A stable MPC with zone control

Several MPC applications implement a control strategy in which some of the system outputs are controlled within specified ranges or zones, rather than at fixed set points [J.M. Maciejowski, Predictive Control with Constraints, Prentice Hall, New Jersey, 2002]. This means that these outputs will be treated as controlled variables only when the predicted future values lie outside the boundary of their corresponding zones. The zone control is usually implemented by selecting an appropriate weighting matrix for the output error in the control cost function. When an output prediction is inside its zone, the corresponding weight is zeroed, so that the controller ignores this output. When the output prediction lies outside the zone, the error weight is made equal to a specified value and the distance between the output prediction and the boundary of the zone is minimized. The main problem of this approach, as long as stability of the closed loop is concerned, is that each time an output is switched from the status of non-controlled to the status of controlled, or vice versa, a different linear controller is activated. Thus, throughout the continuous operation of the process, the control system keeps switching from one controller to another. Even if a stabilizing control law is developed for each of the control configurations, switching among stable controllers not necessarily produces a stable closed loop system.Here, a stable MPC is developed for the zone control of open-loop stable systems. Focusing on the practical application of the proposed controller, it is assumed that in the control structure of the process system there is an upper optimization layer that defines optimal targets to the system inputs. The performance of the proposed strategy is illustrated by simulation of a subsystem of an industrial FCC system.     

Predictive direct torque control with reduced ripples for induction motor drive based on T‐S fuzzy speed controller

Finite‐state model predictive control (FS‐MPC) has been widely used for controlling power converters and electric drives. Predictive torque control strategy (PTC) evaluates flux and torque in a cost function to generate an optimal inverter switching state in a sampling period. However, the existing PTC method relies on a traditional proportional‐integral (PI) controller in the external loop for speed regulation. Consequently, the torque reference may not be generated properly, especially when a sudden variation of load or inertia takes place. This paper proposes an enhanced predictive torque control scheme. A Takagi‐Sugeno fuzzy logic controller replaces PI in the external loop for speed regulation. Besides, the proposed controller generates a proper torque reference since it plays an important role in cost function design. This improvement ensures accurate tracking and robust control against different uncertainties. The effectiveness of the presented algorithms is investigated by simulation and experimental validation using MATLAB/Simulink with dSpace 1104 real‐time interface.     

基于模糊线性自抗扰的柔性多状态开关控制研究

为抑制系统干扰对三端口柔性多状态开关(FMSS)直流侧电压的影响,提出了一种基于模糊线性自抗扰控制(LADRC)的三端口FMSS控制策略。首先,根据LADRC算法设计出LADRC控制器来替代电压外环和电流内环中的PI控制器,以此增强系统的抗干扰性能;其次,通过模糊控制改进电流内环的LADRC控制器,从而得到一种用于干扰抑制的模糊LADRC控制器,实现控制器参数可随扰动实时变化,以达到抑制干扰的目的;最后,在MATLAB/Simulink中建立三端口FMSS仿真模型,对控制策略进行仿真验证。仿真结果表明,与采用LADRC控制策略相比,所提控制策略具有更好的抗干扰性能和稳定性,能有效地抑制FMSS直流侧电压波动。     

Robust MPC for Linear Systems with Structured Time‐Varying Uncertainties and Saturating Actuator

In this paper, a synthesis of model predictive control (MPC) algorithm is presented for uncertain systems subject to structured time‐varying uncertainties and actuator saturation. The system matrices are not exactly known, but are affine functions of a time varying parameter vector. To deal with the nonlinear actuator saturation, a saturated linear feedback control law is expressed into a convex hull of a group of auxiliary linear feedback laws. At each time instant, a state feedback law is designed to ensure the robust stability of the closed‐loop system. The robust MPC controller design problem is formulated into solving a minimization problem of a worst‐case performance index with respect to model uncertainties. The design of controller is then cast into solving a feasibility of linear matrix inequality (LMI) optimization problem. Then, the result is further extended to saturation dependent robust MPC approach by introducing additional variables. A saturation dependent quadratic function is used to reduce the conservatism of controller design. To show the effectiveness, the proposed robust MPC algorithms are applied to a continuous‐time stirred tank reactor (CSTR) process.     

Theoretical analysis of unconstrained nonlinear model predictive control

Model predictive control (MPC) is a well-established controller design strategy for linear process models. Because many chemical and biological processes exhibit significant nonlinear behaviour, several MPC techniques based on nonlinear process models have recently been proposed. The most significant difference between these techniques is the computational approach used to solve the nonlinear model predictive control (NMPC) optimization problem. Consequently, analysis of NMPC techniques is often connected to the computational approach employed. In this paper, a theoretical analysis of unconstrained NMPC is presented that is independent of the computational approach. A nonlinear discrete-time, state-space model is used to predict the effects of future inputs on future process outputs. It is shown that model inverse, pole-placement, and steady-state controllers can be obtained by suitable selection of the control and prediction horizons. Moreover, the NMPC optimization problem can be modified to yield nonlinear internal model control (NIMC). The computational requirements of NIMC are considerably less than NMPC, but the NIMC approach is currently restricted to nonlinear models with well-defined and stable inverses. The NIMC controller is shown to provide superior servo and regulatory performance to a linear IMC controller for a continuous stirred tank reactor.     

Dual closed‐loop tracking control for wheeled mobile robots via active disturbance rejection control and model predictive control

A dual closed‐loop tracking control is proposed for a wheeled mobile robot based on active disturbance rejection control (ADRC) and model predictive control (MPC). In the inner loop system, the ADRC scheme with an extended state observer (ESO) is proposed to estimate and compensate external disturbances. In the outer loop system, the MPC strategy is developed to generate a desired velocity for the inner loop dynamic system subject to a diamond‐shaped input constraint. Both effectiveness and stability analysis are given for the ESO and the dual closed‐loop system, respectively. Simulation results demonstrate the performances of the proposed control scheme.     

Disturbance observer based multi-variable control of ball mill grinding circuits

Ball mill grinding circuits are essentially multi-variable systems characterized with couplings, time-varying parameters and time delays. The control schemes in previous literatures, including detuned multi-loop PID control, model predictive control (MPC), robust control, adaptive control, and so on, demonstrate limited abilities in control ball mill grinding process in the presence of strong disturbances. The reason is that they do not handle the disturbances directly by controller design. To this end, a disturbance observer based multi-variable control (DOMC) scheme is developed to control a two-input-two-output ball mill grinding circuit. The systems considered here are with lumped disturbances which include external disturbances, such as the variations of ore hardness and feed particle size, and internal disturbances, such as model mismatches and coupling effects. The proposed control scheme consists of two compound controllers, one for the loop of product particle size and the other for the loop of circulating load. Each controller includes a PI feedback part and a feed-forward compensation part for the disturbances by using a disturbance observer (DOB). A rigorous analysis is also given to show the reason why the DOB can effectively suppress the disturbances. Performance of the proposed scheme is compared with those of the MPC and multi-loop PI schemes in the cases of model mismatches and strong external disturbances, respectively. The simulation results demonstrate that the proposed method has a better disturbance rejection property than those of the MPC and PI methods in controlling ball mill grinding circuits.     

Closed-loop stable model predictive control of integrating systems with dead time

Model predictive control (MPC) applications in the process industry usually deal with process systems that show time delays (dead times) between the system inputs and outputs. Also, in many industrial applications of MPC, integrating outputs resulting from liquid level control or recycle streams need to be considered as controlled outputs. Conventional MPC packages can be applied to time-delay systems but stability of the closed loop system will depend on the tuning parameters of the controller and cannot be guaranteed even in the nominal case. In this work, a state space model based on the analytical step response model is extended to the case of integrating time systems with time delays. This model is applied to the development of two versions of a nominally stable MPC, which is designed to the practical scenario in which one has targets for some of the inputs and/or outputs that may be unreachable and zone control (or interval tracking) for the remaining outputs. The controller is tested through simulation of a multivariable industrial reactor system.     

Synthesis of Mixed Objective Output Feedback Robust Model Predictive Control

Aiming at the constrained polytopic uncertain system with energy‐bounded disturbance and unmeasurable states, a novel synthesis scheme to design the output feedback robust model predictive control(MPC)is put forward by using mixed H₂/H_∞ design approach. The proposed scheme involves an offline design of a robust state observer using linear matrix inequalities(LMIs)and an online output feedback robust MPC algorithm using the estimated states in which the desired mixed objective robust output feedback controllers are cast into efficiently tractable LMI‐based convex optimization problems. In addition, the closed‐loop stability and the recursive feasibility of the proposed robust MPC are guaranteed through an appropriate reformulation of the estimation error bound (EEB). A numerical example subject to input constraints illustrates the effectiveness of the proposed controller.     

Comparison of three control strategies for optimization of spray dryer operation

Spray drying is the preferred process to reduce the water content of many chemicals, pharmaceuticals, and foodstuffs. A significant amount of energy is used in spray drying to remove water and produce a free flowing powder product. In this paper, we present and compare the performance of three controllers for operation of a four-stage spray dryer. The three controllers are a proportional-integral (PI) controller that is used in industrial practice for spray dryer operation, a linear model predictive controller with real-time optimization (MPC with RTO, MPC-RTO), and an economically optimizing nonlinear model predictive controller (E-NMPC). The MPC with RTO is based on the same linear state space model in the MPC and the RTO layer. The E-NMPC consists of a single optimization layer that uses a nonlinear system of ordinary differential equations for its predictions. The PI control strategy has a fixed target that is independent of the disturbances, while the MPC-RTO and the E-NMPC adapt the operating point to the disturbances. The goal of spray dryer operation is to optimize the profit of operation in the presence of feed composition and ambient air humidity variations; i.e. to maximize the production rate, while minimizing the energy consumption, keeping the residual moisture content of the powder below a maximum limit, and avoiding that the powder sticks to the chamber walls. We use an industrially recorded disturbance scenario in order to produce realistic simulations and conclusions. The key performance indicators such as the profit of operation, the product flow rate, the specific energy consumption, the energy efficiency, and the residual moisture content of the produced powder are computed and compared for the three controllers. In this simulation study, we find that the economic performance of the MPC with RTO as well as the E-NMPC is considerably improved compared to the PI control strategy used in industrial practice. The MPC with RTO improves the profit of operation by 8.61%, and the E-NMPC improves the profit of operation by 9.66%. The energy efficiency is improved by 6.21% and 5.51%, respectively.     

Disturbance modeling for offset-free linear model predictive control

An offset-free controller is one that drives controlled outputs to their desired targets at steady state. In the linear model predictive control (MPC) framework, offset-free control is usually achieved by adding step disturbances to the process model. The most widely-used industrial MPC implementations assume a constant output disturbance that can lead to sluggish rejection of disturbances that enter the process elsewhere. This paper presents a general disturbance model that accommodates unmeasured disturbances entering through the process input, state, or output. Conditions that guarantee detectability of the augmented system model are provided, and a steady-state target calculation is constructed to remove the effects of estimated disturbances. Conditions for which offset-free control is possible are stated for the combined estimator, steady-state target calculation, and dynamic controller. Simulation examples are provided to illustrate trade-offs in disturbance model design.     

MPC for tracking zone regions

This paper deals with the problem of tracking target sets using a model predictive control (MPC) law. Some MPC applications require a control strategy in which some system outputs are controlled within specified ranges or zones (zone control), while some other variables – possibly including input variables - are steered to fixed target or set-point. In real applications, this problem is often overcome by including and excluding an appropriate penalization for the output errors in the control cost function. In this way, throughout the continuous operation of the process, the control system keeps switching from one controller to another, and even if a stabilizing control law is developed for each of the control configurations, switching among stable controllers not necessarily produces a stable closed loop system. From a theoretical point of view, the control objective of this kind of problem can be seen as a target set (in the output space) instead of a target point, since inside the zones there are no preferences between one point or another. In this work, a stable MPC formulation for constrained linear systems, with several practical properties is developed for this scenario. The concept of distance from a point to a set is exploited to propose an additional cost term, which ensures both, recursive feasibility and local optimality. The performance of the proposed strategy is illustrated by simulation of an ill-conditioned distillation column.     

A data‐driven bilinear predictive controller design based on subspace method

In this paper, a new data‐driven model predictive control (MPC), based on bilinear subspace identification, is considered. The system's nonlinear behavior is described with a bilinear subspace predictor structure in an MPC framework. Thus, the MPC formulation results in a fixed structure objective function with constraints regardless of the underlying nonlinearity. For unconstrained systems, the identified subspace predictor matrices can be directly used as controller parameters. Therefore, we design optimization algorithms that exploit this feature. The open‐loop optimization problem of MPC that is nonlinear in nature is solved with series quadratic programming (SQP) without any approximations. The computational efficiency already demonstrated with the current formulation presents further opportunities to enable online control of nonlinear systems. These improvements and close integration of modeling and control also eliminate the intermediate design step, which provides a means for data‐driven controller design in generalized predictive controller (GPC) framework. Finally, the proposed control approach is illustrated with a verification study of a nonlinear continuously stirred tank reactor (CSTR) system. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

基于参数优化的永磁同步电动机直接转矩控制系统自抗扰控制器研究

针对基于PI控制器的永磁同步电动机直接转矩控制系统存在转矩波动大、易受负载变化影响的问题,设计了一种基于转速外环的自抗扰控制器,代替PI控制器以改善永磁同步电动机直接转矩控制系统的性能;采用粒子群优化算法对自抗扰控制器的相关参数进行了优化计算,改进了控制器的调节性能。仿真和实验结果表明,基于参数优化自抗扰控制器的永磁同步电动机直接转矩控制系统具有较高的抗负载扰动能力,更快的响应速度和良好的动、静态性能。     

Optimal grade transition control for liquid‐propylene polymerization reactor

A nonlinear control system integrating an off‐line optimizer and a nonlinear model‐based controller is developed to perform optimal grade transition operations in a continuous pilot plant reactor. A simple black‐box model is developed and used to determine optimal trajectories of inputs and outputs for a series of three polypropylene grades. The simplified model is also used to develop a nonlinear controller. This controller is similar to generic model control; however, the integral action is omitted and an on‐line updating scheme is incorporated to update pre‐specified model parameters using delayed process measurements. The time optimal inputs, which are calculated by the off‐line optimizer, are introduced to the plant in a feedforward manner. At the same time, the deviations from the optimal output are corrected using the feedback nonlinear controller. The simulations on a complex mechanistic model of the process reveal that the nonlinear control scheme performs well for both set point tracking and disturbance rejection. This paper integrates well‐known methodologies, such as the generic‐model control algorithm, parameter update schemes, and off‐line optimization, together to develop an applicable and robust control technique for continuous polymerization reactors. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Stochastic model predictive control for probabilistically constrained Markovian jump linear systems with additive disturbance

Model predictive control (MPC) for Markovian jump linear systems with probabilistic constraints has received much attention in recent years. However, in existing results, the disturbance is usually assumed with infinite support, which is not considered reasonable in real applications. Thus, by considering random additive disturbance with finite support, this paper is devoted to a systematic approach to stochastic MPC for Markovian jump linear systems with probabilistic constraints. The adopted MPC law is parameterized by a mode‐dependent feedback control law superimposed with a perturbation generated by a dynamic controller. Probabilistic constraints can be guaranteed by confining the augmented system state to a maximal admissible set. Then, the MPC algorithm is given in the form of linearly constrained quadratic programming problems by optimizing the infinite sum of derivation of the stage cost from its steady‐state value. The proposed algorithm is proved to be recursively feasible and to guarantee constraints satisfaction, and the closed‐loop long‐run average cost is not more than that of the unconstrained closed‐loop system with static feedback. Finally, when adopting the optimal feedback gains in the predictive control law, the resulting MPC algorithm has been proved to converge in the mean square sense to the optimal control. A numerical example is given to verify the efficiency of the proposed results.     

Pitch Loop Control of a VTOL UAV Using Fractional Order Controller

Pitch loop control is the fundamental tuning step for vertical takeoff and landing (VTOL) unmanned aerial vehicles (UAVs), and has significant impact on the flight. In this paper, a fractional order strategy is designed to control the pitch loop of a VTOL UAV. First, an auto-regressive with exogenous input (ARX) model is acquired and converted to a first-order plus time delay (FOPTD) model. Next, based on the FOPTD model, a fractional order [proportional integral] (FO[PI]) controller is designed. Then, an integer order PI controller based on the modified Ziegler-Nichols (MZNs) tuning rule and a general integer order proportional integral derivative (PID) controller are also designed for comparison following three design specifications. Simulation results have shown that the proposed fractional order controller outperforms both the MZNs PI controller and the integer order PID controller in terms of robustness and disturbance rejection. At last, ARX model based system identification of AggieAir VTOL platform is achieved with experimental flight data.     

Adaptive air-fuel ratio control with MLP network

This paper presents an application of adaptive neural network model-based predictive control (MPC) to the air-fuel ratio of an engine simulation. A multi-layer perceptron (MLP) neural network is trained using two on-line training algorithms: a back propagation algorithm and a recursive least squares (RLS) algorithm. It is used to model parameter uncertainties in the nonlinear dynamics of internal combustion (IC) engines. Based on the adaptive model, an MPC strategy for controlling air-fuel ratio is realized, and its control performance compared with that of a traditional PI controller. A reduced Hessian method, a newly developed sequential quadratic programming (SQP) method for solving nonlinear programming (NLP) problems, is implemented to speed up nonlinear optimization in the MPC.     

自适应鲁棒最优PI控制器

提出一种具有鲁棒性能的自适应最优PI控制器, 它首先基于控制回路在正常运行操作中产生的过程输入和输出信号, 通过信号分解和频域分析在线辨识出过程对象在重要频率点的频率特性, 然后计算出可同时满足鲁棒性能指标λ和最小负载扰动特性的最优PI控制器参数, 同时控制性能可以很方便地根据实际需要通过改变鲁棒性能指标λ来调节. PI控制器的自适应过程不需要过程对象和控制器的任何先验知识, 也不需要中断控制回路的正常运行, 仿真实验表明了自适应控制器的有效性和可行性.