Development of a computer control model for slab reheating furnaces

The development of a two-dimensional computer control model with discrete state space form for the slab reheating furnaces is addressed. The model as developed gives the temperature profile of all slabs or the arbitrarily slab in the furnace by means of the real-time knowledge of working conditions. Industrial experimental data show excellent agreement between simulation results developed from the model and corresponding conditions in the real process. Study of the process involved using computer simulation shows that potential energy savings are possible in this process. A computer control strategy based on the application of the model is presented as well. The work presented here has been accepted by a number of steel companies in China.     

Nonlinear model predictive control of the strip temperature in an annealing furnace

A nonlinear model predictive controller is designed for the strip temperature in a combined direct- and indirect-fired strip annealing furnace. Based on a tailored first-principles dynamical model and the estimated current system state, the receding horizon controller selects optimal trajectories for both the fuel supply and the strip velocity so that the strip temperature is controlled to its desired target temperature. The controller additionally maximizes the throughput and minimizes the energy consumption. In the control algorithm, the dynamic optimization problem with equality constraints is numerically solved by using the Gauss–Newton method. The gradient and the approximated Hessian matrix of the objective function are analytically computed using an adjoint-based method. The capabilities of the proposed controller are demonstrated for a validated high-fidelity simulation model of an industrial annealing furnace.     

Nonlinear offset-free model predictive control

This paper addresses offset-free reference tracking of asymptotically constant reference signals using Model Predictive Control. Existing results for linear models are extended to general nonlinear models. The core of the proposed method employs a disturbance model and an observer to estimate its state. Typical disturbance models are shown and the implications of using them are discussed. Conditions are given for which this setup eliminates the tracking error asymptotically. Basically, we prove that error free output estimation and error free nominal tracking imply offset-free Model Predictive Control.     

Simple fractional order controller combined with a Smith predictor for temperature control in a steel slab reheating furnace

This paper proposes a simple fractional order controller combined with a Smith predictor scheme for controlling the temperature of a steel slab reheating furnace. The dynamic model of the preheating zone of this process is obtained from an identification procedure applied in an industrial furnace. This identification procedure yields a second order plus time delay transfer function which undergoes large time delay changes. A fractional order integral controller combined with a Smith predictor is therefore designed. Simulated results compare the performances of the proposed fractional order controller with a standard PI controller, also combined with a Smith predictor, an LQR controller, and an H _∞ robust controller, in the case of the nominal process, and when the time delay varies. Four performance indexes have been used in this comparison: three related to the output performance (settling time, overshooting, and integral absolute error (IAE)), and a fourth one related to the control effort (TV). The analysis of these indexes shows that the simple fractional order controller provides lower values of the compared indexes when time delay becomes much higher than the nominal value.     

Simultaneous optimization of slab permutation scheduling and heat controlling for a reheating furnace

In this report, for a reheating furnace, which is employed in one of the processes for producing steel sheets from slabs, we propose a modelling method that simultaneously optimizes both the permutation scheduling of slabs and the heat controlling of the furnace. The proposed modelling scheme is based on a hybrid model composed of a nonlinear advection equation that expresses the behavior of the slab temperature and a discrete model for feeding slabs. The model predictive control problem of this model, which will be reduced to a mixed integer programming problem, is formulated by discretizing the advection equation in time and space by means of the method of characteristics and spatially piecewise-linearizing the nonlinear term. It is shown by numerical simulations that the proposed model predictive control method is very effective from the viewpoint of the control performance and the computational burden.     

Nonlinear model predictive control of a magnetic levitation system

The paper presents a fast nonlinear model predictive control (MPC) scheme for a magnetic levitation system. A nonlinear dynamical model of the levitation system is derived that additionally captures the inductor current dynamics of the electromagnet in order to achieve a high MPC performance both for stabilization and fast setpoint changes of the levitating mass. The optimization algorithm underlying the MPC scheme accounts for control constraints and allows for a time and memory efficient computation of the single iteration. The overall control performance of the levitation system as well as the low computational costs of the MPC scheme is shown both in simulations and experiments with a sampling frequency of 700 Hz on a standard dSPACE hardware.     

Nonlinear model predictive control of a reactive distillation column

This paper considers the application of nonlinear model predictive control (NLMPC) to a highly nonlinear reactive distillation column. NLMPC was applied as a nonlinear programming problem using orthogonal collocation on finite elements to approximate the ODEs that constitute the model equations for the reactive distillation column. Diagonal PI controls were used to identify that the [L/D,V] and the [L/D,V/B] configurations performed best. NLMPC was applied using the [L/D,V] configuration and found to provide a factor of 2–3 better performance than the corresponding PI controller. The effect of process/model mismatch on the performance of the NLMPC controller was also evaluated.     

Nonlinear predictive control for a NNARX hydro plant model

A neural network (NN)-based nonlinear predictive control (NPC) is described for control of turbine power with variation in gate position. The studied plant includes the tunnel, surge tank and penstock effect dynamics. Multilayer perceptron neural network is chosen to represent a neural network nonlinear autoregressive with exogenous signal model of hydro power plant. With the said NN model configuration, quasi-Newton and Levenberg–Marquardt iterative optimization algorithms are applied in order to determine optimal predictive control parameters. The controlled response is simulated on different amplitude step function and trapezoidal shape reference signal. The study also discusses comparison with an approximate predictive control approach, being linearized around operating points. It is shown that NPC strategy gives impressive results in comparison to the approximated one.     

采用dsDNA-MC优化的非线性系统预测控制

将基于DNA双链结构的膜计算优化方法（dsDNA-MC）用于输入受限的非线性预测控制器设计,提出了基于dsDNA-MC优化的非线性系统预测控制算法。在对单输入单输出非线性系统预测控制分析的基础上,将非线性系统预测控制问题归结为具有输入约束的非线性系统优化问题,并采用dsDNA-MC算法来求解这一问题。仿真结果表明该算法可行、有效。     

Nonlinear model predictive control of functional electrical stimulation

Minimizing the amount of electrical stimulation can potentially mitigate the adverse effects of muscle fatigue during functional electrical stimulation (FES) induced limb movements. A gradient projection-based model predictive controller is presented for optimal control of a knee extension elicited via FES. A control Lyapunov function was used as a terminal cost to ensure stability of the model predictive control. The controller validation results show that the algorithm can be implemented in real-time with a steady-state RMS error of less than 2°. The experiments also show that the controller follows step changes in desired angles and is robust to external disturbances.     

Nonlinear model predictive control with polytopic invariant sets

Ellipsoidal invariant sets have been widely used as target sets in model predictive control (MPC). These sets can be computed by constructing appropriate linear difference inclusions together with additional constraints to ensure that the ellipsoid lies within a given inclusion polytope. The choice of inclusion polytope has a significant effect on the size of the target ellipsoid, but the optimal inclusion polytope cannot in general be computed systematically. This paper shows that use of polytopic invariant sets overcomes this difficulty, allowing larger stabilizable sets without loss of performance. In the interests of online efficiency, consideration is focused on interpolation-based MPC.     

Nonlinear model predictive control for path following problems

This paper presents a general nonlinear model predictive control scheme for path following problems. Path following problem of nonlinear systems is transformed into a parameter‐dependent regulation problem. Sufficient conditions for recursive feasibility and asymptotic convergence of the given scheme are presented. Furthermore, a polytopic linear differential inclusion‐based method of choosing a suitable terminal penalty and the corresponding terminal constraint are proposed. To illustrate the implementation of the nonlinear model predictive control scheme, the path following problem of a car‐like mobile robot is discussed, and the control performance is confirmed by simulation results. Copyright © 2014 John Wiley & Sons, Ltd.     

Nonlinear model predictive control using trust-region derivative-free optimization

Gradient-based optimization may not be suited if the objective and constraint functions in a nonlinear model predictive control (NMPC) optimization problem are not differentiable. Some well-known derivative-free optimization (DFO)-algorithms are investigated, and a novel warm-start modification to the Wedge DFO-algorithm is proposed. Together with a gradient-based SQP-algorithm these are applied to the NMPC problem and compared in a single-shooting NMPC formulation to a subsea oil–gas separation process. The findings are that DFO is significantly more robust against the numerical issues, compared to a gradient-based SQP tested. Moreover, the warm-start modification reduces the computational complexity.     

Nonlinear model predictive control with regulable computational cost

Nonlinear model predictive control (NMPC) suffers from problems of closed loop instability and huge computational burden, which greatly limit its applications in real plants. In this paper, a new NMPC algorithm, whose stability is robust with respect to regulable computational cost, is presented. First, a new generalized pointwise min‐norm (GPMN) control, as well as its analytic form considering a super‐ball type input constraint, is given. Second, the GPMN controller is integrated into a normal NMPC algorithm as a structure of control input profile to be optimized, called GPMN enhanced NMPC (GPMN‐ENMPC). Finally, a numerical example is presented and simulation results exhibit the advantage of the GPMN‐ENMPC algorithm: computational cost can be regulated according to the computational resources with guaranteed stability. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Nonlinear model predictive control using deterministic global optimization

This paper presents a Nonlinear Model Predictive Control (NMPC) algorithm utilizing a deterministic global optimization method. Utilizing local techniques on nonlinear nonconvex problems leaves one susceptible to suboptimal solutions at each iteration. In complex problems, local solver reliability is difficult to predict and dependent upon the choice of initial guess. This paper demonstrates the application of a deterministic global solution technique to an example NMPC problem. A terminal state constraint is used in the example case study. In some cases the local solution method becomes infeasible, while the global solution correctly finds the feasible global solution. Increased computational burden is the most significant limitation for global optimization based online control techniques. This paper provides methods for improving the global optimization rates of convergence. This paper also shows that globally optimal NMPC methods can provide benefits over local techniques and can successfully be used for online control.     

Nonlinear model predictive control for the ALSTOM gasifier

In this work a nonlinear model predictive control based on Wiener model has been developed and used to control the ALSTOM gasifier. The 0% load condition was identified as the most difficult case to control among three operating conditions. A linear model of the plant at 0% load is adopted as a base model for prediction. A nonlinear static gain represented by a feedforward neural network was identified for a particular output channel—namely, fuel gas pressure, to compensate its strong nonlinear behaviour observed in open-loop simulations. By linearising the neural network at each sampling time, the static nonlinear model provides certain adaptation to the linear base model at all other load conditions. The resulting controller showed noticeable performance improvement when compared with pure linear model based predictive control.     

Nonlinear model predictive control using parameter varying BP-ARX combination model

A novel back-propagation AutoRegressive with eXternal input (BP-ARX) combination model is constructed for model predictive control (MPC) of MIMO nonlinear systems, whose steady-state relation between inputs and outputs can be obtained. The BP neural network represents the steady-state relation, and the ARX model represents the linear dynamic relation between inputs and outputs of the nonlinear systems. The BP-ARX model is a global model and is identified offline, while the parameters of the ARX model are rescaled online according to BP neural network and operating data. Sequential quadratic programming is employed to solve the quadratic objective function online, and a shift coefficient is defined to constrain the effect time of the recursive least-squares algorithm. Thus, a parameter varying nonlinear MPC (PVNMPC) algorithm that responds quickly to large changes in system set-points and shows good dynamic performance when system outputs approach set-points is proposed. Simulation results in a multivariable stirred tank and a multivariable pH neutralisation process illustrate the applicability of the proposed method and comparisons of the control effect between PVNMPC and multivariable recursive generalised predictive controller are also performed.     

Nonlinear model predictive control from data: a set membership approach

A new approach to design a Nonlinear Model Predictive Control law that employs an approximate model, derived directly from data, is introduced. The main advantage of using such models lies in the possibility to obtain a finite computable bound on the worst‐case model error. Such a bound can be exploited to analyze the robust convergence of the system trajectories to a neighborhood of the origin. The effectiveness of the proposed approach, named Set Membership Predictive Control, is shown in a vehicle lateral stability control problem, through numerical simulations of harsh maneuvers. Copyright © 2012 John Wiley & Sons, Ltd.     

离线椭圆集的非线性模型预测控制算法研究

针对一类带有约束的非线性系统,提出一种非线性时间最优模型预测控制算法。这种方法首先基于Jacobian线性化将非线性进行线性化,能够推导一系列凸优化问题,而且产生的线性化误差在Lipschitz条件下确定上边界范围。然后采用双重模式策略,在离线情况下构造一系列椭圆集来描述[t]步可行区域,每个椭圆集的平衡点根据上一个椭圆来选取,最后再根据在线计算合适的输入使系统稳定。采用逐步倒退计算的方法能够确保迭代的可行性和稳定性,大大减少了计算负担。数值例子证明了算法的有效性。