Zero-order Hold Research Articles

Robust Event-Triggered Energy-to-Peak Filtering for Polytopic Uncertain Systems over Lossy Network with Quantized Measurements

The event-triggered energy-to-peak filtering for polytopic discrete-time linear systems is studied with the consideration of lossy network and quantization error. Because of the communication imperfections from the packet dropout of lossy link, the event-triggered condition used to determine the data release instant at the event generator (EG) can not be directly applied to update the filter input at the zero order holder (ZOH) when performing filter performance analysis and synthesis. In order to balance such nonuniform time series between the triggered instant of EG and the updated instant of ZOH, two event-triggered conditions are defined, respectively, whereafter a worst-case bound on the number of consecutive packet losses of the transmitted data from EG is given, which marginally guarantees the effectiveness of the filter that will be designed based on the event-triggered updating condition of ZOH. Then, the filter performance analysis conditions are obtained under the assumption that the maximum number of packet losses is allowable for the worst-case bound. In what follows, a two-stage LMI-based alternative optimization approach is proposed to separately design the filter, which reduces the conservatism of the traditional linearization method of filter analysis conditions. Subsequently a codesign algorithm is developed to determine the communication and filter parameters simultaneously. Finally, an illustrative example is provided to verify the validity of the obtained results.

New Results on $H_\infty$ Tracking Control Based on the T–S Fuzzy Model for Sampled-Data Networked Control System

This study deals with the problem of H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> tracking control for a sampled-data networked control system based on a Takagi-Sugeno fuzzy model. An error model is established by combining the input delay and parallel distributed compensation techniques so as to transform the sampling period of a sampler, a signal transmission delay, and data packet dropouts to the refreshing interval of a zero-order hold. The method introduces a new augmented Lyapunov-Krasovskii functional to derive a sufficient condition to ensure a prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> tracking performance with less conservativeness than others. A fuzzy controller can easily be designed using the condition. A numerical example demonstrates the validity of the method.

Exact solutions to a class of feedback systems on [formula omitted

This paper provides a novel approach to the problem of attitude tracking for a class of almost globally asymptotically stable feedback laws on SO(n). The closed-loop systems are solved exactly for the rotation matrices as explicit functions of time, the initial conditions, and the gain parameters of the control laws. The exact solutions provide insight into the transient dynamics of the system and can be used to prove almost global attractiveness of the identity matrix. Applications of these results are found in model predictive control problems where detailed insight into the transient attitude dynamics is utilized to approximately complete a task of secondary importance. Knowledge of the future trajectory of the states can also be used as an alternative to the zero-order hold in systems where the attitude is sampled at discrete time instances.

On the iterative learning control for stochastic impulsive differential equations with randomly varying trial lengths

In this paper, a new class of stochastic impulsive differential equations involving Bernoulli distribution is introduced. For tracking the random discontinuous trajectory, a modified tracking error associated with a piecewise continuous variable by zero-order holder is defined. In the sequel, a new random ILC scheme by adopting global and local iteration average operators is designed too. Sufficient conditions to guarantee the convergence of modified tracking error are obtained by using the tools of mathematical analysis via an impulsive Gronwall inequality. Finally, two illustrative examples are presented to demonstrate the performance and the effectiveness of the averaging ILC scheme to track the random discontinuous trajectory.

Measurement and mathematical model of a driver's intermittent compensatory steering control

The compensatory (feedback) component of a human driver's steering control is examined. In particular, the effect of the cognitive process is studied. Model predictive control theory is used to implement models of intermittency in cognitive processing. Experiments using a fixed-base driving simulator with periodic occlusion of the visual display are used to reveal the nature of the driver's steering behaviour. An intermittent serial-ballistic control strategy is found to match the measured behaviour better than intermittent zero-order hold or continuous control. The findings may enable some insight to driver-vehicle interaction and vehicle handling qualities.

A state space-based explicit integration method for real-time hybrid simulation

Real-time hybrid simulation (RTHS) combines experimental testing with numerical simulation. It provides an alternative method to evaluate the performance of structures subjected to dynamic loading such as earthquake or wind. During RTHS, a numerical integration algorithm is employed to directly solve the equation of motion and generate command displacements for the experimental test structure online. This paper presents an improved explicit numerical integration method for RTHS based on discrete state space formulation. The improved integration method utilizes an extrapolation-based prediction procedure for command displacement by applying a zero-order hold. The predicted command displacement is then used to compute the final command displacement by applying a first-order hold. Both the stability and the accuracy of the proposed integration method are investigated using control theory and numerical and experimental simulations. The proposed method demonstrates improved performance compared with other integration methods. The robustness and feasibility of the proposed method were verified through experimental RTHS on two different computational platforms including a National Instruments system and a dSPACE embedded controller. The proposed method may also be implemented on other platforms containing an xPC target and MATLAB environment. By placing the algorithm on the dSPACE system, any dynamically rated actuator with a controller that can receive analog signal may be used for RTHS. Copyright © 2015 John Wiley & Sons, Ltd.

Methods and Tools for Robust Optimal Control of Batch Chromatographic Separation Processes

This contribution concerns the development of generic methods and tools for robust optimal control of high-pressure liquid chromatographic separation processes. The proposed methodology exploits a deterministic robust formulation, that employs a linearization of the uncertainty set, based on Lyapunov differential equations to generate optimal elution trajectories in the presence of uncertainty. Computational tractability is obtained by casting the robust counterpart problem in the framework of bilevel optimal control where the upper level concerns forward simulation of the Lyapunov differential equation, and the nominal open-loop optimal control problem augmented with the robustified target component purity inequality constraint margin is considered in the lower level. The lower-level open-loop optimal control problem, constrained by spatially discretized partial differential equations, is transcribed into a finite dimensional nonlinear program using direct collocation, which is then solved by a primal-dual interior point method. The advantages of the robustification strategy are highlighted through the solution of a challenging ternary complex mixture separation problem for a hydrophobic interaction chromatography system. The study shows that penalizing the changes in the zero-order hold control gives optimal solutions with low sensitivity to uncertainty. A key result is that the robustified general elution trajectories outperformed the conventional linear trajectories both in terms of recovery yield and robustness.

Comparative study of discretization zero dynamics behaviors in two multirate cases

It is well known that the existence of unstable zero dynamics is recognized as a major barrier in many control systems. When the usual digital control with zero-order hold (ZOH) or fractional-order hold (FROH) input is used, unstable zero dynamics inevitably appear in the discrete-time model even though the continuous-time system with relative degree more than two is of minimum phase. This paper investigates the zero dynamics, as the sampling period tends to zero, of sampled-data models composed of a generalized sample hold function (GSHF), a continuous-time nonlinear plant and a sampler in cascade. More precisely, we show how an approximate sampled-data model can be obtained for nonlinear systems with two special GSHF cases such that sampled zero dynamics of the resulting model can be arbitrarily placed. Further, two GSHFs with appropriate parameters provide nonlinear zero dynamics as stable as possible, or with improved stability properties even when unstable, for a given continuous-time plant. It is also shown that the intersample behavior arising from the multirate input can be localised by appropriately selecting the design parameters based on the stability condition of the zero dynamics. The results presented here generalize well-known ideas from the linear to nonlinear cases.

Leader-following consensus of multi-agent systems via sampled-data control with randomly missing data

The objective of this paper is to inspect the leader-following consensus of distributed multi-agent system (MAS) under sampled-data control. The communication flow among neighbor agents is described by an undirected graph. The control protocols are designed by using sampling period technique and zero-order hold circuit along with missing data. A stochastic variable satisfying Bernoulli distributed white noise sequences is introduced to model the missing data. Moreover, by employing the input-delay approach, we transform the sampling data into time-varying delayed data and on the basis of receiving data, two sampled-data control models are proposed. Through the construction of a suitable Lyapunov–Krasovskii functional and by the utilization of integral inequalities, new delay-dependent consensus conditions for the concerned system are derived in the form of linear matrix inequalities (LMIs) which can be readily solved by utilizing any of the valid software packages. The effectiveness of the proposed algorithms is illustrated by two numerical simulations.

Periodic event/self‐triggered consensus for general continuous‐time linear multi‐agent systems under general directed graphs

This study considers the decentralised periodic event-triggered consensus problem for continuous-time linear multi-agent systems (MASs) under general directed graphs. The authors discretise the continuous-time MASs based on zero-order hold, and propose an event-triggered consensus control (ETCC) algorithm rendering the states of agents reach consensus. They prove that under the proposed ETCC implemented in multiple steps, there is no Zeno-like behaviour exhibited in the sense of sampling. To relax the requirement of the periodic monitoring in the ETCC, it is further proposed a self-triggered consensus control algorithm, where the next triggering instant is predetermined by each agent at the previous triggering instant. For the case where the states of MASs are unavailable, the authors further propose an observer-based ETCC algorithm. Simulation results are given to illustrate the theoretical results.

Derivative Level-Crossing Sampling

A new continuous-time level-crossing sampling LCS technique, which is called derivative LCS (DLCS), and associated reconstruction are proposed for bandpass signals. The derivative of the input is level-crossing sampled, and the result is transmitted; at the receiver, these samples are zero-order held and integrated, automatically resulting in piecewise-linear reconstruction, which has much lower quantization error than zero-order-hold (ZOH) reconstruction. Two refinements are presented, namely companded DLCS and adaptive-resolution DLCS. For some signals, the schemes proposed can significantly reduce the number of samples generated per unit of time, compared to schemes based on ZOH reconstruction, for a given signal-to-error ratio (SER), without the need for elaborate reconstruction techniques, such as linear prediction. Contrary to Nyquist-rate-clocked systems, DLCS and its variants exploit the varying spectral context and sparse structure of bursty signals by generating samples only when the signal rate of change requires it, thus promising to lead to low dynamic power dissipation in the associated hardware. Simulation results are presented.

Current Control for Synchronous Motor Drives: Direct Discrete-Time Pole-Placement Design

This paper deals with discrete-time models and current control methods for synchronous motors with a magnetically salient rotor structure, such as interior permanent-magnet synchronous motors and synchronous reluctance motors (SyRMs). The dynamic performance of current controllers based on the continuous-time motor model is limited, particularly if the ratio of the sampling frequency to the fundamental frequency is low. An exact closed-form hold-equivalent discrete motor model is derived. The zero-order hold of the stator-voltage input is modeled in stationary coordinates, where it physically is. An analytical discrete-time pole-placement design method for two-degrees-of-freedom proportional-integral current control is proposed. The proposed method is easy to apply: only the desired closed-loop bandwidth and the three motor parameters (Rs, Ld, Lq) are required. The robustness of the proposed current control design against parameter errors is analyzed. The controller is experimentally verified using a 6.7-kW SyRM drive.

Circular Obstacle Avoidance Control of the Compass-Type Biped Robot Based on a Blending Method of Discrete Mechanics and Nonlinear Optimization

This paper considers an obstacle avoidance control problem for the compass-type biped robot, especially circular obstacles are dealt with. First, a sufficient condition such that the swing leg does not collide the circular obstacle is derived. Next, an optimal control problem for the discrete compass-type robot is formulated and a solving method of the problem by the sequential quadratic programming is presented in order to calculate a discrete control input. Then, a transformation method that converts a discrete control input into a continuous zero-order hold input via discrete Lagrange-d’ Alembert principle is explained. From the results of numerical simulations, it turns out that obstacle avoidance control for the continuous compass-type robot can be achieved by the proposed method.

Asymptotic Properties of Sampling Zero Dynamics for Nonlinear Systems in the Case of Time Delay and Relative Degree Two

It is well-known that stability of zero dynamics is often inevitable to the controller design. And most real world plants often involve a time delay. This paper investigates the zero dynamics, as the sampling period tends to zero, of a sampled-data model composed of a zero-order hold (ZOH), a continuous-time plant with a time delay and a sampler in cascade. We first present how an approximate sampled-data model can be obtained for the nonlinear system with relative degree two, and the local truncation error between the output of obtained model and the true system output is of order , where T is the sampling period and r is the relative degree. Furthermore, we also propose the additional zero dynamics in the sampling process, which are called the sampling zero dynamics, and the condition for assuring the stability of sampling zero dynamics for the desired model is derived. The results presented here generalize a well-known notion of sampling zero dynamics from the linear case to nonlinear systems.

Stochastic Observability of Linear Systems under Access Constraints

AbstractUsing information theoretic measures, this paper investigates the observability of discrete‐time linear stochastic systems which have insufficient communication channels to accommodate all the sensors simultaneously. The communication status is described by a binary‐valued access sequence. For time‐varying systems, it is proved that within a finite time interval the stochastic observability is preserved by an access sequence which is combined by individually designed sub sequences corresponding to certain sub intervals. For the time‐invariant case, further results are given along with two periodic access strategies. The equivalence between stochastic observability of the zero order holder (ZOH) inclusive case and that of the non‐ZOH inclusive case is also discussed. Simulations illustrate our conclusion which covers some existing results.

New stabilization conditions for continuous fuzzy models using their discretized forms

Purpose– The purpose of this paper is to deal with the stabilization of the continuous-time Takagi-Sugeno (TS) fuzzy models by using their discretized models.Design/methodology/approach– In this case, a discrete model is obtained from the discretization of the continuous TS fuzzy model. The gains obtained from a non-parallel distributed compensation controller ensuring the stabilization of the discrete model are used to check if the discrete control law used in the continuous time without any zero-order hold can stabilize the continuous TS model.Findings– This method is compared to another published method.Originality/value– Therefore, the originality of this paper consists in the fusion of the two continuous and discrete cases to obtain new stabilization conditions in the continuous case. Simulation examples show the interest of the proposed approach.

Asymptotic properties of zero dynamics for nonlinear discretized systems with time delay via Taylor method

Most real world plants often operate in continuous-time case and involve time delay. These models are typically described by ordinary differential equations. However, to utilize and analyze these data, the control signals must first be discretized. In this paper, a new discretization method for obtaining an approximate sampled-data model of a nonlinear continuous-time system with time delay is proposed. The presented approach is based on the Taylor method and zero-order hold assumption, which can be used to approximate the system output and its derivatives in such a way as to obtain a local truncation error between the output of the resulting sampled-data model and true continuous-time system output. More importantly, on the basis of this discretized representation, we explicitly derive the mathematical structure of nonlinear discrete-time zero dynamics in the case of time delay. The main contribution is to analyze the stability of sampling zero dynamics for the proposed model with time delay. The ideas presented here generalize the well-known results from the linear system to nonlinear case.

Zero dynamics of sampled-data models for nonlinear multivariable systems in fractional-order hold case

The paper is concerned with the properties of approximate sampled-data models and their zero dynamics, as the sampling period tends to zero, composed of a fractional order hold (FROH), a continuous-time multivariable plant and a sampler in cascade. The emphasis of this paper is the stability of discrete zero dynamics with the generalized gain β of the FROH, where we also present a condition to assure the stability of the sampling zero dynamics, which they have no counterpart in the underlying continuous-time system, of the resulting model. Similar to the linear case, the parameter β is the only factor in affecting the stability of discrete zero dynamics, and the appropriate β is determined to obtain the FROH that provides zero dynamics as stable as possible, or with improved stability properties even when unstable, for a given continuous-time multivariable plant. The study is also shown that the stability of the sampling zero dynamics is improved compared with a zero-order hold (ZOH).

Easy tuning of fractional‐order holds to reduce transient energy consumption of lightly damped resonant systems

In this study, the authors show that it is particularly advantageous to use the fractional-order hold (FROH) instead of the zero-order hold (ZOH) in the digital control of lightly damped resonant systems, as far as transient energy consumption is concerned. First, they show that for a typical digital controller choice FROH reconstruction may well produce a continuous-time signal with less associated energy than ZOH reconstruction. Second, they focus on lightly damped resonant systems, where high energy savings are likely to occur because of the initially swinging nature of the discrete-time control signals driving these systems. Then, they propose an easy procedure to tune the FROH, which is not bound to z-domain controller design, and is therefore radically different from most, if not all, procedures published so far. Finally, they provide some simulation-based application examples confirming the significant control energy reduction attained, in excess of 50%, while not hindering the output performance.

Discretization of Nonlinear Non-affine Time Delay Systems Based on Second-order Hold

When calculating the sampled-date representation of nonlinear systems second-order hold (SOH) assumption can be applied to improving the precision of the discretization results. This paper proposes a discretization method based on Taylor series and the SOH assumption for the nonlinear systems with the time delayed non-affine input. The mathematical structure of the proposed discretization method is explored. This proposed discretization method can provide a precise and finite dimensional discretization model for the nonlinear time-delayed non-affine system by keeping the truncation order of the Taylor series. The performance of the proposed discretization method is evaluated by doing the simulation using a nonlinear system with the time-delayed non-affine input. Different input signals, time-delay values and sampling periods are considered in the simulation to investigate the proposed method. The simulation results demonstrate that the proposed method is practical and easy for time-delayed nonlinear non-affine systems. The comparison between SOH assumption with first-order hold (FOH) and zero-order hold (ZOH) assumptions is given to show the advantages of the proposed method.