is to present an improved algorithm of “Branch and Bound” method for control structure screening. The new algorithm uses a best- first search approach, which is more efficient than other algorithms based on depth-first search approaches. Detailed explanation of the algorithms is provided in this paper along with a case study on Tennessee–Eastman process to justify the theory of branch and bound method. The case study uses the Hankel singular value to screen control structure for stabilization. The branch and bound method provides a global ranking to all possible input and output combinations. Based on this ranking an efficient control structure with least complexity for stabilizing control is detected which leads to a decentralized proportional cont

Active flutter control for flexible vehicles, volume 1

An active flutter control methodology based on linear quadratic gaussian theory and its application to the control of a super critical wing is presented. Results of control surface and sensor position optimization are discussed. Both frequency response matching and residualization used to obtain practical flutter controllers are examined. The development of algorithms and computer programs for flutter modeling and active control design procedures is reported