Pablo Ballesteros

Disturbance Rejection through LPV Gain-Scheduling Control with Application to Active Noise Cancellation

Abstract A design method for the design of discrete-time gain-scheduling controllers for the rejection of disturbances with time-varying dynamics is presented. The disturbance is modeled as the output of a linear parameter-varying system in linear-fractional-transformation form. The work is motivated by the rejection of harmonic disturbances with time-varying frequencies, a problem that arises in active noise and vibration control. The design method is described in detail and experimental real-time results obtained with an active noise control headset are presented. Over existing approaches (such as adaptive filtering or gain-scheduled observer-based state feedback) the proposed method has the advantage that it leads to a stable closed-loop system even for arbitrarily fast changes of the disturbance frequencies.

Active vibration control for harmonic disturbances with time-varying frequencies through LPV gain scheduling

A design method for a discrete-time H∞-optimal gain-scheduling controller that rejects harmonic disturbances with time-varying, known frequencies is presented. This is motivated by active vibration control and the controller is experimentally validated on an active vibration control test bench. The harmonic disturbances are modeled as outputs of a linear parameter varying system (LPV) where the frequencies are the varying parameters. The design method and the controller synthesis are discussed and experimental results for constant and time-varying frequencies are shown. The design method leads to a controller that stabilizes the closed-loop system even for arbitrarily fast changes in the disturbance frequencies. In the real-time experiment, the controller suppresses a disturbance consisting of six independent harmonics with frequencies that vary over ranges of 20 Hz.

A frequency-tunable LPV controller for narrowband active noise and vibration control

A design method for a discrete-time gain scheduling controller for the rejection of a harmonic disturbance with known but time-varying frequency for a single-input single-output linear plant is presented. The controller is obtained through the gain scheduling design method for linear parameter-varying (LPV) systems. This results in a controller where the frequency of the disturbance is the gain-scheduling variable of the controller and closed loop stability is guaranteed for the whole range of frequencies specified in the design. The work is motivated by active noise and vibration control (ANC/AVC), and experimental real time results obtained with an ANC headset and an AVC test bed are presented. The design method is very straightforward and the experimental results show that the controller is well suited for narrowband ANC and AVC.

Experimental evaluation of an LPV-gain-scheduled observer for rejecting multisine disturbances with time-varying frequencies

A linear time-varying (LTV) discrete-time controller for the rejection of harmonic disturbances with time-varying frequencies on linear time-invariant (LTI) systems is proposed and validated in real-time experiments. The controller is an observer-based state feedback controller with a time-varying observer system matrix and a time-invariant state feedback gain. For the controller design, the combination of plant and disturbance is modeled as a polytopic linear parameter-varying (pLPV) system and linear matrix inequalities (LMIs) derived from quadratic stability theory and LMIs for an upper bound on the H2 performance are used. The design guarantees closed-loop stability even for arbitrarily fast changes of the varying parameters. The controller is tested on an active noise control headset for a disturbance signal consisting of four harmonics.

LPV Gain-Scheduled Observer-Based State Feedback for Active Control of Harmonic Disturbances with Time-Varying Frequencies

The design of controllers for the rejection of multisine disturbances with time-varying frequencies is considered. The frequencies are assumed to be known. Such a control problem frequently arises in active noise and vibration control (ANC/AVC) applications where the disturbances are caused by imbalances due to rotating or oscillating masses or periodically fluctuating excitations, for example the torque of a combustion engine, and the rotational speed is measured. Application examples are automobiles and aircrafts.

LPV Gain-Scheduled Output Feedback for Active Control of Harmonic Disturbances with Time-Varying Frequencies

In this chapter, the same control problem as in the previous chapter is considered, which is the rejection of harmonic disturbances with time-varying frequencies for linear time-invariant (LTI) plants. In the previous chapter, gain-scheduled observer-based state-feedback controllers for this control problem were presented. In the present chapter, two methods for the design of general gain-scheduled output-feedback controllers are presented. As in the previous chapter, the control design is based on a description of the system in linear parameter-varying (LPV) form. One of the design methods presented is based on the polytopic linear parameter-varying (pLPV) system description (which has also been used in the previous chapter) and the other method is based on the description of an LPV system in linear fractional transformation (LPV-LFT) form. The basic idea is to use the well-established norm-optimal control framework based on the generalized plant setup shown in Fig. 1 with the generalized plantG and controllerK.

Design of structured discrete-time LPV gain-scheduling controllers through state augmentation and partial state feedback

A method to design discrete-time linear parameter-varying (LPV) gain-scheduling controllers with prescribed order through state augmentation and partial state feedback is presented. Prescribed polytopic linear parameter-varying (pLPV) dynamics are added to the plant for the control design using state augmentation. Static state-feedback gains are calculated via convex linear matrix inequalities (LMIs) and interpolated with pLPV techniques. The resulting controller consists of the prescribed pLPV dynamics and the time-varying gains. The order of the controller is fixed and reduced compared to existing approaches. As an example, a sixth-order controller for suppression of a harmonic disturbance with three time-varying frequencies is designed and implemented in real time in an active vibration control (AVC) test bench.

An LPV discrete-time controller for the rejection of harmonic time-varying disturbances in a lightweight flexible structure

In this work, control system design and implementation for active vibration control (AVC) of flexible structures with piezoelectric actuators is studied. The goal is to reduce the effect of harmonic disturbances with known time-varying frequencies acting on a system. As a test bed, a thin flexible aluminum cantilevered beam with two symmetrically bonded piezoelectric actuators is used. The harmonic excitation is generated by two DC motors each of them with an unbalanced mass. A discrete-time model is obtained through black-box system identification methods. The control algorithm design is based on a plant description with a disturbance model as a linear parameter varying (LPV) system in linear fractional transformation (LFT) form. This results in a gain-scheduled controller where the harmonic disturbance frequencies are the scheduling variables. The experimental real-time results show the effectiveness of the controller and its capability to suppress time-varying harmonic disturbances, whose frequencies are measured directly from the DC motors. The design method leads to a controller that stabilizes the closed-loop system even for arbitrarily fast changes in the disturbance frequencies. In the real-time experiment, the controller suppresses a disturbance consisting of two independent harmonics with frequencies that vary over a range of 15 Hz.

TWO-PARAMETER PLPV MODELING OF NONSTATIONARY HARMONICALLY RELATED MULTISINE DISTURBANCES FOR REDUCED-ORDER GAIN-SCHEDULING CONTROL

A two-parameter polytopic linear parameter-varying (pLPV) modeling approach for nonstationary harmonically related multisine disturbances is presented, and a pLPV controller based on this model is introduced. An exact model for disturbances with known nonstationary frequencies is used. The number of the scheduling parameters is reduced to two using the disturbance model presented. The controller only consists of the disturbance model. Therefore, the controller order is the minimal order required for asymptotic disturbance rejection. Experimental results validate the effectiveness of the controller using an active vibration control (AVC) test bed.

H ∞ and state-feedback controllers for vibration suppression in a single-link flexible robot

The demand on more efficient structures has increased the use of lightweight flexible structures in industrial applications. The main objective of this work is to suppress vibration at the free end of a single-link rotational robot subjected to fast movements. The control architecture is made up of two independent control loops; the first loop is employed to control the position of the hub and the second loop is used to attenuate the vibration of the arm. The position control of the hub is achieved through a proportional integral derivative (PID) controller with feedforward gains. The active vibration control (AVC) is achieved implementing two different controllers. An observer-based state-feedback controller and an H∞ suboptimal controller. These are used to damp the first resonance frequency of the system. A pair of piezoelectric patches is used as actuator. The system is considered as a cantilevered beam, and its model is obtained using black box system identification techniques. The inertial force induced by the movement is considered for the second loop as a transient disturbance at the measure point. The arm with a payload is subjected to different joint trajectories, which excites the free vibration mode of the arm at the end of the movement. Experimental results show the effectiveness of the observer-based state-feedback controller and suboptimal H∞ controllers for the rejection of this unwanted vibration. The controllers are capable of suppressing the disturbance in a short period of time.