Multirate Output Research Articles

Design of event trigger based multirate sliding mode load frequency controller for interconnected power system

This paper proposes an event triggered (ET) multi-rate output feedback sliding mode control technique for load frequency control (LFC) in multi-area interconnected power systems. Uncertainties and disturbances are commonly found in LFC problem. The designed controller attains quasi sliding mode in discrete time (DT) for linear time invariant (LTI) interconnected power executing system with limited matched variability. Event-triggered control is used to minimalize the control updates resulting in reduced utilization of resources. The ET rule is designed using Lyapunov stability analysis. The efficacy of the presented controller in the presence of generation rate constraint (GRC) and governor dead band (GDB) is authenticated through simulation results. A comparative study of the proposed controller and the reported ET control scheme for power executing system is also presented for a peer-reported two-area power executing system.

Advanced Nonswitching Discrete Time Sliding Mode Control for Speed Tracking of a DC Motor

In this article, a detailed analysis of fast output sampling (FOS)-based multirate output feedback (MROF) technique is done in the context of discrete time sliding mode control (DTSMC) based on nonswitching reaching law. In addition, for better performance and improved robustness, the relative degree of the sliding variable is chosen as two instead of one. Quantitative analysis of robustness in terms of ultimate band for the relative degree two (RD2) approach is done and compared with that of relative degree one (RD1) approach. First, only RD1 and RD2 approaches are proposed for speed tracking of a dc motor under parametric uncertainty. Then the same task is done using MROF-based RD1 and RD2 approaches. The proposed work is validated experimentally and is used for tracking a reference speed of a dc motor.

Adaptive observer design for a class of Lipschitz nonlinear systems with multirate outputs and uncertainties: Application to attitude estimation with gyro bias

AbstractThe design of an adaptive observer for a class of multi‐input multi‐output Lipschitz nonlinear systems with uncertainties and multirated outputs is proposed in this paper. The sampling instants of the different outputs can be asynchronous and irregular. The exponential convergence of the proposed observer is proved with the help of a Lyapunov approach. The stability is ensured, provided that some conditions, including a persistent excitation condition and a maximum value condition on the sample rate of each output, are verified. The performances of the observer are illustrated through simulations of the attitude estimation problem using sensors from an inertial measurement unit and considering gyro bias.

On-line model identification for the machining process based on multirate process data

Accurate identification of the model parameters of the machining process based on on-line process data is a crucial prerequisite for its model-based control and diagnostics. A typical machining process generates multi-output and multirate data streams. Whereas various sensors provide in-process information about the process, many important process outcomes including product qualities can be only measured in postprocess manner. This paper proposes to improve the identification by using both in-process and postprocess data and by analyzing the identifiability of model parameters. The identification of the model parameters based on multirate output is formulated using the maximum-likelihood estimation and the Fisher information matrix for a multirate-sampled system is derived to study the identifiability of model parameters. A strategy is developed to improve accuracy and robustness of the model identification considering the identifiability. The proposed method is tested on two batches of multirate process data from the cylindrical grinding process. The test results demonstrate using both in-process and postprocess data improves the identifiability and the proposed identification strategy results in improved prediction performance.

Output feedback based event-triggered sliding mode control for delta operator systems

In this paper, we present an output feedback based design of event-triggered sliding mode control for delta operator systems. For discrete-time systems, multi-rate output sampling based state estimation technique is very useful if the output information is available. But at high sampling rates, the discrete-time representation of the system using shift operator becomes numerically ill-conditioned and as a result, the observability matrix becomes singular as the sampling period tends to zero. Here, a new formulation of multi-rate state estimation (MRSE) for a small sampling period is presented. We first propose a new observability matrix and then discuss its relationship with the observability matrix defined in the conventional sense. For the delta operator system with matched uncertainty, we have presented the design of MRSE based sliding mode control (SMC). Additionally, to make the control efficient in terms of resource utilization, MRSE based event-triggered SMC is proposed. The absence of Zeno phenomenon is guaranteed as the control input is inherently discrete in nature. Finally, the effectiveness of the proposed method is illustrated through numerical simulations, considering a ball and beam system and a general linear system as a numerical example.

Multirate output feedback-based robust sensorless control of doubly-fed induction motor

A robust sensorless control of doubly-fed induction motor (DFIM) is proposed in this paper. The stator of the DFIM is connected to the grid and the rotor is fed via controlled voltage source. Since the speed or flux measurement is not used, the sensorless control is achieved by using multirate output feedback (MROF)-based output feedback technique. The robustness towards parametric variations and matched disturbances is achieved by using MROF-based sliding mode control (SMC). The linear equations of doubly-fed induction motor are utilised for application of MROF and the state reference commands are computed from torque and speed reference commands separately. The proposed MROF-SMC controller is shown to be tracking given torque and speed commands.

Multirate output feedback-based robust sensorless control of doubly-fed induction motor

Multirate output feedback-based robust sensorless control of doubly-fed induction motor

Robust soft sensor development using multi-rate measurements

Two different types of measurements are often available for the key quality variables in process industries - (a) an accurate “slow-rate” laboratory measurements, and (b) a less accurate “fast-rate” online analyser measurements. Also, the analyser measurements are prone to fail due to hardware issues. Therefore, the main objective of this work is to present a novel approach for developing an accurate, fast-rate, inferential model of quality variables which is robust to outliers. For this purpose, we present a maximum likelihood based approach to integrate the multi-rate output data in the model building task, using Expectation Maximization algorithm. The efficacy of the proposed approach is demonstrated using a simulation example.

On the Zero-Freeness of Tall Multirate Linear Systems

In this paper, tall discrete-time linear systems with multirate outputs are studied. In particular, we focus on their zeros. In systems and control literature zeros of multirate systems are defined as those of their corresponding time-invariant blocked systems. Hence, the zeros of tall blocked systems resulting from blocking of linear systems with multirate outputs are mainly explored in this work. We specifically investigate zeros of tall blocked systems formed by blocking tall multirate linear systems with generic parameter matrices. It is demonstrated that tall blocked systems generically have no finite nonzero zeros; however, they may have zeros at the origin or at infinity depending on the choice of blocking delay and the input, state and output dimensions.

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.

Multirate Output Feedback Based Stochastic Sliding Mode Control

In this paper, a multirate output feedback (MROF) based discrete-time sliding mode control for the stochastic system with slowly varying bounded uncertainty is proposed. The states are estimated by the multirate Kalman filter and are used for designing the stochastic sliding mode controller which guarantee the stability under the bounded uncertainty and the uncertain noise covariance. The proposed algorithm has advantage of computational and implementation simplicity as it requires only the past output and input information. The stochastic sliding band (SSB) is also calculated which is found to be wider as compared to the state feedback case. Finally, the design procedure for stochastic sliding mode controller is demonstrated with an illustrative example.

Investigation of Spatial Control Strategies for AHWR: A Comparative Study

Large nuclear reactors such as the Advanced Heavy Water Reactor (AHWR), are susceptible to xenon-induced spatial oscillations in which, though the core average power remains constant, the power distribution may be nonuniform as well as it might experience unstable oscillations. Such oscillations influence the operation and control philosophy and could also drive safety issues. Therefore, large nuclear reactors are equipped with spatial controllers which maintain the core power distribution close to desired distribution during all the facets of operation and following disturbances. In this paper, the case of AHWR has been considered, for which a number of different types of spatial controllers have been designed during the last decade. Some of these designs are based on output feedback while the others are based on state feedback. Also, both the conventional and modern control concepts, such as linear quadratic regulator theory, sliding mode control, multirate output feedback control and fuzzy control have been investigated. The designs of these different controllers for the AHWR have been carried out using a 90th order model, which is highly stiff. Hence, direct application of design methods suffers with numerical ill-conditioning. Singular perturbation and time-scale methods have been applied whereby the design problem for the original higher order system is decoupled into two or three subproblems, each of which is solved separately. Nonlinear simulations have been carried out to obtain the transient responses of the system with different types of controllers and their performances have been compared.

Optimal Preview Control for Discrete-Time Systems in Multirate Output Sampling

This paper studies the disturbance preview optimal control problem for discrete-time systems with multirate output sampling. By constructing the error system and using the discrete lifting technique, we reduce the multirate preview control problem to a single-rate one for a formal augmented system. Then, applying preview control theory, the optimal preview control law of the augmented error system is obtained. Meanwhile, we introduce a discrete integrator to eliminate the static error. Then we study a method to design a controller with preview action for the original system. And the existence conditions of the controller are also discussed in detail. Finally, numerical simulation is included to illustrate the effectiveness of the proposed method.

Multirate Output Feedback Control of Nonlinear Networked Control Systems

This technical note studies output feedback stabilization of nonlinear networked control systems (NCSs) under multirate sampling. Network induced constraints are modeled as norm-bounded uncertainties and a general framework for multirate nonlinear NCS design is established. Under standard continuity and consistency assumptions, we analyze dissipativity of the proposed multirate output feedback structure in the presence of channels uncertainties and disturbance inputs. Our result is then applied to preserve input-to-state stability (ISS) in a semiglobal practical sense and also to derive sufficient conditions that guarantee exponential stability of the uncertain multirate NCS in the absence of disturbances.

Multirate Output Feedback with Discrete Time Sliding Mode Control for Inverted Pendulum System

In this paper, a multirate output feedback (MROF) based on discrete time sliding mode control (DSMC) method is proposed. The MROF controller is designed to maintain the inverted pendulum at upright position by controlling the tracking position of a cart. This method is practical because it only used the output samples and the measurement of the system states feedback is not necessary. The MROF output sampling is used to estimate the unmeasured states and subsequently applied to the uncertain system. The simulation results validated the advantages of the proposed controller despite the existence of nonlinearities in inverted pendulum system.

Minimum Ultimate Band Design of Discrete Sliding Mode Control

AbstractThe paper presents a generalized understanding on the dynamics of the sliding variable for discrete time sliding mode control systems via a fresh approach involving several bands in the space of the sliding variable. Using this analysis, controller parameters can be obtained once the ultimate band is chosen. It is shown that on choosing the least ultimate band, the control becomes non‐switching and Gao's reaching law becomes identical to Utkin's reaching law. On other occasions, the ultimate band obtained using this approach is clearly less than that obtained in previous works using Gao's reaching law. The analysis is presented for both state feedback and multirate output feedback cases.

Shape memory alloy actuated structural control with discrete time sliding mode control using multirate output feedback

This paper presents the design and experimental evaluation of discrete time sliding mode controller using multirate output feedback to minimize structural vibration of a cantilever beam using shape memory alloy wires as control actuators and piezoceramics as sensor and disturbance actuator. Linear dynamic models of the smart cantilever beam are obtained using online recursive least square parameter estimation. A digital control system that consists of Simulink™ modeling software and dSPACE DS1104 controller board is used for identification and control. The effectiveness of the controller is shown through simulation and experimentation by exciting the structure at resonance.

Networked Multirate Output Feedback Control for Setpoints Compensation and Its Application to Rougher Flotation Process

This paper investigates the setpoints compensation for a class of complex industrial processes. Plants at the device layer are controlled by the local regulation controllers, and a multirate output feedback control approach for setpoints compensation is proposed such that the local plants can reach the dynamically changed setpoints and the given economic objective can also be tracked via certain economic performance index (EPI). First, a sampled-data multivariable output feedback proportional integral (PI) controller is designed to regulate the performance of local plants. Second, the outputs and control inputs of the local plants at the device layer are sampled at operation layer sampling time to form the EPI. Thus, the multirate problem is solved by a lifting method. Third, the static setpoints are generated by real-time optimization and the dynamic setpoints are calculated by the compensator according to the error between the EPI and objective at each operation layer step. Then, a networked case is studied considering unreliable data transmission described by a stochastic packet dropout model. Finally, a rougher flotation process model is employed to demonstrate the effectiveness of the proposed method.

Discrete-time adaptive sliding mode control for uncertain systems based on multi-rate output measurement

This article presents the design of a discrete-time adaptive sliding mode control (SMC) for uncertain systems using the noisy multi-rate output measurement. It is assumed that the dynamic systems are described by a discrete-time state equation with mismatched uncertainties. The proposed discrete-time adaptive SMC is composed of the equivalent and the nonlinear switching controls, and it is derived based on a new sliding surface. A new least squares estimator (LSE) to take the estimates for the un-measurable states and the uncertainties is designed without the information of the statistics for the measurement noises and the initial state. In the design of the proposed discrete-time adaptive SMC, the un-measurable states and the uncertainties are, respectively, replaced as their estimates obtained from the proposed LSE, and the sliding coefficient matrices are selected such that the states for the systems are ultimately bounded, and the effect of the external disturbances to give the states is reduced as small as possible. The effectiveness of the proposed method is indicated through the simulation experiment in a simple system.

Roll control using discrete-time robust sliding hyperplanes and fast output sampling

Robustness to unmatched parametric uncertainty is prime requirement of roll control algorithm, especially when it is modelled in discrete time domain and implemented through on-board processor. Sliding mode control is a well established nonlinear control technique, which ensures a robust performance in presence of matched uncertainties and disturbances. In case of the discrete version of sliding mode control, due to finite operational sampling frequency, the system trajectories cannot be forced to slide on the switching manifold. The trajectories remain confined to certain domain around the sliding surface and this is known as Quasi Sliding Mode (QSM) motion. The bound of QSM decides the accuracy and performance of the discrete version of sliding mode. By design, the discrete-time sliding modes are robust to the matched bounded perturbations, however, unmatched perturbations directly affect the boundary layer width and hence the performance of the system. In the present paper, discrete time Lyapunov inequality based sliding hyperplane is designed, which enables robustness to unmatched perturbations arising due to uncertain system matrix A. Further, the requirement of full state-vector for the design of control and sliding surface is met through the multi-rate output feedback (MROF). This control strategy is then demonstrated with application to roll position control of missile with a bandwidth limited actuator.