Classical Control Theory Implementation of a Robust Control System on a Laboratory Oil Rig Model Based on Quantitative Feedback Theory (Qft) in Matlab/Simulink, for National Industrial Sustainable Development

Abstract

The report presents the design of a Proportional plus Derivative (PD) controller, with the laboratory servo Rig as the plant model that gives a robust tracking performance when applied, with the magnetic brakes at both extremes of its travel (i.e., servo fit with brake and servo fit without brake), corresponding to a system with and without noise disturbance signals respectively, using Classical multiple input single output (MISO) quantitative feedback theory (QFT) approach (Feng and Lozano, 1999). The servo Rig is an exact miniature model of an Oil Rig installation in the real physical world, and so a study/analysis and understanding of the model comparatively makes the Oil Rig infrastructure easily understood and accurately modelled [the model being represented by mathematical equations in either continuous time (t), discrete time (z), sampled data and delayed response or in complex frequency (s) domain] and controlled as a consequence. The design processes include: The use of data collection and model fitting programs provided, to establish a set of transfer functions that reasonably represent the behaviours observed on the actual Servo Rig. Establishing a suitable set of design criteria for the tracking performance of the Rigs. Designing a suitable Robust (in a tracking sense) controller. Testing the controller in simulation and on several Rigs. Various frequency response techniques and analysis and mathematical modelling (based on abstraction of real systems, using s-domain transfer functions) have been employed, which include the traditional (i.e., Bode) sensitivity function, Bode log-magnitude, and gain plots, Nichol‟s chart design criteria, allowable plant parameter variations, pole/zero placement, Nyquist M and N circles plots, construction of plant templates, PD compensation method, disturbance rejection and the synthesis of a pre-filter using the nominal loop tracking transfer function. At the end of our design and on comparison, the SIMULINK as well as the real-time (or online) models in MATLAB for the Oil Rig setup systematically gave out accurate and identical outputs (i.e., the two superimposed models on each other correctly fitted each other), suggesting a successful design of our controller. It also gave same order of mathematical equations representations, thus Classical Control approach provides a formal solution to control systems design. The investigation of the behaviour of the system used in this control laboratory is based entirely on the MATLAB (matrix laboratory) software program.