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