Model predictive control for systems with time delay

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Model predictive control for systems with time delay

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model predictive control for systems with time delay

Efficient Robust Fuzzy Model Predictive Control of Discrete Nonlinear Time-Delay Systems via Razumikhin Approach Abstract: In this paper, two efficient robust fuzzy model predictive control algorithms are investigated for discrete nonlinear systems with multiple time delays and bounded disturbances.

The famous Takagi-Sugeno T-S fuzzy systems are utilized to represent nonlinear systems. Instead of the Lyapunov-Krasovskii functional, the Lyapunov-Razumikhin function is adopted to deal with time delays because it involves invariant sets in the original state space of the system. A sequence of explicit control laws corresponding to a sequence of constraint sets are computed offline so that the online computational burden associated with the classical model predictive control algorithms is significantly reduced.

Discrete-Time Model Predictive Control

In particular, the set invariance theory behind the Razumikhin approach, which is more complicated than the one for nondelayed systems, is directly observed. Additionally, it is proved that all delayed states can enter the terminal set in finite time. Moreover, robust positive invariance and input-to-state stability for time-delay systems concerning disturbances are realized. Additionally, an online optimization algorithm is also provided based on the offline computed ellipsoidal sets.

Therefore, the conservatism induced by the Razumikhin approach is relaxed, while the computational cost is not significantly increased. Article :.

model predictive control for systems with time delay

Date of Publication: 02 July DOI: Need Help?This paper investigates the problem of model predictive control for a class of nonlinear systems subject to state delays and input constraints. The time-varying delay is considered with both upper and lower bounds.

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A new model is proposed to approximate the delay. And the uncertainty is polytopic type. For the state-feedback MPC design objective, we formulate an optimization problem.

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Under model transformation, a new model predictive controller is designed such that the robust asymptotical stability of the closed-loop system can be guaranteed.

Finally, the applicability of the presented results are demonstrated by a practical example. The ideas of model predictive control and receding horizon control have been developed since s. It has been shown from [ 1 ] that model predictive control MPC is an effective way to handle multivariable constrained control problems, which appear in the chemical process control, the petrochemical industries, gas pipeline, and so on.

In [ 23 ], the authors gave us an overview of the origins of model predictive control and the recent results. The original MPC technique is aimed at solving an open-loop optimization problem with constraints at every sampling instant, implementing only the first control step of solutions. In practical control systems, parameter uncertainties cannot be avoided. In the literatures, two kinds of parameter uncertainties are often included in the uncertain systems.

They are norm-bounded parameter uncertainty and polytopic parameter uncertainty. In addition, time-delay often appears in industrial processes, which results in degradation and instability in such systems [ 4 ]. References [ 56 ] studied the networked control with time-delay; [ 7 ] investigated linear switched systems with time-varying delay.

The authors in [ 8 ] discussed the problem of dissipativity analysis of stochastic neural networks systems of discrete-time form with time-varying and finite-distributed delays. The authors in [ 9 ] designed a novel output-feedback controller for the suspension systems with input delay. Moreover, there exist some physical limits, for instance power limitations and value saturation, in many industrial processes, which result in constraints on input and output.

Therefore, considerable researchers have been attracted to study the robust control problem of constrained uncertain systems with state delays [ 1011 ].

Many results about MPC technique for time-delay systems have been addressed. To mention a few, in [ 12 ], the authors proposed that the control strategy for uncertain systems could be developed into a delay system via the MPC. However, it is proper only if the delay indices are known. Recently, the authors in [ 10 ] presented an improved delay-dependent robust MPC to reduce the conservatism, still with a known delay. The work in [ 4 ] put forward an MPC method for time-varying state-delay systems with uncertainty and constrained control input.

However, since the stability is guaranteed under the fixed constant weighting matrix at all time, the method is very limited and the conservatism may be generated. Motivated by the above observation, the problem of MPC for time-varying delay systems with parameter uncertainties and input constraints is studied in this paper.

We summarize the main contributions of this paper as follows. A new model predictive controller is designed under the model transformation by approximating the state delay, such that the robust asymptotical stability of the closed-loop system is guaranteed.

Model Predictive Control for Discrete-Time Linear Systems with Time Delays and Unknown Input

The existence of the controller can be expressed by the convex optimization algorithm. The rest of this paper is organized as follows.

Section 2 formulates the problem to be solved. Section 3 proposes an MPC method for delay systems with uncertainties and constraints. Section 4 illustrates the effectiveness of the method proposed in this paper with a practical example. This paper is concluded in Section 5. The nonnegative coefficients for each time satisfies the following: In this paper we aims at designing the following controller for system in 1 : with the performance index as follows at every time : where where and are known positive definite symmetric weighting matrices, denotes the predicted state at time and denotes the control signal at timewhen.

Based on the concept of MPC, before the next sampling time comes, we just implement the first compute input signal. Then we repeat the aforementioned optimization problem after updating it with the actual state.This study investigates the problem of robust model predictive control RMPC for active suspension systems with time-varying delays and input constraints.

The uncertainty is of convex polytopic type. Based on the Lyapunov-Krasovskii functional method, sufficient stability conditions of the time-varying delays systems are derived by linear matrix inequalities LMIs terms. Finally, a quarter-vehicle model is exploited to demonstrate the effectiveness of the proposed method.

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Zou, T. Chen, and S. Li, H. Liu, H. Gao, and P. Martins, A. Yamashita, Bruno F. Yang, W. Qiu, Y Ma, M. Chadli, L. Park, O. Kwon, Ju H. Park, S. Lee, and E. Kang and W.

Bououden, M.Advances in Discrete Time Systems. More than 25 years after model predictive control MPC or receding horizon control RHC appeared in industry as an effective tool to deal with multivariable constrained control problems, a theoretical basis for this technique has started to emerge, see [ 1 - 3 ] for reviews of results in this area. The focus of this chapter is on MPC of constrained dynamic systems, both linear and nonlinear, to illuminate the ability of MPC to handle constraints that makes it so attractive to industry.

We first give an overview of the origin of MPC and introduce the definitions, characteristics, mathematical formulation and properties underlying the MPC. Furthermore, MPC methods for linear or nonlinear systems are developed by assuming that the plant under control is described by a discrete-time one.

Although continuous-time representation would be more natural, since the plant model is usually derived by resorting to first principles equations, it results in a more difficult development of the MPC control law, since it in principle calls for the solution of a functional optimization problem.

As a matter of fact, the performance index to be minimized is defined in a continuous-time setting and the overall optimization procedure is assumed to be continuously repeated after any vanishingly small sampling time, which often turns out to be a computationally intractable task. On the contrary, MPC algorithms based on discrete-time system representation are computationally simpler.

The system to be controlled which usually described, or approximated by an ordinary differential equation is usually modeled by a difference equation in the MPC literature since the control is normally piecewise constant. Hence, we concentrate our attention from now onwards on results related to discrete-time systems. By and large, the main disadvantage of the MPC is that it cannot be able of explicitly dealing with plant model uncertainties. For confronting such problems, several robust model predictive control RMPC techniques have been developed in recent decades.

We review different RMPC methods which are employed widely and mention the advantages and disadvantages of these methods. The basic idea of each method and some method applications are stated as well. However model and measurement uncertainties are often stochastic, and therefore RMPC can be conservative since it ignores information on the probabilistic distribution of the uncertainty. It is possible to adopt a stochastic uncertainty description instead of a set-based description and develop a stochastic MPC SMPC algorithm.

Some of the recent advances in this area are reviewed. The main advantages of NCSs are low cost, simple installation and maintenance, and potentially high reliability.

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However, the use of the network will lead to intermittent losses or delays of the communicated information. These losses will tend to deteriorate the performance and may even cause the system to become unstable.

MPC framework is particularly appropriate for controlling systems subject to data losses because the actuator can profit from the predicted evolution of the system. In section 7, results from our recent research are summarized. We propose a new networked control scheme, which can overcome the effects caused by the network delay.

At the beginning of research on NCSs, more attention was paid on single plant through network. Recently, fruitful research results on multi-plant, especially, on multi-agent networked control systems have been obtained.Skip to Main Content.

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Learning-based Model Predictive Control for Autonomous Racing

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Sign In. Delay Compensation in Model Predictive Current Control of a Three-Phase Inverter Abstract: When control schemes based on finite control set model predictive control are experimentally implemented, a large amount of calculations is required, introducing a considerable time delay in the actuation.

This delay can deteriorate the performance of the system if not considered in the design of the controller. In this paper, the problem is described, and the solution to this issue is clearly explained using a three-phase inverter as an example.

Experimental results to validate this solution are shown. Article :. Date of Publication: 19 May DOI: Need Help?Skip to Main Content. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity.

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Email Address. Sign In. The Razumikhin approach is adopted for time-delay systems because it involves a Lyapunov function associated with the original nonaugmented state space of system dynamics when compared to the Krasovskii approach.

As such, the Razumikhin approach has a good potential to avoid the inherent complexity of the Krasovskii approach especially in the presence of large delays and disturbances.

model predictive control for systems with time delay

Based on which, both online and offline MPC approaches for systems with time-varying delay are provided. In addition, persistent disturbances are considered that robust positive invariance and input-to-state stability under such circumstances are realized. In the offline approach, a sequence of explicit control laws that correspond to a sequence of robust constraints sets are computed offline. And it is proved that system states including all possibly delayed states can be steered to the terminal constraint set in finite time.

Moreover, it allows the exact time delay to be unknown in the proposed two approaches. In particular, for systems with time-varying delay, the special positively invariant set theory and finite-time control theory based on the Razumikhin approach are directly revealed via the proposed offline approach. Article :.

Model Predictive Control for Discrete-Time Linear Systems with Time Delays and Unknown Input

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model predictive control for systems with time delay

If the error persists, contact the administrator by writing to support infona. You can change the active elements on the page buttons and links by pressing a combination of keys:. I accept. Polski English Login or register account. A compensation algorithm of Ethernet time delay based on model predictive control. Abstract In this paper, a compensation algorithm based on model predictive control is presented for Ethernet control systems with uncertain transmission delay.

The delay of feedback path and forward path is obtained through time delay prediction. According to the request of system performance, the control system design is compensated by using dynamic matrix control algorithm to overcome the bad effect caused by the network delay.

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The algorithm is simulated and the simulation results show that the control strategy is effective. Authors Close. Assign yourself or invite other person as author. It allow to create list of users contirbution. Assignment does not change access privileges to resource content. Wrong email address. You're going to remove this assignment. Are you sure? Yes No. Keywords telecommunication control closed loop systems compensation control systems delays local area networks predictive control dynamic matrix control algorithm Ethernet time delay compensation algorithm model predictive control transmission delay feedback delay control system design Delay effects Delay Prediction algorithms Predictive models Heuristic algorithms Actuators telecommunication control closed loop systems compensation control systems delays local area networks predictive control dynamic matrix control algorithm Ethernet time delay compensation algorithm model predictive control transmission delay feedback delay control system design Delay effects Delay Prediction algorithms Predictive models Heuristic algorithms Actuators.

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