Optimal LQG Control Across a Packet-Dropping Link

We examine optimal Linear Quadratic Gaussian control for a system in which communication between the sensor (output of the plant) and the controller occurs across a packet-dropping link. We extend the familiar LQG separation principle to this problem that allows us to solve this problem using a standard LQR state-feedback design, along with an optimal algorithm for propagating and using the information across the unreliable link. We present one such optimal algorithm, which consists of a Kalman Filter at the sensor side of the link, and a switched linear filter at the controller side. Our design does not assume any statistical model of the packet drop events, and is thus optimal for an arbitrary packet drop pattern. Further, the solution is appealing from a practical point of view because it can be implemented as a small modification of an existing LQG control design

Development and evaluation of methods for control and modelling of multiple-input multiple-output systems

In control, a common type of system is the multiple-input multiple-output (MIMO) system, where the same input may affect multiple outputs, or conversely, the same output is affected by multiple inputs. In this thesis two methods for controlling MIMO systems are examined, namely linear quadratic Gaussian (LQG) control and decentralized control, and some of the difficulties associated with them.One difficulty when implementing decentralized control is to decide which inputs should control which outputs, also called the input-output pairing problem. There are multiple ways to solve this problem, among them using gramian based measures, which include the Hankel interaction index array, the participation matrix and the Σ2 method.\ua0 These methods take into account system dynamics as opposed to many other methods which only consider the steady-state system. However, the gramian based methods have issues with input and output scaling. Generally, this is handled by scaling all inputs and outputs to have equal range. However, in this thesis it is demonstrated how this can cause an incorrect pairing. Furthermore, this thesis examines other methods of scaling the gramian based measures, using either row or column sums, or by utilizing the Sinkhorn-Knopp algorithm. It is shown that there are considerable benefits to be gained from the alternative scaling of the gramian based measures, especially when using the Sinkhorn-Knopp algorithm. The use of this method also has the advantage that the results are completely independent of the original scaling of the inputs and outputs.An expansion to the decentralized control structure is the sparse control, in which a decentralized controller is expanded to include feed-forward or MIMO blocks. In this thesis we explore how to best use the gramian based measures to find sparse control structures, and propose a method which demonstrates considerable improvement compared to existing methods of sparse control structure design.A prerequisite to implementing control configuration methods is an understanding of the processes in question. In this thesis we examine the pulp refining process and design both static and dynamic models for pulp and paper properties such as shives width, fiber length and tensile index, and various available inputs. We demonstrate that utilizing internal variables (primarily consistencies) estimated from temperature measurements yields improved results compared to using solely measured variables. The measurement data from the refiners is noisy, sometimes sparse and generally irregularly sampled. This thesis discusses the challenges posed by these constraints and how they can be resolved.\ua0\ua0 An alternative way to control a MIMO system is to implement an LQG controller, which yields a single control structure for the entire system using a state based controller. It has been proposed that LQG control can be an effective control scheme to be used on networked control systems with wireless channels. These channels have a tendency to be unreliable with packet delays and packet losses. This thesis examines how to implement an LQG controller over such unreliable communication channels, and derives the optimal controller minimizing the cost function expressed in actuated controls.When new methods of control system design and analysis are introduced in the control engineering field, it is important to compare the new results with existing methods. Often this requires application of the methods on examples, and for this purpose benchmark processes are introduced. However, in many areas of control engineering research the number of examples are relatively few, in particular when MIMO systems are considered. For a thorough assessment of a method, however, as large number of relevant models as possible should be used. As a remedy, a framework has been developed for generating linear MIMO models based on predefined system properties, such as model type, size, stability, time constants, delays etc. This MIMO generator, which is presented in this thesis, is demonstrated by using it to evaluate the previously described scaling methods for the gramian based pairing methods

Stochastic optimal control over unreliable communication links

In this paper LQG control over unreliable communication links is derived. That is to say, the communication channels between the controller and the actuators and between the sensors and the controller are unreliable. This is of growing importance as networked control systems and use of wireless communication in control are becoming increasingly common. The problem of how to optimize LQG control in this case is examined in the situation where communication between the components is done with acknowledgments. Previous solutions to finite horizon discrete time hold-input LQG control for this case do not fully utilize the available information. Here a new solution is presented which resolves this limitation. The solution is linear and covers communication channels subject to both packet losses and delays. The new control scheme is compared with previous solutions for LQG control in simulations, which demonstrates that a significant improvement in the cost can be achieved by fully utilizing the available information

Stability Analysis of Networked Control in Smart Grids

A suitable networked control scheme and its stability analysis framework have been developed for controlling inherent electromechanical oscillatory dynamics observed in power systems. It is assumed that the feedback signals are obtained at locations away from the controller/actuator and transmitted over a communication network with the help of phasor measurement units (PMUs). Within the generic framework of networked control system (NCS), the evolution of power system dynamics and associated control actions through a communication network have been modeled as a hybrid system. The data delivery rate has been modeled as a stochastic process. The closed-loop stability analysis framework has considered the limiting probability of data dropout in computing the stability margin. The contribution is in quantifying allowable data-dropout limit for a specified closed loop performance. The research findings are useful in specifying the requirement of communication infrastructure and protocol for operating future smart grids