Stabilization of Compressor Surge Using Gain-Scheduled Controller

Gain scheduling is a control method that is used in nonlinear systems to optimize their controlled performance and robustness over a wide range of operating conditions. It is one of the most commonly used controller design approaches for nonlinear systems. In this control technique, the controller consists of a collection of linear controllers, each of which provides satisfactory closed-loop stability and performance for a small operating region, and combined they guarantee the stability of the system along the entire operating range. The operating region of the system is determined by a scheduling signal, also known as the scheduling variable, which may be either exogenous or endogenous with respect to the plan. A good design of the gain-scheduled controller requires a suitable selection of the scheduling variables to properly reflect the dynamics of the system. In this thesis, we apply the gain scheduling control method to the control of compression systems with active magnetic bearings (AMBs). First, a gain-scheduled controller is designed and tested for the rotor levitation control of the AMB system. The levitation controller is designed to guarantee robust rotor levitation over a wide range of rotating speeds. We show through numerical simulation that the rotor vibration is contained in the presence of uncertainties introduced by speed dependent gyroscopic forces. Next, we implement the gain scheduling control method to the active stabilization of compressor surge in a compression system using the AMBs as actuators. Recently, Yoon et al. [1] showed that AMBs can be used to stabilize the surge instability in a compression system. In this thesis, we demonstrate that gain scheduling control can effectively extend the stable operating region of the compression system beyond the limits presented in [1]. For the stabilization of surge, a gain-scheduled controller was obtained by combining six linear controllers that together they cover the full operating range of the compression system. We were able to demonstrate through numerical simulation that the designed surge controller is effective in suppressing the instability down to a throttle valve opening of 12%, and in the presence of random flow disturbance and actuator saturation. An observer-based technique was implemented to achieve a bumpless and smooth transfer when switching between the linear controllers

Design of Robust AMB Controllers for Rotors Subjected to Varying and Uncertain Seal Forces

This paper demonstrates the design and simulation results of model based controllers for AMB systems, subjected to uncertain and changing dynamic seal forces. Specifically, a turbocharger with a hole-pattern seal mounted across the balance piston is considered. The dynamic forces of the seal, which are dependent on the operational conditions, have a significant effect on the overall system dynamics. Furthermore, these forces are considered uncertain. The nominal and the uncertainty representation of the seal model are established using results from conventional modelling approaches, i.e. Computational Fluid Dynamics (CFD) and Bulkflow, and experimental results. Three controllers are synthesized: I) An H∞ controller based on nominal plant representation, II) A μ controller, designed to be robust against uncertainties in the dynamic seal model and III) a Linear Parameter Varying (LPV) controller, designed to provide a unified performance over a large operational speed range using the operational speed as the scheduling parameter. Significant performance improvement is shown for robust control, incorporating model uncertainty, compared to nominal model based control

Multi - objective sliding mode control of active magnetic bearing system

Active Magnetic Bearing (AMB) system is known to inherit many nonlinearity effects due to its rotor dynamic motion and the electromagnetic actuators which make the system highly nonlinear, coupled and open-loop unstable. The major nonlinearities that are associated with AMB system are gyroscopic effect, rotor mass imbalance and nonlinear electromagnetics in which the gyroscopics and imbalance are dependent to the rotational speed of the rotor. In order to provide satisfactory system performance for a wide range of system condition, active control is thus essential. The main concern of the thesis is the modeling of the nonlinear AMB system and synthesizing a robust control method based on Sliding Mode Control (SMC) technique such that the system can achieve robust performance under various system nonlinearities. The model of the AMB system is developed based on the integration of the rotor and electromagnetic dynamics which forms nonlinear time varying state equations that represent a reasonably close description of the actual system. Based on the known bound of the system parameters and state variables, the model is restructured to become a class of uncertain system by using a deterministic approach. In formulating the control algorithm to control the system, SMC theory is adapted which involves the formulation of the sliding surface and the control law such that the state trajectories are driven to the stable sliding manifold. The surface design involves the transformation of the system into a special canonical representation such that the sliding motion can be characterized by a convex representation of the desired system performances. Optimal Linear Quadratic (LQ) characteristics and regional pole-clustering of the closed-loop poles are designed to be the objectives to be fulfilled in the surface design where the formulation is represented as a set of Linear Matrix Inequality optimization problem. For the control law design, a new continuous SMC controller is proposed in which asymptotic convergence of the system’s state trajectories in finite time is guaranteed. This is achieved by adapting the equivalent control approach with the exponential decaying boundary layer technique. The newly designed sliding surface and control law form the complete Multi-objective SMC (MO-SMC) and the proposed algorithm is applied into the nonlinear AMB in which the results show that robust system performance is achieved for various system conditions. The findings also demonstrate that the MO-SMC gives better system response than the reported ideal SMC (I-SMC) and continuous SMC (C-SMC)

A novel design approach for switched LPV controllers

A novel design procedure for switched linear parameter-varying (LPV) controller is proposed. The new procedure, based on the Youla parameterisation ideas, decomposes the controller design into two steps. One focuses on ensuring global stability and the other on fulfilling the local performance specifications. This scheme allows the design of each local controller independently of each other, which may achieve higher performance without compromising the global stability and also simplifies the synthesis and the implementation of the local controllers. Any standard LPV synthesis procedure can be used to design these controllers. On the other hand, the stability during switching is ensured with convex constraints and no restrictions are imposed on the switching among controllers. The use of the proposed procedure is illustrated with an active magnetic bearing example.Fil: Bianchi, Fernando Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Politécnica de Catalunya; EspañaFil: Sanchez Peña, Ricardo Salvador. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Instituto Tecnológico de Buenos Aires; Argentin

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version