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

In control, the most common type of system is the multiple-input multiple-output(MIMO) system, where the same input may affect multiple outputs, orconversely, the same output is affected by multiple inputs. In thisthesis two methods for controlling MIMO systems are examined, namelylinear quadratic Gaussian (LQG) control and decentralized control,and some of the difficulties associated with them. One difficulty when implementing decentralized control is to decidewhich inputs should control which outputs, that is the input-outputpairing problem. There are multiple ways to solve this problem, amongthem using gramian based measures, which include the Hankel interactionindex array, the participation matrix and the Sigma2 method.These methods take into account system dynamics as opposed to manyother methods which only consider the steady-state system. However,the gramian based methods have issues with input and output scaling.Generally, this is resolved by scaling all inputs and outputs to haveequal range. However, in this thesis it is demonstrated how this canresult in an incorrect pairing. Furthermore this thesis examines othermethods of scaling the gramian based measures, using either row orcolumn sums, or by utilizing the Sinkhorn-Knopp algorithm. This thesisshows that there are considerable benefits to be gained from the alternativescaling of the gramian based measures, especially when using the Sinkhorn-Knoppalgorithm. The use of this method also has the advantage that theresults are completely independent of the original scaling of theinputs and outputs.An alternative way to control a MIMO system is to implement an LQGcontroller, which yields a single control structure for the entiresystem using a state based controller. It has been proposed that LQGcontrol can be an effective control scheme to be used on networkedcontrol systems with wireless channels. These channels have a tendencyto be unreliable with package delays and package losses. This licentiatethesis examines how to implement an LQG controller over such unreliablecommunication channels, and proposes an optimal controller which minimizesthe cost function.When new methods of control system design and analysis are introducedin the control engineering field, it is important to compare the newresults with existing methods. Often this requires application ofthe methods on examples, and for this purpose benchmark processesare introduced. However, in many areas of control engineering researchthe number of examples are relatively few, in particular when MIMOsystems are considered. For a thorough assessment of a method, however,as large number of relevant models as possible should be used. Asa remedy, a framework has been developed for generating linear MIMOmodels 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 toevaluate the previously described scaling methods for the gramianbased pairing methods

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