Multirate Control Scheme Research Articles

Multirate Harmonic Compensation Control for Low Switching Frequency Converters: Scheme, Modeling, and Analysis

Using the grid-interfacing voltage-source converters (VSCs) to perform harmonic control as a smart ancillary function is increasingly studied in recent years. Different from the traditional dedicated harmonic compensation converters, the main function of the high-power smart converters is still delivering real power at a low switching frequency (e.g., 2 kHz). It is challenging to compensate harmonics with low switching frequency VSCs due to the low sampling rate and large system delay. This article proposes a multirate control scheme and derives the accurate multirate model to improve harmonic control. The multirate control scheme consists of high-rate harmonic control and synchronous sampled fundamental control. With the proposed control scheme, the advantages of the conventional synchronous sampling method and the benefits of the high sampling rate are achieved simultaneously. To accurately model the low switching VSC with two different sampling rates, the lifting method is introduced to achieve the discrete-time system model for this linear periodic time-varying system. The frequency response and stability analysis are carried out based on the lifted model. The modeling method, as well as the enhanced harmonic control performance of the multirate control structure, is validated in the experiments.

Sampled-data stabilization of a class of lower-order nonlinear systems with input delays based on a multi-rate control scheme

This paper focuses on the problem of sampled-data stabilization for a class of low-order lower-triangular nonlinear systems with large input delays. A new predictor-based multi-rate sampled-data control scheme is proposed to guarantee that the resulting system is globally strongly stable under some assumptions. Compared with the existing methods, the present strategy just needs to know the approximate prediction of state variables, and the stabilizing performance of a given continuous-time feedback controller can be preserved at the sampling instants. It is noted that the proposed controller takes the form of a power series. Its truncation at a finite order is regarded as approximate controller which is proved to be effective in the practical implementation. Two simulation examples are finally given to illustrate the advantages and effectiveness of the proposed control scheme.

Vehicle Path Prediction Using Yaw Acceleration for Adaptive Cruise Control

In this paper, we propose a vehicle path prediction employing yaw acceleration for adaptive cruise control (ACC). First, a path prediction method employing yaw acceleration is proposed to improve the path prediction performance of ego vehicles. In the proposed method, the vehicle path is predicted by using a clothoidal cubic polynomial curve model, and for this purpose, the curvature rate, yaw rate, and longitudinal velocity are required. The curvature rate can be mathematically obtained by differentiating the yaw rate without a camera sensor. To obtain the yaw acceleration from the noisy measured yaw rate, we derive the state-space model from the steer wheel angle for the yaw rate. Then, the KF is designed by using the state-space model to estimate the yaw acceleration. Second, a multirate longitudinal control method is proposed to improve the longitudinal control performance. The multirate KF employs the constant acceleration model in order to estimate the relative distance and velocity of the target vehicle at a faster sampling rate. Then, the desired acceleration is achieved to maintain a safe headway distance or velocity by means of the longitudinal controller. Consequently, the whole ACC system operates with a faster sampling rate so that multirate control scheme reduces ripples in both the relative longitudinal distance and the desired acceleration. The performance of the proposed method was evaluated via simulations and experiments.

Rejecting fast narrow-band disturbances with slow sensor feedback for quality beam steering in selective laser sintering

A fundamental problem arises in feedback control when the system is subject to fast disturbances but can only get slowly updated sensor feedback. The problem is particularly challenging when the disturbances have frequency components near or beyond the sensor’s Nyquist sampling frequency. Such difficulties occur to selective laser sintering, an additive manufacturing process that employs galvo scanners to steer high-power laser beams and relies on non-contact, slow sensing such as visual feedback to enhance the product quality. In pursuit of addressing the fundamental challenge in quality control under slow sensor feedback, this paper introduces a multi-rate control scheme to compensate beyond-Nyquist disturbances with application to selective laser sintering. This is achieved by designing a special bandpass filter with tailored frequency response beyond the slow Nyquist frequency of the sensor, along with integrating model-based predictor that reconstructs signals from limited sensor data. Verification of the algorithm is conducted by both simulation and experimentation on a galvo scanner that directs the energy beam in the additive manufacturing process.

Nonlinear discrete-time multirate adaptive control of non-linear vibrations of smart beams

The nonlinear adaptive digital control of a smart piezoelectric beam is considered. It is shown that in the case of a sampled-data context, a multirate control strategy provides an appropriate framework in order to achieve vibration regulation, ensuring the stability of the whole control system. Under parametric uncertainties in the model parameters (damping ratios, frequencies, levels of non linearities and cross coupling, control input parameters), the scheme is completed with an adaptation law deduced from hyperstability concepts. This results in the asymptotic satisfaction of the control objectives at the sampling instants. Simulation results are presented.

Disturbance observer-based multirate control for rejecting periodic disturbances to the Nyquist frequency and beyond

Intersample behavior cannot be ignored when a sampled-data control system is subject to periodic disturbances beyond the Nyquist frequency. In this paper, a disturbance observer-based multirate control scheme is proposed to deal with such a periodic disturbance problem. First, using discrete-time Fourier series, the effect of the periodic disturbance on steady-state response of the plant output including intersample information is derived. Next, based on the steady-state output response, a sufficient condition is provided for minimization of the disturbance effect on the output. It turns out that solving the sufficient condition is a problem of quadratic optimization with several equality constraints. The proposed approach is applied on vibration control of mechanical resonant modes beyond the Nyquist frequency in a commercial hard disk drive. Perfect disturbance elimination and disturbance deduction of 72% in fast-rate discrete-time response are observed in the simulation and experiment, respectively.

Sliding mode-based control of thin Shape Memory Alloy actuators using a spatial hysteresis approximation

Shape Memory Alloy (SMA) actuators rely their operation on a thermally driven phase change. The SMA’s stroke position control problem thus involves the material temperature in a direct or indirect way. In thin SMA actuators, deviations between the actual and the estimation of the temperature profile can affect the performance of model-based control. In this work, an intermediary strategy, between a model-free and a model-based one, is proposed, where local approximations to the hysteretic trajectories are used in place of a complete hysteresis description. The localized trajectory is then spatially shifted to encapsulate the hysteretic behavior. A sliding mode based controller is constructed by this implementation exhibiting accurate tracking behavior. The advantages against existing model-free controllers are further investigated over a multi-rate control scheme. The results show that efficient tracking position control can be reached even at very low output feedback frequencies.

Multirate adaptive control of uncertain resonances beyond the Nyquist frequency in high-performance mechatronic systems

In this paper, an add-on multirate adaptive control scheme is proposed to compensate for uncertain mechanical resonant modes beyond the Nyquist frequency in mechatronic systems. The multirate adaptive controller is incorporated into the existing sampled-data control system sampled at a slow rate. To integrate well with the pre-designed feedback controller, an auxiliary error instead of the regulation error is utilized to design the multirate adaptive controller. By using a polynomial transformation technique and a recursive least-squares algorithm with a dead-zone, the proposed multirate adaptive control ensures boundedness of all the closed-loop signals and convergence of the auxiliary error. Our simulation and experimental results on the head-positioning servo control system of a hard disk drive demonstrate the effectiveness of our proposed compensation scheme in attenuating the vibration for uncertain resonances beyond the Nyquist frequency.

Robust Multirate Control Scheme With Predictive Virtual Lanes for Lane-Keeping System of Autonomous Highway Driving

In this paper, we propose a new approach for a robust multirate lane-keeping control scheme with predictive virtual lanes. First, the multirate lane-keeping control scheme is proposed to improve the lane-keeping performance and to reduce the ripple in the yaw rate. To improve the lane-keeping performance on a curved road, the integral of the lateral offset error is added to the state feedback controller. A multirate Kalman filter (KF) has been developed to resolve the problems caused by slow lane detection due to the vision processing system. This multirate KF estimates vehicle states at a fast rate using a microprocessor. Utilizing the estimated states, the linear quadratic state feedback control operates at the same fast update rate of the microprocessor. Thus, a multirate control scheme can reduce the ripple in the yaw rate. Second, we propose a virtual lane prediction method that compensates for the momentary failure of lane detection from unexpected problems. If the camera sensor momentarily fails while obtaining lane information, the predicted virtual lane can be substituted for the lane detection using the camera sensor in the proposed control scheme. Thus, the proposed control scheme can normally operate when the lane information is momentarily unavailable. The performance of the proposed method was evaluated via experiments.

A non-uniform multi-rate control strategy for a Markov chain-driven Networked Control System

In this work, a non-uniform multi-rate control strategy is applied to a kind of Networked Control System (NCS) where a wireless path tracking control for an Unmanned Ground Vehicle (UGV) is carried out. The main aims of the proposed strategy are to face time-varying network-induced delays and to avoid packet disorder. A Markov chain-driven NCS scenario will be considered, where different network load situations, and consequently, different probability density functions for the network delay are assumed. In order to assure mean-square stability for the considered NCS, a decay-rate based sufficient condition is enunciated in terms of probabilistic Linear Matrix Inequalities (LMIs). Simulation results show better control performance, and more accurate path tracking, for the scheduled (delay-dependent) controller than for the non-scheduled one (i.e. the nominal controller when delays appear). Finally, the control strategy is validated on an experimental test-bed.

Multirate sliding mode disturbance compensation for model predictive control

SummaryIn this paper, a novel hierarchical multirate control scheme for nonlinear discrete‐time systems is presented, consisting of a robust nonlinear model predictive controller (NMPC) and a multirate sliding mode disturbance compensator (MSMDC). The proposed MSMDC acts at a faster rate than the NMPC in order to keep the system as close as possible to the nominal trajectory predicted by NMPC despite model uncertainties and external disturbances. The a priori disturbance compensation turns out to be very useful in order to improve the robustness of the NMPC controller. A dynamic input allocation between MSMDC and NMPC allows to maximize the benefits of the proposed scheme that unites the advantages of sliding mode control (strong reduction of matched disturbances, low computational burden) to those of NMPC (optimality, constraints handling). Sufficient conditions required to guarantee input‐to‐state stability and constraints satisfaction by the overall scheme are also provided. Copyright © 2014 John Wiley & Sons, Ltd.

A new algorithm for dual-rate systems frequency response computation in discrete control systems

This paper addresses an easy computation of the multiple components of the response to a sinusoidal input of a dual-rate linear time-invariant discrete system from the Bode diagram of LTI systems arising from a lifted representation. Based on those results, a generalized Bode diagram is suggested. Some new conclusions derived from this conceptual interpretation are introduced. This diagram provides a better insight in the frequency-response issues in multivariable control than the standard singular value decomposition of the lifted model. As an application, the output ripple suppression in a multirate control scheme is presented.

Multi-rate tracking controller analysis and design for target tracking systems

As the sampling rates of the inner loop and the outer loop of the target tracking control system are different, a typical digital multi-rate control system was formed. If the traditional single-rate design method was applied, the low sampling rate loop will seriously impact the dynamical characteristic of the system. After analyzing and calculating the impact law of the low sampling rate loop to the bandwidth and the stability of the tracking system, a kind of multi-rate control system design method was introduced. Corresponding to the different sampling rates of the inner loop and the outer loop, the multi-rate control strategy was constituted by a high sampling rate sub-controller and a low sampling rate sub-controller. The two sub-controllers were designed separately and connected by means of the sampling rate converter. The low sampling rate controller determined the response rapidity of the system, while the high sampling rate controller applied additionally effective control outputs to the system during a sampling interval of the low sampling rate controller. With the introduced high and low sampling rates sub-controllers, the tracking control system can achieve the same performance as a single-rate controller with high sampling rate, yet it works under a much lower sampling rate. The simulation and experimental results show the effectiveness of the introduced multi-rate control design method. It reduces the settling time by 5 times and the over shoot by 4 times compared with the PID control.

Decentralized Hierarchical Multi-Rate Control of Constrained Linear Systems

AbstractThis paper proposes a decentralized hierarchical multi-rate control scheme for large-scale dynamically-coupled linear systems subject to linear constraints on input and state variables. At the lower level, a set of decentralized and independent linear controllers stabilizes the process, without taking care of the constraints. Each controller receives reference signals from its own upper-level controller, that runs at a lower sampling frequency. By optimally constraining the magnitude and rate of variation of the reference signals to each lower-level controller, quantitative criteria are provided for selecting the ratio between the sampling rates of the upper and lower layers of control at each location, in a way that closed-loop stability is preserved and the fulfillment of the prescribed constraints is guaranteed.

A Nonlinear Model Predictive Control Scheme with Multirate Integral Sliding Mode

In this paper, a hierarchical multirate control scheme for nonlinear discrete-time systems is proposed, composed of a robust model predictive controller (MPC) and a multirate integral sliding mode (MISM) controller. In particular, the MISM controller acts at a faster sampling time than the MPC controller, and reduces the effect of model uncertainties and external disturbances, in order to obtain, at the next sampling instant of the MPC controller, a value of the system state that is as close as possible to the nominal one. To obtain this result, the control variable is composed of two parts: one generated by the MPC controller, and the other by the MISM controller. The a-priori reduction of the disturbance terms turns out to be very useful in order to improve the convergence properties of the MPC controller.

Automatic Vision-Based Optical Fiber Alignment Using Multirate Technique

Automatic optical fiber alignment is the key to reducing the cost of the packaging process for the manufacturing of fiber-optic devices. This paper develops a vision-based active optical fiber alignment technique for coarse positioning using a piezoactuated moving platform that is controlled to reduce the alignment difference to within a certain degree. To overcome the adverse effect of the delay time between the motion control system and the vision system, the methodology based on the multirate control scheme is presented. Experimental results verify the effectiveness of the proposed approach.

Stable Haptic Display of Slowly Updated Virtual Environment With Multirate Wave Transform

This paper proposes a control method that overcomes the instability of a haptic interface arising from both the slow update rates of the virtual environment (VE) and the time delay in a communication line. The instability arising from the time delay in a communication line can be overcome using the wave variables since the time delay on the wave variables becomes passive. The so- called multirate control scheme is applied to cope with the problems presented by the slow update rates of the VE. Since digital sample and hold (rate transitions) can be represented as a series of time delay, the passive nature of time delay on the wave variables is applied. By computing the norm of the scattering matrix, it was verified that rate transitions on the wave variables become passive, so a stable haptic interface was derived with the multirate wave transform. Various experiments have shown that a stable force display can be achieved with the multirate wave transform.

Multirate Digital Servo Drive Based on Acceleration Observer and Disturbance Compensator

This paper presents a digital servo driver that realizes a novel multirate feedback controller based on position, velocity and acceleration feedback. The velocity and acceleration signals are firstly estimated by state observer using optical encoder information, and the estimated velocity is fed into discrete disturbance observer (DDOB) to estimate and compensate the external disturbance. In this scheme, controller with acceleration feedback can be realized by replacing the current loop with acceleration loop. When the DC servo motor is controlled by the proposed acceleration feedback control with disturbance compensation, the total servo system from acceleration to position becomes the acceleration controlled system which is fixed to a nominal double integral dynamics in the presence of parameter variation and torque disturbance. Hence, the fast and precise position control can be carried out easily. The proposed acceleration feedback controller and PD position feedback controller are evaluated experimentally on a DSP, which is implemented multirate control scheme, controlled DC servo motor positioning system. The experimental results show that this digital servo system is robust and remarkably sustains the same performance compared to the single fast rate control scheme.

Preservation of input-to-state stability under sampling and emulation: multi-rate case

The stabilization problem of sampled-data non-linear systems is considered under the low measurement rate constraint. A multi-rate control scheme is proposed that utilizes a numerical integration scheme to approximately predict the current state. We show that if we design a continuous-time controller for a continuous-time plant so that the closed-loop continuous-time system is input-to-state stable and then discretize the controller and implement it using sample and zero order hold devices, then input-to-state stability property will be preserved for the sampled-data multi-rate closed loop system in a practical sense.

A new method of multirate state feedback control with application to an HDD servo system

This paper discusses the redesign method for state feedback multirate control with current estimator. A computationally effective multirate digital control scheme, in which the control outputs are calculated based only on the state estimates at sampling instants, is presented. It is shown that the states of the redesigned state feedback multirate control system match the states of conventional state feedback multirate control system at every sampling instant. This conclusion is further supported by the analysis in frequency domain. The redesigned method is applied to a HDD servo control systems. The experimental results show that the performance of the redesigned multirate system is similar to that of the conventional multirate design in terms of open loop bandwidth, stability margins and tracking performance.