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1.
The main control goal of the fed-batch process is to maximize the yield of target product as well as to minimize the operation costs simultaneously. Considering the existence of time delay and the switching nature in the fed-batch process, a time-delayed switched system is proposed to formulate the 1,3-propanediol (1,3-PD) production process. Some important properties of the system are also discussed. Taking the switching instants and the terminal time as the control variables, a free terminal time delayed optimal control problem is then presented. Using a time-scaling transformation and parameterizing the switching instants into new parameters, an equivalently optimal control problem is investigated. A numerical solution method is developed to seek the optimal control strategy by the smoothing approximation method and the gradient of the cost functional together with that of the constraints. Numerical results show that the mass of target product per unit time at the terminal time is increased considerably.  相似文献   

2.
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3.
The optimal control strategy constructed in the form of a state feedback is effective for small state perturbations caused by changes in modeling uncertainty. In this paper, we investigate a robust suboptimal feedback control (RSPFC) problem governed by a nonlinear time-delayed switched system with uncertain time delay arising in a 1,3-propanediol (1,3-PD) microbial fed-batch process. The feedback control strategy is designed based on the radial basis function to balance the two (possibly competing) objectives: (i) the system performance (concentration of 1,3-PD at the terminal time of the fermentation) is to be optimal; and (ii) the system sensitivity (the system performance with respect to the uncertainty of the time-delay) is to be minimized. The RSPFC problem is subject to the continuous state inequality constraints. An exact penalty method and a novel time scaling transformation approach are used to transform the RSPFC problem into the one subject only to box constraints. The resulting problem is solved by a hybrid optimization algorithm based on a filled function method and a gradient-based algorithm. Numerical results are given to verify the effectiveness of the developed hybrid optimization algorithm.  相似文献   

4.
Switched systems are complicated due to the switching among the subsystems. When the subsystem models are unknown, control problems on switched systems turn to be more intractable. In this paper, the optimal switching problems are investigated for continuous-time switched autonomous systems with unknown dynamics and a finite-horizon cost function. Firstly, a novel data-driven optimal scheduling approach is proposed based on the estimated insertion gradients. Secondly, aiming at switched systems with a prescribed switching sequence, a data-driven optimal switching time approach is proposed based on the estimated derivatives of the cost with respect to the switching times. The two approaches take advantages of plenty state data containing necessary information instead of the system models. Furthermore, the errors of the approaches are analysed and bounded. Finally, simulation results of two examples are given to show the validity of the two approaches.  相似文献   

5.
This paper focuses on binary optimal control of fed-batch fermentation of glycerol by Klebsiella pneumoniaewith pH feedback considering limited number of switches. To maximize the concentration of 1,3-propanediol at terminal time, we propose a binary optimal control problem subjected to time-coupled combinatorial constraint with the ratio of feeding rate of glycerol to that of NaOH as control variables. Based on time-scaling transformation and discretization, the binary optimal control problem is first transformed into a mixed binary parameter optimization problem consisting of not only continuous variables but also binary variables, which is then divided into two subproblems via combinatorial integral approximation decomposition. Finally, a novel fruit fly optimizer with modified sine cosine algorithm and adaptive maximum dwell rounding are applied to solve the obtained subproblems numerically. Numerical results show the rationality and feasibility of the proposed method.  相似文献   

6.
Background1,3-Propanodiol (1,3-PD), is used in the production of polytrimethylene terephthalate (PTT), an aromatic polyester that exhibits high elastic recoveries. It is also employed as a supplement with low solidification properties, a solvent and a lubricant in the formof propylene glycol. 1,3-PD is effectively synthesized by a microbiological way from crude glycerol. The main problem of this technology is using a high concentration of glycerol, which is a limiting factor for bacteria cells growth (especially in batch fermentation).ResultsIn this work, the influence of different glycerol concentration in batch fermentation on Clostridium butyricum DSP1 metabolism was investigated. The biomass was concentrated for two times with the use of membrane module (in case of increasing kinetic parameters). Increased optical density of bacteria cells six times increased the productivity of 1,3-PD in cultivation with 20 g/L of glycerol at the beginning of the process, and more than two times in cultivation with 60–80 g/L. Also the possibility of complete attenuation of 140 g/L of crude glycerol in the batch fermentation was investigated. During the cultivation, changes of protein profiles were analyzed. The most significant changes were observed in the cultivation in the medium supplemented with 80 g/L of glycerol. They related mainly to the DNA protein reconstructive systems, protective proteins (HSP), and also the enzymatic catalysts connected with glycerol metabolic pathway.ConclusionsThe application of filtration module in batch fermentation of crude glycerol by C. butyricum DSP1 significantly increased the productivity of the process.  相似文献   

7.
BackgroundThe production of biofuels from renewable energy sources is one of the most important issues in industrial biotechnology today. The process is known to generate various by-products, for example crude glycerol, which is obtained in the making of biodiesel from rapeseed oil. Crude glycerol may be utilized in many ways, including microbial conversion to 1,3-propanediol (1,3-PD), a raw material for the synthesis of polyesters and polyurethanes.ResultsThe paper presents results of a study on the synthesis of 1,3-propanediol from crude glycerol by a repeated batch method with the use of Clostridium butyricum DSP1. Three cycles of fermentation medium replacement were carried out. The final concentration of 1,3-PD was 62 g/L and the maximum productivity, obtained during the second cycle, reached 1.68 g/L/h. Additionally, experiments conducted in parallel to the above involved using the entire quantity of the culture broth removed from the bioreactor to inoculate successive portions of fermentation media containing crude glycerol at concentrations of 80 g/L and 100 g/L. Under those conditions, the maximum 1,3-PD concentrations were 43.2 g/L and 54.2 g/L.ConclusionsThe experiments proved that by using a portion of metabolically active biomass as inoculum for another fermentation formula it is possible to eliminate the stage of inoculum growth and thereby reduce the length of the whole operation. Additionally, that strategy avoids the phase of microbial adaptation to a different source of carbon such as crude glycerol, which is more difficult to utilize, thus improving the kinetic parameters of 1,3-PD production.  相似文献   

8.
《Journal of The Franklin Institute》2019,356(17):10296-10314
This paper investigates the problem of distributed event-triggered sliding mode control (SMC) for switched systems with limited communication capacity. Moreover, the system output and switching signals are both considered to be sampled by distributed digital sensors, which may cause control delay and asynchronous switching. First of all, a novel distributed event-triggering scheme for switched systems is proposed to reduce bandwidth requirements. Then, a state observer is designed to estimate the system state via sampled system output with transmission delay. Based on the observed system state, a switched SMC law and corresponding switching law are designed to guarantee the exponential stability of the closed-loop system with H∞ performance. Finally, an application example is given to illustrate the effectiveness of the proposed method.  相似文献   

9.
In this paper, the multiple model strategy is applied to the adaptive control of switched linear systems to improve the transient performance. The solvability of the adaptive stabilization problem of each subsystem is not required. Firstly, the two-layer switching mechanism is designed. The state-dependent switching law with dwell time constraint is designed in the outer-layer switching to guarantee the stability of the switched systems. During the interval of dwell time constraint, the parameter resetting adaptive laws are designed in the inner-layer switching to improve the transient performance. Secondly, the minimum dwell time constraint providing enough time for multiple model adaptive control strategy to work fully and maintaining the stability of the switched systems is found. Finally, the proposed switched multiple model adaptive control strategy guarantees that all the closed-loop system signals remain bounded and the state tracking error converges to zero.  相似文献   

10.
This paper concerns the stability of switched systems orchestrating between unstable modes. First, a mode partition is applied to select stabilizing switching from the switching between modes from different subsets. Second, a piecewise Lyapunov-like function is applied to decline at stabilizing switching times. Then, the stability criteria build on mode-partition-dependent average dwell time by collecting enough stabilizing switching behavior to stabilize the destabilizing switching behavior and unstable modes. Finally, the simulation verification shows the feasibility and effectiveness of the method.  相似文献   

11.
This paper investigates the time optimal control and optimal infinite-horizon control for a switched Boolean network. First, the switched Boolean network can be converted into a discrete switched system by using the semi-tensor product of matrices. Second, algorithms for time optimal control and optimal infinite-horizon control of the switched Boolean network are presented. Moreover, constrained optimal infinite-horizon control is studied. Finally, illustrative examples are given to show the efficiency of the obtained results.  相似文献   

12.
This paper investigates the problem of event-triggered adaptive neural network (NN) control for multi-input multi-output (MIMO) switched nonlinear systems with output and state constraints and non-input-to-state practically stable (ISpS) unmodeled dynamics. A nonlinear mapping is firstly utilized to deal with output and state constraints. Also, by developing a new switching signal with persistent dwell-time (PDT) and a switching dependent dynamic signal, the difficulty caused by some non-ISpS unmodeled dynamics is overcome. Then, a type of switching event-triggering mechanisms (ETMs) and event-triggered adaptive NN controllers of subsystems are designed, which handle the issue of asynchronous switching without requiring any known restriction on maximum asynchronous time. A piecewise constant introduced into this ETM effectively ensures a strict positive lower bound of inter-event times. Zeno behavior is thus ruled out. Finally, by proposing a novel class of switching signals with reset PDT, it is ensured that all output and state constrains are never violated and all signals of the switched closed-loop system are semi-global uniform ultimate boundedness (SGUUB). A two inverted pendulum system and a numerical example are provided for illustrating the applicability and validity of the proposed method.  相似文献   

13.
To achieve the flight mode transfer of the tilt-rotor aircraft, this paper develops a smooth switching method for an weighted L2 robust asynchronously switched system. Considering the asynchronous phenomenon that exists in the switching control of the tilt-rotor aircraft, first, a sufficient condition for the existence of the sub-controller is derived, which guarantees the exponential stability and weighted L2 performance. Besides, the on-line system and the off-line system are separately employed to realize the continuity of the control input signals, which further improve the transient performance and smoothness of the asynchronously switched system. The simulations on the tilt-rotor aircraft verify the effectiveness and applicability of the proposed method.  相似文献   

14.
Modelling of switching systems using bond graph is a research issue. There have been many proposals in this context. However, there are many issues that need consideration. This paper proposes the concept of switched power junctions that is a generalisation of the conventional junction concept in bond graph modelling. This approach removes most of the difficulties associated with other methodologies. This method ensures that causality remains invariant during mode switching thus keeping the state vector and its dimension time invariant. Further, the switched power junction displays all feasible system modes at the same time on the same graph. This concept is further illustrated through simulation using examples of switching systems in the electrical domain.  相似文献   

15.
This paper focuses on the optimal control of a DC torque motor servo system which represents a class of continuous-time linear uncertain systems with unknown jumping internal dynamics. A data-driven adaptive optimal control strategy based on the integration of adaptive dynamic programming (ADP) and switching control is presented to minimize a predefined cost function. This takes the first step to develop switching ADP methods and extend the application of ADP to time-varying systems. Moreover, an analytical method to give the initial stabilizing controller for policy iteration ADP is proposed. It is shown that under the proposed adaptive optimal control law, the closed-loop switched system is asymptotically stable at the origin. The effectiveness of the strategy is validated via simulations on the DC motor system model.  相似文献   

16.
This paper studies the event-triggered control for discrete-time switched systems under the influence of denial-of-service (DoS) attacks and output quantization. Firstly, the switching is assumed to be slow enough in the sense of average dwell time, and DoS attacks are assumed to be energy-limited by constraining DoS frequency and DoS duration. Secondly, by designing an event-triggered mechanism which integrates switching, DoS attacks and transmission error, the initial state bound is obtained at a finite time. Then, a novel quantization coding method is designed by introducing a monotonically increasing sequence, which guarantees the unsaturation of the quantizer. On the basis of this, the exponential convergence and Lyapounov stability of the closed-loop system are established. Finally, two-tanks system is illustrated to demonstrate the effectiveness of the theoretical analysis.  相似文献   

17.
In this paper, the adaptive sliding mode control issue for switched nonlinear systems with matched and mismatched uncertainties is addressed, where the persistent dwell-time switching rule is introduced to describe the switching of parameters. Besides, considering the case that the upper bound of the matched uncertainty is unknown, the purpose of this paper is to utilize an adaptive control method to estimate its upper bound parameters. To begin with, a linear sliding surface is constructed, and then the reduced-order sliding mode dynamics can be obtained through a reduced-order method. Next, sufficient conditions can be derived based on the Lyapunov stability and the persistent dwell-time switching analysis techniques ensuring that the reduced-order sliding mode dynamics is globally uniformly exponentially stable. Moreover, a switched adaptive sliding mode control law is designed, which can not only ensure the reachability of the sliding surface but also estimate the upper bound parameters of the matched uncertainty. Finally, a numerical example and a circuit model are introduced to verify the effectiveness of the proposed method.  相似文献   

18.
In this paper, we address the sampling and control issues for switched linear systems. Under synchronous switching and piecewise constant control, a continuous-time switched system is naturally related to a discrete-time sampled-data system. We prove that, with almost any sampling rate, the controllable subspace will be preserved for a switched linear system. We also investigate the possibility of achieving controllability using regular switching mechanisms. We show that, to achieve controllability for a switched linear system, it is sufficient to use cyclic and synchronous switching paths and constant control laws.  相似文献   

19.
This paper addresses the event-triggered tracking control design for state-constrained switched nonstrict feedback nonlinear systems. With the help of a time-varying nonlinear shifting function (TVNSF) introduced into the switched nonlinear system, the proposed solution is seen as a unified tool regardless of whether the constraint conditions are state constraints, output constraint, or even no constraint. Also, by allowing the triggering error to vary with the switching signal in time, the negative effects of the mismatch between the individual controller and the subsystem on system performance are trumped. Moreover, by using constructed individual Lyapunov function that depends on the lower bound of the control gain function of individual subsystem, a novel switching signal satisfying the average dwell time (ADT) is provided to ensure the boundedness of all variables in the closed-loop system. Finally, the proposed theory is carried over into a mass-spring-damper system to verify its effectiveness.  相似文献   

20.
Sampled-data control as an effective mean of digital control has shown its prominent superiority in most practical industries and a zero-order holder (ZOH) is often introduced to maintain continuity of control in the field of sampled-data control system. However, it decreases the control accuracy in a certain extent since the state will be held invariably within each sampling interval. In order to improve the control accuracy, this paper proposes a dynamic model-based control strategy instead of ZOH for a class of switched sampled-data control systems. The model, which is built by abstracting the plant knowledge, is located at the controller side. The controller is set up based on the model state and it provides control input to the switched system. A fixed sampling period is adopted, under which a hybrid-dwell time switching condition is revealed by taking into account asynchronous switching. With reasonable design of switching condition, exponential stability of the closed-loop system can be guaranteed. Finally, advantages of our proposed method are presented through a numerical example by comparing with the result of ZOH-based control.  相似文献   

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