THE LEFT AND RIGHT BLOCK POLE PLACEMENT COMPARISON STUDY: APPLICATION TO FLIGHT DYNAMICS

ABSTRACTIt is known that if a linear-time-invariant MIMO system described by a state space equation has a numberof states divisible by the number of inputs and it can be transformed to block controller form, we candesign a state feedback controller using block pole placement technique by assigning a set of desired Blockpoles. These may be left or right block poles. The idea is to compare both in terms of system’s response.KEYWORDSMIMO, Block Controller Form, State Feedback Controller, Block Pole Placement Technique, Left and/orRight Block Poles.1.INTRODUCTIONIn most applied mathematical research, the aim is to investigate and control a given system. Asystem is defined to mean a collection of objects which are related by interactions and producevarious outputs in response to different inputs.Examples of such systems are chemical plants,aircrafts, spacecraft, biological systems, or even the economic structure of a country or regionssee [1, 4 and 17]. The control problems associated with these systems might be the production ofsome chemical product as efficiently as possible, automatic landing of aircraft, rendezvous withan artificial satellite, regulation of body functions such as heartbeat or blood pressure, and theever-present problem of economic inflation [18].To be able to control a system, we need a validmathematical model. However practical systems are inherently complicated and highly nonlinear. Thus, simplifications are made, such as the linearization of the system. Error analysis canthen be employed to give information on how valid the linear mathematical model is, as anapproximation to the real system [17].