A Data-driven Approach to Robust Control of Multivariable Systems by Convex Optimization

The frequency-domain data of a multivariable system in different operating points is used to design a robust controller with respect to the measurement noise and multimodel uncertainty. The controller is fully parametrized in terms of matrix polynomial functions and can be formulated as a centralized, decentralized or distributed controller. All standard performance specifications like $H_2$, $H_\infty$ and loop shaping are considered in a unified framework for continuous- and discrete-time systems. The control problem is formulated as a convex-concave optimization problem and then convexified by linearization of the concave part around an initial controller. The performance criterion converges monotonically to a local optimal solution in an iterative algorithm. The effectiveness of the method is compared with fixed-structure controllers using non-smooth optimization and with full-order optimal controllers via simulation examples. Finally, the experimental data of a gyroscope is used to design a data-driven controller that is successfully applied on the real system

Robust computer-aided synthesis and optimization of linear multivariable control systems with varying plant dynamics via AUTOCON

AUTOCON is an automated computer-aided design tool for the synthesis and optimization of linear multivariable control systems based upon user-defined control parameter optimization. Violations in stability and performance requirements are computed from constraints on Single Input/Single Output (SISO) open- and closed-loop transfer function frequency responses, and from constraints on the singular-value frequency responses of Multiple Input/Multiple Output (MIMO) transfer functions, for all critical plant variations. Optimum nonlinear programming algorithms are used in the search for local constrained solutions in which violations in stability and performance are caused either to vanish or be minimized for a proper selection of the control parameters. Classical control system stability and performance design can, in this way, be combined with modern multivariable robustness methods to offer general frequency response loop-shaping via a computer-aided design tool. Complete Nichols, Nyquist, Bode, singular-value Bode magnitude and transient response plots are produced, including user-defined boundary responses. AUTOCON is used to synthesize and optimize the lateral/directional flight control system for a typical high-performance aircraft

Research on output feedback control

In designing fixed order compensators, an output feedback formulation has been adopted by suitably augmenting the system description to include the compensator states. However, the minimization of the performance index over the range of possible compensator descriptions was impeded due to the nonuniqueness of the compensator transfer function. A controller canonical form of the compensator was chosen to reduce the number of free parameters to its minimal number in the optimization. In the MIMO case, the controller form requires a prespecified set of ascending controllability indices. This constraint on the compensator structure is rather innocuous in relation to the increase in convergence rate of the optimization. Moreover, the controller form is easily relatable to a unique controller transfer function description. This structure of the compensator does not require penalizing the compensator states for a nonzero or coupled solution, a problem that occurs when following a standard output feedback synthesis formulation

Analysis and design of Coleman transform-based individual pitch controllers for wind-turbine load reduction

As the size of wind turbines increases, the effects of dynamic loading on the turbine structures become increasingly significant. There is therefore a growing demand for turbine control systems to alleviate these unsteady structural loads in addition to maintaining basic requirements such as power and speed regulation. This has motivated the development of blade individual pitch control (IPC) methodologies, many of which employ the Coleman transformation to simplify the controller design process. However, and as is shown in this paper, the Coleman transformation significantly alters the rotational system dynamics when these are referred to the non-rotating frame of reference, introducing tilt-yaw coupling in the process. Unless this transformation is explicitly included in the model employed for IPC design, then the resulting controllers can yield poor performance. Therefore, in this paper, we show how to model the Coleman transformation in a form that is amenable to IPC analysis and synthesis. This enables us to explain why traditional design parameters of gain and phase margin are poor indicators of robust stability and hence motivate the need for a multivariable design approach. The robust multivariable IPC approach advocated in this paper is based upon H∞ loop shaping and has numerous desirable properties, including reliable stability margins, improved tilt-yaw decoupling and simultaneous rejection of disturbance loads over a range of frequencies. The design of a robust multivariable IPC is discussed, and simulation results are presented that demonstrate the efficacy of this controller, in terms of load reduction on both rotating and non-rotating turbine parts

Active vibration damping of the Space Shuttle remote manipulator system

The feasibility of providing active damping augmentation of the Space Shuttle Remote Manipulator System (RMS) following normal payload handling operations is investigated. The approach used in the analysis is described, and the results for both linear and nonlinear performance analysis of candidate laws are presented, demonstrating that significant improvement in the RMS dynamic response can be achieved through active control using measured RMS tip acceleration data for feedback

Synthesis and control of generalised dynamically substructured systems

The experimental technique for testing engineering systems via the method of dynamic substructuring is receiving significant global interest, for example in the fields of large-scale structural, aerospace, and automotive system testing. Dynamically substructured systems (DSSs) enable full-size, critical components of a complete system to be physically tested in real-time, within a laboratory environment, while the remainder of the system is modelled numerically. The intention is that the combined physical-numerical DSS behaves as if it were the complete (or emulated) system.In an ideal mechanical DSS, for example, perfect synchronization of displacements and forces at the interfaces between the numerical and physical components (or substructures) is required. Hence, a key design feature of successful DSS systems is the high fidelity of the control action. Equally, a DSS controller must be able to cope with non-linear, time-varying, and uncertain parameters within the physical substructure dynamics.The main purpose of this paper is to present a generalized DSS framework, together with associated linear and adaptive control strategies, that are specifically tailored to achieve high synchronization performance. The initial studies of this problem, as described in an earlier paper by Stoten and Hyde, are therefore continued by generalizing both the DSS dynamics and the control strategies to include (a) a number of newly defined modes of operation and (b) multivariable dynamics. In addition, comparative implementation and simulation studies are included, based upon the DSS testing of a mechanical system (a planar quasi-motorcycle rig), which was specifically designed to highlight the main features of this research. The comparative studies show that excellent DSS control can be achieved, especially with the addition of an adaptive component to the controller, despite significant changes to the physical substructure dynamics