An improved structure for model predictive control using non-minimal state space realisation

This paper describes a new method for the design of model predictive control (MPC) using non-minimal state space models, in which the state variables are chosen as the set of measured input and output variables and their past values. It shows that the proposed design approach avoids the use of an observer to access the state information and, as a result, the disturbance rejection, particularly the system input disturbance rejection, is significantly improved when constraints become activated. In addition, when there is no model/plant mismatch, the paper shows that the system output constraints can be realised in the proposed approach. Furthermore, closed-form transfer function representation of the model predictive control system enables the application of frequency response analysis tools to the nominal performance of the system.     

Design of fractional order modeling based extended non-minimal state space MPC for temperature in an industrial electric heating furnace

In this paper, an improved approach of extended non-minimal state space (ENMSS) fractional order model predictive control (FMPC) is presented and tested on the temperature model of an industrial heating furnace. In the fractional order model predictive control algorithm, fractional order single-input single-output (SISO) system is discretized via fractional order Grünwald-Letnikov (GL) definition. The ENMSS fractional order model that contains the state variable and the fractional order output tracking error is formulated by choosing appropriate state variables. Meanwhile, the fractional order integral is introduced into the cost function and the GL definition is used to obtain the discrete form of the continuous cost function. Then the control signals are derived by minimizing the fractional order cost function. Lastly, the temperature process control of a heating furnace is illustrated to reflect the performance of the proposed FMPC method. Simulation results show the effectiveness of the proposed FMPC method.     

An improved approach for constrained robust model predictive control

In this paper, we present a new technique to address constrained robust model predictive control. The main advantage of this new approach with respect to other well-known techniques is the reduced conservativeness. Specifically, the technique described in this paper can be applied to polytopic uncertain systems and is based on the use of several Lyapunov functions each one corresponding to a different vertex of the uncertainty's polytope.     

State space model predictive fault-tolerant control for batch processes with partial actuator failure

This paper presents a state space model predictive fault-tolerant control scheme for batch processes with unknown disturbances and partial actuator faults. To develop the model predictive fault-tolerant control, the batch process is first treated into a non-minimal representation using state space transformation. The relevant concepts of the corresponding model predictive fault-tolerant control is thus introduced through state space formulation, where improved closed-loop control performance is achieved even with unknown disturbances and actuator faults, because, unlike traditional model predictive fault-tolerant control, the proposed control method can directly regulate the process output/input changes in the design. For performance comparison, a traditional model predictive fault-tolerant control is also designed. Application to injection velocity control shows that the proposed scheme achieve the design objective well with performance improvement.     

基于子空间辨识的状态空间模型预测控制

针对无法从工业过程中获得准确状态空间模型的问题,提出一种基于子空间辨识的状态空间模型预测控制方法。利用子空间辨识方法得到的状态空间模型作为系统模型,给出约束条件下的预测控制算法。以CD播放器机械臂系统为例,通过状态空间模型预测控制方法实现对系统输出的跟踪控制,仿真结果表明,该方法控制效果良好。     

Multi-objective performance optimisation for model predictive control by goal attainment

This article proposes an approach for performance tuning of model predictive control (MPC) using goal-attainment optimisation of the cost function weighting matrices. The approach is developed for three formulations of the control problem: (i) minimal and (ii) non-minimal design based on the same cost function and (iii) a non-minimal MPC approach with an explicit integral-of-error state variable and modified cost function. This approach is based on earlier research into multi-objective optimisation for proportional-integral-plus control systems. Simulation experiments for a 3-input, 3-output Shell heavy oil fractionator model illustrate the feasibility of MPC goal attainment for multivariable decoupling and attainment of a specific output response. For this example, the integral-of-error state variable offers improved design flexibility and hence, when it is combined with the proposed tuning method, yields an improved closed-loop response in comparison to minimal MPC.     

An improved state-space model structure and a corresponding predictive functional control design with improved control performance

Conventional state-space model predictive control requires a state estimator/observer to access the state information for feedback controller design. Its drawbacks are the numerical convergence stability of the observer and closed-loop control performance deterioration with activated plant input/output constraints. The recent direct use of measured input and output variables to formulate a non-minimal state-space (NMSS) model overcomes these problems, but the subsequent controller is too sensitive to model mismatch. In this article, an improved structure of NMSS model that incorporates the output-tracking error is first formulated and then a subsequent predictive functional control design is proposed. The proposed controller is tested on both model match and model mismatch cases for comparison with previous controllers. Results show that control performance is improved. In addition, a linear programming method for constraints dealing and a closed form of transfer function representation of the control system are provided for further insight into the proposed method.     

基于T-S模糊模型的状态反馈预测控制

将T-S模糊模型和状态反馈预测控制相结合,提出了一种基于T-S模糊模型的预测控制算法.该算法把T-S模糊模型作为预测模型得到状态和输出的预估值,并利用可测的过程变量对输出预估值进行反馈修正,然后利用最优控制理论,由修正后的预估值和给定值计算出控制整个系统的控制律.本文还对串级CSTR控制系统的不同的初态、设定值及干扰情况下进行了仿真,仿真结果表明了该方法的有效性和可行性.     

状态反馈预测控制干扰解耦的研究

讨论状态反馈预测控制系统设计中的干扰解耦设计问题，给出了状态反馈预测控制系统干扰可解耦设计的充分必要条件。基于状态空间模型，给出了状态反馈预测控制系统设计参数——预测时域按干扰解耦设计的选取方法。它可改善控制系统的性能，提高控制系统的抗干扰能力。仿真结果表明了状态反馈预测控制系统干扰解耦设计的有效性。     

An improved robust model predictive control approach to systems with linear fractional transformation perturbations

In this paper, a robust model predictive control approach is proposed for a class of uncertain systems with time-varying, linear fractional transformation perturbations. By adopting a sequence of feedback control laws instead of a single one, the control performance can be improved and the region of attraction can be enlarged compared with the existing model predictive control (MPC) approaches. Moreover, a synthesis approach of MPC is developed to achieve high performance with lower on-line computational burden. The effectiveness of the proposed approach is verified by simulation examples.     

基于扩张状态观测器的车辆横摆稳定模型预测控制器设计

针对车辆横摆稳定性控制问题,本文提出一种基于扩张状态观测器的线性模型预测控制器设计方法.首先,将非线性车辆模型线性化,建立带有模型误差干扰项的线性模型,其中线性化导致的模型误差采用扩张状态观测器估计得到,并证明了观测器的稳定性.然后基于此模型设计线性预测控制器,近似实现了非线性预测控制器的控制效果,同时降低了计算量.最后,通过不同路况下的仿真实验结果,验证了所提方法的计算性能和控制效果.     

Generalized terminal state constraint for model predictive control

A terminal state equality constraint for Model Predictive Control (MPC) laws is investigated, where the terminal state/input pair is not fixed a priori but it is a free variable in the optimization. The approach, named “generalized” terminal state constraint, can be used for both tracking MPC (i.e. when the objective is to track a given steady state) and economic MPC (i.e. when the objective is to minimize a cost function which does not necessarily attains its minimum at a steady state). It is shown that the proposed technique provides, in general, a larger feasibility set with respect to the existing approaches, given the same prediction horizon. Moreover, a new receding horizon strategy is introduced, exploiting the generalized terminal state constraint. Under mild assumptions, the new strategy is guaranteed to converge in finite time, with arbitrarily good accuracy, to an MPC law with an optimally-chosen terminal state constraint, while still enjoying a larger feasibility set. The features of the new technique are illustrated by an inverted pendulum example in both the tracking and the economic contexts.     

增广非最小状态空间法的稳定平台预测控制研究

针对传统的模型预测控制器鲁棒性较差及模糊PID控制系统比较复杂的问题,提出了利用增广非最小状态空间模型与模型预测控制相结合的稳定平台预测控制。建立了稳定平台广义被控对象的数学模型,以增广形式的非最小状态空间模型为基础,结合滚动时域控制原则和线性二次型最优控制,通过对稳定平台离散模型的非最小状态空间形式进行增广变换,给出了基于Laguerre函数的状态反馈增益矩阵算法,设计了增广非最小状态模型下的预测控制器,实现了对导向钻井稳定平台控制系统的仿真研究。仿真结果表明稳定平台预测控制系统可以很好地满足钻井工程对控制精度和动态特性的要求,而且对有时变性的盘阀摩擦干扰力矩及模型参数摄动具有较强的鲁棒性。     

An improved design of aggregation-based model predictive control

Linear aggregation in the input is an effective method to reduce the online computational burden of model predictive control (MPC) but at the cost of degradations in the closed-loop performance. In this paper, an improved aggregation-based MPC algorithm is developed to reduce these degradations. In this algorithm, a time-varying base vector is utilized in conjunction with the quasi-equivalent aggregation strategy. Furthermore, by relaxing the constraints with a sequence of reachable sets, a switching strategy is adopted to enlarge the attractive region of the resulting aggregation-based MPC.     

Interactions between control and process design under economic model predictive control

Economic model predictive control (EMPC) is a model-based control scheme that integrates process control and economic optimization, which can potentially allow for time-varying operating policies to maximize economic performance. The manner in which an EMPC operates a process to optimize economics depends on the process dynamics, which are fixed by the process design. This raises the question of how process and EMPC designs interact. Works which have addressed process and control design interactions for steady-state operation have sought to simultaneously develop process designs and control law parameters to find the most profitable way to operate a process that is able to prevent process constraints from being violated and to optimize capital costs in the presence of disturbances. Because EMPC has the potential to operate a process in a transient fashion, this work first focuses on how EMPC and process design interact in the absence of disturbances. Using small-scale process examples, we seek to understand the fundamental nature of the interactions between EMPC and process design, including how these interactions can impact computational complexity of the controller and the design procedure. We subsequently utilize the insights gained to suggest controller design variables which might be considered as decision variables for a simultaneous process and control design problem when disturbances are considered.     

Off-line approach to dynamic output feedback robust model predictive control

This paper presents an off-line approach to the dynamic output feedback robust model predictive control (OFRMPC) for a system with both polytopic uncertainty and bounded disturbance. For the off-line optimization, a sequence of controller parameters and the corresponding regions of attraction are calculated for all combinations of the pre-specified estimated states and estimation error sets (EESs). These controller parameters and the corresponding regions of attraction are stored in a look-up table. On-line, the controller parameters are searched in this look-up table corresponding to real-time EES, and to the region of attraction with the closest containment of real-time estimated state. This method considerably reduces the on-line computational burden. Two numerical examples are given to illustrate the effectiveness of the approach.     

Stabilizing decentralized model predictive control of nonlinear systems

This note presents a stabilizing decentralized model predictive control (MPC) algorithm for nonlinear discrete time systems. No information is assumed to be exchanged between local control laws. The stability proof relies on the inclusion of a contractive constraint in the formulation of the MPC problem.     

基于混沌粒子群优化的约束状态反馈预测控制算法

提出一种基于混沌粒子群优化的约束状态反馈预测控制算法,用于解决带有输入约束和状态约束的控制问题.将混沌粒子群优化引入到约束状态反馈预测控制的滚动优化过程中,增强了算法在约束范围内的局部搜索和全局搜索能力.通过对一个实际的带有约束的线性离散系统控制优化问题的解决,验证了基于混沌粒子群优化的状态反馈预测控制算法的可行性和有效性,与传统的二次规划算法的比较结果说明了此算法的优越性,证明了状态反馈预测控制系统良好的鲁棒性.