Multirate Control Systems Research Articles

Distributed Multirate Control of Battery Energy Storage Systems for Power Allocation

With the increasing integration of intermittent energy sources into the smart grid, distributed battery energy storage systems (DBESSs) are employed to balance power generation and demand. Power allocation among DBESSs plays an important role in maintaining the stability of energy systems. So far, the control of DBESSs has focused on either continuous-time control for continuous-time battery dynamics or discrete-time control for discretized battery dynamics. However, in realistic industrial applications, DBESSs have continuous-time dynamics in nature, and their control is implemented on digital controllers. To tackle this issue, a distributed multirate control system is designed in this article for continuous-time DBESSs. It allocates power by keeping the same relative State-of-Charge (SoC) variation rate for all DBESSs. For the accurate computation of the output/input power without global information, the control strategy consists of distributed multirate estimators each for a DBESS. The operating rate of the estimation algorithm is designed multiple times higher than the sampling rate of the measurement of battery and the sampling rate of the battery controller. With the proposed multirate estimator, a smaller estimation error is achieved. The same relative SoC variation rate and the stability of closed-loop system can be guaranteed. Simulation studies are given to demonstrate the effectiveness of the proposed control strategy.

Design of Multi-Rate Multi-Zone Wireless Fuzzy Temperature Control System for Greenhouse Application

sensor sampling rate (SSR) may be an effective and crucial field in networked control systems. Changing sensor sampling period after designing the networked control system is a critical matter for the stability of the system. In this article, a wireless networked control system with multi-rate sensor sampling is proposed to control the temperature of a multi-zone greenhouse. Here, a behavior based Mamdany fuzzy system is used in three approaches, first is to design the fuzzy temperature controller, second is to design a fuzzy gain selector and third is to design a fuzzy error handler. The main approach of the control system design is to control the input gain of the fuzzy temperature controller depending on the current zone and current sensor rate for each zone. Due to the low input gain of the fuzzy controller, the steady state output error of the greenhouse temperature is in the range (0.55 – 11.22) % when the system using five sensors of different sampling rates and in the range (2.43 - 16.74) % when the system using five sensors with the same sampling rates. Next, after designing the fuzzy error handler, this error doesn’t exceed 1.6%, but in most cases it is less than 0.15%.The work is Simulink designed and implemented using Matlab R2012b. The Zigbee wireless network is proposed for the system, it is implemented in Matlab using True time 2.0 library.

Design of a Multi-rate Control System Using Null-Space in State-space Representation

Design of a Multi-rate Control System Using Null-Space in State-space Representation

State Estimation Based on Multirate Kalman Filter for Power Systems Driven by Switching Inverter

This paper presents a design methodology of a Kalman filter for a multirate control system with a fast input system. There are many applications whose sensory system is slower than the input system in a power system. The sensory system is required to perform fast sensing while ensuring a low signal-to-noise ratio, although it requires additional time compared with that of a low-resolution converter. The Kalman filter is an effective tool in such a situation and it estimates parameters while eliminating noise. Because the optimality of this filter is ensured when the system model and noise variance on the system are well identified, rigorous discretization should be considered on the multirate control system. With this in mind, the paper presents the design method of a multirate Kalman filter as is the case for a single-rate controller. Further, the noise variance and oversampling ratio of the multirate controller is confirmed using the Monte Carlo method. Numerical simulation of a voltage inverter theoretically validates the design methodology.

Design of a multi-rate control system in state-space representation using input redundancy

Design of a multi-rate control system in state-space representation using input redundancy

Reduction of Quantization Error in Multirate Output Feedback Control

[abstFig src='/00280005/04.jpg' width='250' text='Multirate output feedback control' ] In the new design method we propose for a multirate output feedback control system, the hold interval of control input is longer than the sampling interval of plant output. In this system, unknown state variables are calculated using control input and plant output without observers. The multirate output feedback control system has been extended by introducing new design parameters that are designed independent of the calculation of the state variable. To our knowledge, however, no systematic design scheme has ever been proposed for design parameters in this case. In this study, quantization error is dealt with statistically and design parameters are decided to minimize quantization error.

Design Method for Improvement of Transient-State Intersample Output of Multirate Systems Including Integrators

[abstFig src='/00280005/12.jpg' width='300' text='Comparison of output responses' ] This paper discusses a design method for a multirate system including integrators, where the update interval of the control input is shorter than the sampling interval of the plant output. In such a multirate control system, intersample output might oscillate between sampled outputs in the steady state even if the sampled output converges to the reference input. This is because the control input can be updated between the sampled outputs. In a conventional method, a predesigned control law is extended such that the steady-state ripples are eliminated independent of a discrete-time response. However, the conventional method is invalid when integrators are included in a controlled plant. In this study, a difference operation in discrete time is used to address this issue. Moreover, the transient-state intersample response is improved independent of a pre-designed discrete-time response.

Guaranteed Cost Control for Multirate Networked Control Systems with Both Time-Delay and Packet-Dropout

Compared with traditional networked control systems, the sampling rates of the nodes are not the same in the multirate networked control systems (NCSs). This paper presents a new stabilization method for multirate NCSs. A multirate NCSs with simultaneous considering time-delay and packet-dropout is modeled as a time-varying sampling system with time-delay. The proposed Lyapunov function deceases at each input signal updating point, which is largely ignored in prior works. Sufficient condition for the stochastic mean-square stability of the multirate NCSs is given, and the cost function value is less than a bound. Numerical examples are presented to illustrate the effectiveness of the proposed control scheme.

Fundamental Issues and Prospective Directions in Networked Multirate Control Systems

In view of the synchronized uniform equidistant sampling method that is widely used in network control systems (NCSs), multirate sampling control for NCSs is presented by considering the natural characteristics of NCSs. Two kinds of typical structures of network multirate control systems (NMCSs) are presented and the multirate sampling mechanisms are formulated. Then, fundamental issues and prospective directions in NMCSs are preliminarily discussed. The contents involve modeling, sampling pattern selection, control strategies, scheduling algorithms, and codesign of NMCSs. The purpose of this paper is to arouse more attention of researchers in related subjects, so that a complete theory for NCSs can be established.

Design of the Noise Response Independent of the Sampled Response in a Multi-rate System

This paper proposes a new method for designing a multi-rate control system, in which the sampling interval of the plant output is an integer multiple of the hold interval of the control input. The objective of this study is to enhance a noise response without changing an existing closed-loop transfer function. To this end, an existing control law is redesigned independent of the closed-loop transfer function. In this study, the noise response is designed independent of the sampled reference response, and the effectiveness of the proposed method is shown.

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.

Robust Explicit Solution of Multirate Predictive Control System with External Disturbances

This paper considers the problem of robust predictive control for a class of uncertain multirate systems, in which the output sampling period is several times larger than the one of input updating. By means of dynamic programming and multiparametric quadratic programming (mp-QP) techniques, this work proposes a novel robust explicit model predictive control (REMPC) algorithm such that the higher on-line updating speed of input can be attained. Firstly, the optimization problem is decomposed into several subproblems. For each subproblem, a constraint condition only involving current state and input is constructed. Then taking current state and future inputs as parameter variables we can obtain a robust explicit solution for the new reformulated optimization subproblem by mp-QP method. Especially, by choosing a maximal robust positive invariant set as the terminal constraint set of the optimization problem, closed-loop robust stability of the multirate control system subject to external disturbance can be guaranteed. Finally, a numerical simulation is given to show the effectiveness of the proposed method.

Multi-rate digital redesign of cascaded and dynamic output feedback systems

In this paper, a new indirect digital redesign method is presented for multi-rate sampled-data control systems with cascaded and dynamic output feedback controllers. These analogue controllers are often pre-designed based on desirable frequency specifications, such as bandwidth, natural angular frequency, etc. To take advantage of the digital controller over the analogue controller, digital implementation of these analogue controllers are often desirable. As only measured input-output signals are available, an ideal state reconstructing algorithm is utilised to obtain the multi-rate discrete-time states of the original continuous-time system. Based on the Chebyshev quadrature method, the gains of the multi-rate cascaded and the output feedback digital controllers are determined from their continuous-time counterparts according to the different sampling rates employed in the different parts of the closed-loop system. As a result, the respective analogue controllers with the high-frequency and low-frequency characteristics can be implemented using the respective fast-rate sampling and slow-rate sampling digital controllers. Unlike the classical direct bilinear transform method, which is an open-loop direct digital redesign method, the proposed digital controllers take into account the state-matching of the original continuous-time closed-loop system and the digitally redesigned sampled-data closed-loop system. To further improve the state-matching performance, an improved digital redesign approach is also developed to construct the multi-rate cascaded and dynamic output feedback digital controllers. Illustrative examples are given to demonstrate the effectiveness of the developed methods.

Design of a multirate PD control system for improvement in the steady-state intersample response

The present paper proposes a new design method for a multirate system, in which the continuous-time plant is controlled by updating the discrete-time control input, in which the sampling interval of the plant output is an integer multiple of the hold interval of the control input. In the multirate system, the intersample response might oscillate even if the sample response converges to the reference response because the control input can vary between sampling instants. In the present paper, a multirate proportional-derivative control system is enhanced such that the steady-state intersample ripples are eliminated. In the proposed method, the intersample response can be improved independently of the sample response because an existing closed-loop response is maintained. Moreover, the control performance is not affected by the phase lag caused by the integral compensation because the integral compensation is not used for the elimination of the intersample ripples. Finally, in order to control a plant with unknown or time-varying parameters, the designed multirate control system is extended to a self-tuning controller. As a result, an unknown or time-varying plant can be controlled using the proposed method.

Two-Degree-of-Freedom Design for Integral Compensation in a Multirate Control System

Two-Degree-of-Freedom Design for Integral Compensation in a Multirate Control System

Robust Repetitive Perfect Tracking Control of HDDs Based on Re-learning Scheme

This paper presents an improved method of a repetitive controller based on perfect tracking control (PTC) in order to reject the variable repeatable runout (RRO) of hard disk drives (HDDs). The author's group proposed repetitive PTC (RPTC) with a switching mechanism. RPTC is realized by using periodic a signal generator (PSG) and PTC. The PSG produces a feedforward signal from the periodic disturbance, and the PTC generates a control input to cancel the periodic error in the steady state. However, we have not considered the difference between the RROs of tracks. This paper proposes a re-learning scheme by taking into account the correlation of adjacent tracks. Finally, the advantages of RPTC using the proposed scheme are demonstrated through simulations and experiments using a hard disk drive equipment with discrete track recording media (DTR). Head-positioning controllers of hard disk drives (HDDs) are generally composed of two control modes: the track- seeking mode and the track-following mode. High-speed po- sitioning and small residual vibration are important in the track-seeking mode, and the disturbance rejection perfor- mance is important in the track-following mode. Digital two-degree-of-freedom controllers generally have two samplers for the reference signal r(t) and the output y(t), and one holder on the input u(t). Therefore, there exist three time periodsTr, Ty ,a ndTu which represent the sampling time of r(t), y(t), and u(t), respectively. In the case of HDDs, the position error is detected by the discrete servo signals em- bedded in the disks. Therefore, the output sampling period Ty is decided by the number of these signals and the rotation frequency of the spindle motor. However, it is possible to set the control period Tu shorter than Ty because of the recent de- velopment of microprocessor. Thus, the servo system can be regarded as a multirate control system where Tu ≤ Ty. Then, many multirate controllers have been proposed both for the track-seeking mode and the track-following mode (1)-(3) . Recently, magnetic printing media, discrete track record- ing media (DTR) and pre-formatted media with perpendicu- lar anisotropy are studied for high track density as new gen- eration media (4) . These new generation media can record servo information in the manufacturing process of disks al- though the conventional disk uses servo track writers after disks are installed in drives. This improved technology can provide high recording density compared with conventional disks. However, it is known that the servo information of these pre-formatted media generally has large decentering from the rotating center. Therefore, higher track-following

An efficient explicit algorithm for multi-rate predictive control systems

In this paper, explicit model predictive control (MPC) schemes for discrete-time linear-invariant multi-rate systems with constraints on inputs and states are studied. An efficient multi-rate predictive control algorithm is proposed by solving a multiparametric linear programming (mp-LP), and the explicit state feedback control laws are developed. Further, based on the closed-loop multi-rate piecewise affine (PWA) structure, stability analysis is presented by linear matrix inequality (LMI). The simulation results show the effectiveness of the explicit MPC for multi-rate system.

H∞Control for Multirate Networked Control Systems with Deadband Scheduling

This paper is concerned with the problem ofH∞control for multirate networked control systems with deadband scheduling policy and transmission delay. The transmission deadbands are set at the sensor nodes and the controller nodes to reduce the network traffic, and then the systems are modeled as discrete-time switch system with uncertain parameters. Using the Lyapunov theory, a robustH∞controller is designed to maintain the asymptotic stability of the closed-loop systems. Finally, a simulation example is presented to show the advantage of the deadband scheduling policy and the efficiency of the proposed theoretical results.

Optimal State Feedback Control in Operator Domain for Multi-Rate Networked Control Systems with Long Time Delay

By multi-rate networked control systems (NCS), we mean the sampling periods of the sensor, the controller and the actuator in networked control systems are not the same, that is to say there are more than one sampling rate in networked control systems. For the long time delay multi-rate NCS with event-driven controller and actuator, a stochastic discrete model is established under operator. The state feedback control laws for the multi-rate NCS in operator domain are designed by using a dynamic programming approach. The derived optimal LQG controller can be used as a delay-compensator for multi-rate NCS with long time delays. An example is given to verify the theory results of this paper.

RST controller design for a non-uniform multi-rate control system

In this work, a non-uniform multi-rate controller which includes an RST control stage is introduced. Due to several issues, in some systems the use of non-uniform (irregular) multi-rate sampling becomes inevitable. When using a uniform (regular) multi-rate controller in this kind of situations, control performance is usually degraded (if it is compared to that obtained in the nominal, uniform sampling context). Thus, the design of a non-uniform controller proper for this sampling scheme is needed to keep the performance. A sequence of different non-uniform sampling frames can be considered, and different controllers must be designed for each frame using appropriate methods. When switching among these controllers, stability problems can appear. So, the control system stability will be assured in terms of Linear Matrix Inequalities (LMIs). To achieve some advantages at the design step, the discrete-time input–output representation will be used. But, since the classical, uniform z−i delay operator could not be able to represent non-uniform sampling situations, the so-called non-uniform operator will be required. Simulation results illustrate that this control proposal is able to keep control system performance and preserve stability.