Multivariable PID control with application to gas turbine engines
To meet increasing and often conflicting demands on performance, stability, fuel consumption and functionality, modem jet engines are becoming increasingly complex. Improved compressor performance is a major factor in this development process. Optimum compressor efficiency is achieved in operating regions close to flow instability. Surveying basic concepts and control methods of compressor instabilities, an overview of the fundamentals of surge and rotating stall is presented. To maximise the potential of an aero gas turbine compression system, it is proposed to use more advanced control strategies, such as multi variable control. Multivariable control may offer the prospect of lower safety margin requirements leading to greater compressor efficiency. Alternatively, it may result in more agility in combat through improved engine responses and prolonged engine life. A multivariable control technique is proposed and tested on a Rolls-Royce three-spool high bypass ratio turbofan engine. Since elements of the 2x2 system can be represented by linear third order models, a muItivariable PID controller will be sufficient provided the design requirements are not too rigorous. To have a simple and efficient design, a systematic decentralised PI (PID) control design strategy is developed. Decoupling a given 2x2 process by a stable decoupler, the elements of the resulting diagonal matrix are approximated by first (second) order plus dead time processes using the proposed model reduction techniques. Then, SISO controllers are designed for each element using the developed tuning formulae. Any practical design method should be simple, easy to apply, flexible, generic or extendable, and applicable to complex control schemes to fulfil more demanding control requirements. It will be advantageous if the design algorithm can also directly address the design requirements, be repeatable for any control objective, constraint and category of processes, have a design parameter, and can consider any number of objectives and constraints. Formulating the PI (PID) control design problem as an optimisation problem, a non-dimensional tuning (NDT) method satisfying the above-mentioned design properties is presented. For a given first (second) order plus dead time process, the NOT method is used in conjunction with either a single-objective or a multi-objective optimisation approach to design PI (PID) controllers satisfying conflicting design requirements. In addition, considering load disturbance rejection as the primary design objective, a simple analytical PI tuning method is presented. The design problem is constrained with a specified gain or phase margin. Compared to the corresponding conventional SISO controller, it is demonstrated that the resulting decentralised controller considerably improves the overall surge risk to the engine during the transient manoeuvres while maintaining similar thrust levels. Due to non-linearity of jet engine models, gain scheduling is necessary. Designing decentralised controllers at various operating points, the gain-scheduled controller accommodates the non-linearity in engine dynamics over the full thrust range.