Multivariable Minimum Variance Research Articles

Adaptive modal vibration control for smart flexible beam with two piezoelectric actuators by multivariable self-tuning control

It has been popular for decades that the vibrations of space structures are suppressed with smart actuators. However, the higher mode vibrations are often motivated when a control strategy is applied to attenuate the vibration for the smart structures. Moreover, if the multi-mode vibration of a smart structure is suppressed with multi-actuators, a proper multivariable control law will be adopted to solve the coupling problem caused by the multi-actuators of the smart structure. Therefore, in the paper, a decoupling technique for two modal vibrations of a smart flexible beam with two piezoelectric patches is adopted by adaptive control. The proposed control law is designed with a multivariable minimum variance self-tuning control. Considering the first two orders of modal vibrations, two piezoelectric patches are configured on the flexible beam according to the strain of the first two orders of modal vibrations along the longitudinal direction of the beam. A dynamical model for the flexible beam with two piezoelectric actuators is constructed by the mode superposition method. With the dynamical model, simulations are implemented to suppress the free vibration of the flexible beam. Moreover, experiments are carried out to verify the effectiveness of the multivariable minimum variance self-tuning control for vibration suppression of the flexible structure. The control results clearly show that the free vibration amplitude of the cantilevered beam with two control voltages applied to the two piezoelectric patches is less than that with one control voltage applied to the first piezoelectric actuator. Thus, multivariable minimum variance self-tuning control is a more efficient approach for suppressing multimodal vibration for a smart flexible beam with two piezoelectric actuators compared with the conventional velocity feedback control.

Minimum-Variance Control for Astronomical Adaptive Optics with Resonant Deformable Mirrors

Adaptive Optics (AO) systems use a Deformable Mirror (DM) to counter in real-time the nefarious effects of atmospheric turbulence on ground-based telescope imaging. This article presents a brief historical overview of AO design, seen as a strongly multi-variable Minimum-Variance (MV) disturbance rejection problem associated with a hybrid continuous/discrete time MV control problem. It is shown that for a wide class of LTI DM and turbulence models, this hybrid MV problem can be transformed into an equivalent discrete-time LQG formulation. A discrete-time stochastic model enables to compute the optimal control in standard reconstructed feedback form and to evaluate performance degradation for simpler sub-optimal solutions. An example of tip-tilt DM control for the European Extremely Large Telescope (E-ELT) is presented.

Multivariable Control Performance Assessment Based on Generalized Minimum Variance Benchmark

This paper is concerned with the control performance assessment based on the multivariable generalized minimum variance benchmark. An explicit expression for the feedback controller-invariant (the generalized minimum variance) term of the multivariable control system is obtained, which is used as a standard benchmark for the assessment of the control performance for multi input multi output (MIMO) process. The proposed approach is based on the multivariable minimum variance benchmark. In comparison with the minimum variance benchmark, the developed method is more reasonable and practical for the control performance assessment of multivariable systems. The approach is illustrated by a simulation example and an industrial application.

Co-Ordinated Self-Tuning Control for Turbine and Exciter of a Turboalternator

ABSTRACT Multivariable minimum variance self-tuning control of the exciter voltage and turbine speed of an isolated a–c turbogenerator system connected to a large-scale power network is considered. Simulation studies, employing a high-order non-linear representative system model are reported, with emphasis on rigorous assessment of performance within an operational context. Three-phase faults, with and without permanent line-switching, dynamic and transient stability, are amongst problems addressed, and comparison with conventional control philosophies is made. Convergence of the self-tuning algorithm under a wide range of operating conditions is demonstrated, and results indicate that a self-tuning controller, based on minimal advance plant knowledge, provides a viable, robust alternative to conventional schemes within the power system environment.

A multivariable self-tuning controller

A multivariable self-tuning controller is derived extending the scalar version of Clarke and Gawthrop (1975). Because the control terms are penalized in the cost function, fluctuations and peaking in control signals are reduced compared with the multivariable minimum variance self-tuning controller (Borisson, 1979). Time-varying reference signals as well as certain nonminimum-phase systems can be handled without difficulty with the proposed controller. Several examples illustrate the power of the derived self-tuning controller.

Self-tuning regulators for a class of multivariable systems

Control of a class of multivariable systems described by linear vector difference equations with constant but unknown parameters is discussed. A multivariable minimum variance strategy is first presented. This gives a generalization of the minimum variance strategy for single-input single-output systems. A multivariable self-tuning regulator based on the minimum variance strategy is then proposed. It uses a recursive least squares estimator and a linear controller obtained directly from the current estimates. The asymptotic properties of the algorithm are discussed. If the estimated parameters converge, the resulting controller will under certain conditions give the minimum variance strategy. The analysis also gives insight into the case when several single-input single-output self-tuning regulators are operating in cascade mode.