基于累积平方误差–总平方波动指标的模型预测控制器性能评价及自愈

本文针对模型预测控制器实际投运中遇到性能下降问题,提出了一种基于累积平方误差(ISE)–总平方波动(TSV)指标的模型预测控制器性能评价及自愈方法.先基于累积平方误差(ISE)和总平方波动(TSV)指标对模型预测控制器进行实时性能评价,再根据无限时域模型预测控制器(MPC)的逆特性,基于ISE–TSV指标的分析,提出了...     

A General Robust MPC Design for the State‐Space Model: Application to Paper Machine Process

Applying model predictive control (MPC) in some cases such as complicated process dynamics and/or rapid sampling leads us to poorly numerically conditioned solutions and heavy computational load. Furthermore, there is always mismatch in a model that describes a real process. Therefore, in this paper in order to prevail over the mentioned difficulties, we design a robust MPC using the Laguerre orthonormal basis in order to speed up the convergence at the same time with lower computation adding an extra parameter “a” in MPC. In addition, the Kalman state estimator is included in the prediction model and accordingly the MPC design is related to the Kalman estimator parameters as well as the error of estimations which helps the controller react faster against unmeasured disturbances. Tuning the parameters of the Kalman estimator as well as MPC is another achievement of this paper which guarantees the robustness of the system against the model mismatch and measurement noise. The sensitivity function at low frequency is minimized to tune the MPC parameters since the lower the magnitude of the sensitivity function at low frequency the better command tracking and disturbance rejection results. The integral absolute error (IAE) and peak of the sensitivity are used as constraints in optimization procedure to ensure the stability and robustness of the controlled process. The performance of the controller is examined via the controlling level of a Tank and paper machine processes.     

Adaptive receding horizon predictive control for constrained discrete-time linear systems with parameter uncertainties

This paper proposes a discrete-time model predictive control (MPC) scheme combined with an adaptive mechanism. To this end, first, an adaptive parameter estimation algorithm suitable for MPC is proposed, which uses the available input and output signals to estimate the unknown system parameters. It enables the prediction of a monotonically decreasing worst-case estimation error bound over the prediction horizon of MPC. These distinctive features allow for future model improvement to be explicitly considered in MPC. Thus, a less conservative adaptive-type MPC controller can be developed based on the proposed estimation method. Second, we show how the discrete-time adaptive-type state-feedback MPC controller is constructed by combining the on-line parameter estimation scheme with a modified robust MPC method based on the comparison model. The developed MPC controller guarantees feasibility and stability of the closed-loop system theoretically in the presence of input and state constraints. A numerical example is given to demonstrate its effectiveness.     

A GESO based MPC approach to contour error control of networked motion control system

This paper presents a generalised extended state observer (GESO) based model predictive control (MPC) approach to contour error control for networked multi-axis motion system (NMAMS) with network-induced delays. First, the uncertainties induced by the network-induced delays are modelled as an additive bounded disturbance, and a novel model predictive controller based on the GESO is designed for the uniaxial trajectory tracking control system. The GESO is used to estimate the system state and the disturbance simultaneously, and the effects of the uncertainties induced by the delays are eliminated by the proposed GESO based controller. Then the contour error estimation method is adopted, and a PID controller is designed to compensate the contour error. Finally, experiments are carried out to demonstrate the effectiveness of the proposed method.     

A frequency response matching method for the design of digital controllers with constraints on the pole-zero locations

The purpose of the frequency response matching technique is to design a digital controller such that the frequency response of the resulting closed-loop system matches a specified frequency response model. The simplex method is employed to determine the controller's parameter values which minimize a function of the error between the two responses. This method permits constraints on the controller's gain and the pole-zero locations to be applied, for example, in order to reduce the highly oscillatory response of the output of the controller, a phenomenon which can be observed when applying other frequency response matching techniques. An example illustrating the use of the method, particularly at low sampling frequencies, is given.     

A data-based approach for multivariate model predictive control performance monitoring

An intelligent statistical approach is proposed for monitoring the performance of multivariate model predictive control (MPC) controller, which systematically integrates both the assessment and diagnosis procedures. Model predictive error is included into the monitored variable set and a 2-norm based covariance benchmark is presented. By comparing the data of a monitored operational period with the “golden” user-predefined one, this method can properly evaluate the performance of an MPC controller at the monitored operational stage. Characteristic direction information is mined from the operating data and the corresponding classes are built. The eigenvector angle is defined to describe the similarity between the current data set and the established classes, and an angle-based classifier is introduced to identify the root cause of MPC performance degradation when a poor performance is detected. The effectiveness of the proposed methodology is demonstrated in a case study of the Wood-Berry distillation column system.     

Use of model predictive controller in dual-loop control of three-phase PWM AC/DC converter

In the classical dual-loop voltage control scheme for an AC/DC converter, this paper proposes a simple stabilizing inner-loop model predictive controller (MPC) to regulate the output current and q-frame current to their references. The proposed MPC minimizes a cost function of the tracking error without any use of numerical methods using the specific property of the input matrix of the converter. It is shown that this MPC globally stabilizes the converter in the presence of input constraints. As the same manner of the classical dual-loop control scheme, PI controllers are adopted in the outerloop to regulate the output voltage while maintaining the maximum power factor. The simulation results show that the proposed inner-loop MPC considerably enhances the closed-loop performance despite the load changes.     

A wideband beam shaping reflector antenna using model predictive control

A novel method based on model predictive control (MPC) is presented for synthesis and optimization of a wide band reflector antenna with cosecant squared and flat‐topped radiation patterns. The proposed system is a doubly curved reflector antenna with nonlinear dynamic equation. This article investigates design and optimization of a double ridged horn reflector antenna operating within the frequency range of 8 to 18 GHz. In order to synthesize the proposed reflector antenna, MPC is used to achieve the desired radiation cosecant pattern. This method utilizes system model and tries to find the best control effort for minimizing the cost function by predicting the future behavior. The system differential equation is comprised of first and second order derivatives, so MPC can be a good solution for synthesis of a doubly reflector antenna. MPC optimizer operates based on state space model, so the proposed system is linearized in the operating range. Maximum error, the average error and side lobe level of this method for the radiation pattern of the proposed wideband antenna respectively are 1.4, 0.9, and ?20 dB. Simulation results of the radiation pattern in CST and HFSS software show that the proposed reflector antenna can be used in broadband surveillance radar systems.     

基于模型预测控制的电动车辆队列控制研究

针对车辆队列建模时参数不确定导致控制存在误差的问题,以及队列中跟随车辆稳定性问题,分析车辆纵向动力学,设计一个鲁棒MPC控制器和滑移率控制器来提高队列车辆的控制精度和稳定性.首先对纵向MPC控制器进行改进,提高车辆队列控制精度；同时为防止跟随车辆的轮胎打滑,设计一个MPC滑移率控制器对跟随车辆的轮胎滑移率进行控制约束,保证了跟随车辆的纵向稳定性.最后,进行仿真实验验证其有效性.仿真实验结果表明,与传统的LQR、MPC控制器相比,改进的鲁棒MPC纵向控制器控制精度更高,同时MPC滑移率控制器可防止跟随车辆的轮胎打滑,保证了跟随车辆的纵向稳定性.     

六自由度机械臂约束预测控制系统的设计

本文提出了一种基于约束预测控制的机械臂实时运动控制方法.该控制方法分为两层,分别设计了约束预测控制器和跟踪控制器.其中,约束预测控制器在考虑系统物理约束的条件下,在线为跟踪控制器生成参考轨迹;跟踪控制器采用最优反馈控制律,使机械臂沿参考轨迹运动.为了简化控制器的设计和在线求解,本文采用输入输出线性化的方式简化机械臂动力学模型.同时,为了克服扰动,在约束预测控制器中引入前馈策略,提出了带前馈一反馈控制结构的预测控制设计.因此,本文设计的控制器可以使机械臂在满足物理约束的条件下快速稳定地跟踪到目标位置.通过在PUMA560机理模型上进行仿真实验,验证了预测控制算法的可行性和有效性.     

A control matching model predictive control approach to string stable vehicle platooning

A predictive control strategy for vehicle platoons is presented in this paper, accommodating both string stability and constraints (e.g., physical and safety) satisfaction. In the proposed design procedure, the two objectives are achieved by matching a model predictive controller (MPC), enforcing constraints satisfaction, with a linear controller designed to guarantee string stability. The proposed approach neatly combines the straightforward design of a string stable controller in the frequency domain, where a considerable number of approaches have been proposed in literature, with the capability of an MPC-based controller enforcing state and input constraints.A controller obtained with the proposed design procedure is validated both in simulations and in the field test, showing how string stability and constraints satisfaction can be simultaneously achieved with a single controller. The operating region that the MPC controller is string stable is characterized by the interior of feasible set of the MPC controller.     

Oops! I cannot do it again: Testing for recursive feasibility in MPC

One of the most fundamental problems in model predictive control (MPC) is the lack of guaranteed stability and feasibility. It is shown how Farkas’ Lemma in combination with bilevel programming and disjoint bilinear programming can be used to search for problematic initial states which lack recursive feasibility, thus invalidating a particular MPC controller. Alternatively, the method can be used to derive a certificate that the problem is recursively feasible. The results are initially derived for nominal linear MPC, and thereafter extended to the additive disturbance case.     

Block factorization of step response model predictive control problems

By introducing a stage-wise prediction formulation that enables the use of highly efficient quadratic programming (QP) solution methods, this paper expands the computational toolbox for solving step response MPC problems. We propose a novel MPC scheme that is able to incorporate step response data in a traditional manner and use the computationally efficient block factorization facilities in QP solution methods. In order to solve the MPC problem efficiently, both tailored Riccati recursion and condensing algorithms are proposed and embedded into an interior-point method. The proposed algorithms were implemented in the HPMPC framework, and the performance is evaluated through simulation studies. The results confirm that a computationally fast controller is achieved, compared to the traditional step response MPC scheme that relies on an explicit prediction formulation. Moreover, the tailored condensing algorithm exhibits superior performance and produces solution times comparable to that achieved when using a condensing scheme for an equivalent (but much smaller) state-space model derived from first-principles. Implementation aspects necessary for high performance on embedded platforms are discussed, and results using a programmable logic controller are presented.     

Model predictive control for batch processes: Ensuring validity of predictions

The intuitive and simple ideas that support model predictive control (MPC) along with its capabilities have been the key to its success both in industry and academia. The contribution this paper makes is to further enhance the capabilities of MPC by easing its application to industrial batch processes. Specifically, this paper addresses the problem of ensuring the validity of predictions when applying MPC to such processes. Validity of predictions can be ensured by constraining the decision space of the MPC problem. The performance of the MPC control strategy relies on the ability of the model to predict the behaviour of the process. Using the model in the region in which it is valid improves the resulting performance. In the proposed approach four validity indicators on predictions are defined: two of them consider all the variables in the model, and the other two consider the degrees of freedom of the controller. The validity indicators are defined from the latent variable model of the process. Further to this, these are incorporated as constraints in the MPC optimization problem to bound the decision space and ensure the proper use of the model. Finally, the MPC cost function is modified to enable fine case-specific tuning if desired. Provided the indicators are quadratic, the controller yields a quadratic constrained quadratic programming problem for which efficient solvers are commercially available. A fed-batch fermentation example shows how MPC ensuring validity of predictions improves performance and eases tuning of the controller. The target in the example provided is end-point control accounting for variations in the initial measurable conditions of the batch.     

在线优化线性反馈增益的非线性鲁棒预测控制方法

以鲁棒控制不变集作为预测控制的终端约束集,设计了一种新的鲁棒预测控制算法.将预测控制在不同采样点的待优化控制律考虑为线性反馈控制律,并通过在线优化求解线性反馈增益.从理论上证明了若采用所设计的鲁棒预测控制器,则系统是输入状态稳定的.最后通过计算机仿真验证了所提出设计方法的可行性.     

Robust nonlinear MPC without terminal constraint for tracking changing setpoints in the presence of non-additive unknown disturbance

This paper develops a novel robust tracking model predictive control (MPC) without terminal constraint for discrete-time nonlinear systems capable to deal with changing setpoints and unknown non-additive bounded disturbances. The MPC scheme without terminal constraint avoids difficult computations for the terminal region and is thus simpler to design and implement. However, the existence of disturbances and/or sudden changes in a setpoint may lead to feasibility and stability issues in this method. In contrast to previous works that considered changing setpoints and/or additive slowly varying disturbance, the proposed method is able to deal with changing setpoints and non-additive non-slowly varying disturbance. The key idea is the addition of tightened input and state (tracking error) constraints as new constraints to the tracking MPC scheme without terminal constraints based on artificial references. In the proposed method, the optimal tracking error converges asymptotically to the invariant set for tracking, and the perturbed system tracking error remains in a variable size tube around the optimal tracking error. Closed-loop input-to-state stability and recursive feasibility of the optimization problem for any piece-wise constant setpoint and non-additive disturbance are guaranteed by tightening input and state constraints as well as weighting the terminal cost function by an appropriate stabilizing weighting factor. The simulation results of the satellite attitude control system are provided to demonstrate the efficiency of the proposed predictive controller.     

基于模型预测控制的数据中心节能调度算法

如今日益增长的数据中心能耗,特别是冷却系统能耗已日益受到重视,降低系统能耗能够减少数据中心碳排放.提出了一种基于模型预测控制（model prediction control,简称MPC）的节能调度策略,该策略可以有效地减小数据中心冷却能耗.该方法采用动态电压频率调节技术来调整计算节点频率,从而减少节点间的热循环;所有节点的峰值温度可被保持在温度阈值下,在任务的执行中稳态误差较小.该方法可以通过动态频率调节来抑制由于负载类型变化造成的模型不确定性带来的内部扰动,分析结果表明,基于模型预测的温控算法系统开销较小,具有良好的可扩展性.基于该算法设计的控制器能够有效地降低输入温度,提高数据中心能耗效率.通过在实际数据中心内运行的模拟网上书店,该方法与安全最小热传递算法和传统反馈温控算法这两种经典方法相比,无论是在正常条件下还是在扰动存在的情况下都能取得较好的温度抑制效果,系统性能如吞吐率也达到最大.在相同的负载条件下,该方法能够获得最小的输入峰值温度和最小的冷却能耗.     

On the explicit dead-time compensation for robust model predictive control

Computational simplicity is one of the most important aspects to take into account in robust model predictive control (MPC). In dead-time processes, it is common to use an augmented state-space representation in order to apply robust MPC strategies but, this procedure may affect computational aspects. In this paper, explicit dead-time compensation will be used to avoid augmented representation. This technique will be analyzed in terms of robust stability and constraint satisfaction for discrete-time linear systems. The results of this discussion will be applied to a robust tube-based MPC strategy which is able to guarantee robust stability and constraint satisfaction of a dead-time system by considering a prediction model without dead-time. Moreover, taking advantage of the proposed scheme, the robust MPC will be particularized for first-order plus dead-time models which simplifies significantly controller synthesis. The proposed dead-time compensation method will be applied to different robust MPC strategies in two case studies: (i) a simulated quadruple-tank system, and (ii) an experimental scaled laboratory heater process.     

非线性CSTR过程预测控制器设计

针对非线性CSTR(continuously stirred tank reactor)过程,提出一种新的预测控制的设计与仿真实现.在对一类特殊非线性过程分析的基础上,从系统的输入输出数据出发,基于子空间辨识算法建立双线性系统模型来近似描述被控系统;设计新的预测控制算法实现对CSTR过程的跟踪控制;为补偿模型失配以消除控制中的稳态误差,将积分作用包含在预测控制器的设计中,实现对控制输出的良好跟踪性能;最后通过一个仿真实例验证算法的有效性.     

Application of gap metric to model bank determination in multilinear model approach

This paper presents a gap metric based method which aims to perform the operating range decomposition and the minimum linear model bank determination of a nonlinear system when multilinear model approach is employed to design a controller for this nonlinear system. For a prescribed distance level, the minimum linear model bank determined by the proposed method can provide sufficient information for multilinear model controller design of the nonlinear system. To illustrate the usefulness of the proposed method, two examples of nonlinear systems are presented. Moreover, a mixed logical dynamical model-based MPC (MLD–MPC) controller is designed based on the minimum model bank. Simulations confirm the method for selecting linear model bank in multilinear model approach.