Model predictive control for a class of systems with isolated nonlinearity

The paper is concerned with an overall convergent nonlinear model predictive control design for a kind of nonlinear mechatronic drive systems. The proposed nonlinear model predictive control results in the improvement of regulatory capacity for reference tracking and load disturbance rejection. The design of the nonlinear model predictive controller consists of two steps: the first step is to design a linear model predictive controller based on the linear part of the system at each sample instant, then an overall convergent nonlinear part is added to the linear model predictive controller to combine a nonlinear controller using error driven. The structure of the proposed controller is similar to that of classical PI optimal regulator but it also bears a set-point feed forward control loop, thus tracking ability and disturbance rejection are improved. The proposed method is compared with the results from recent literature, where control performance under both model match and mismatch cases are enlightened.     

T–S fuzzy model predictive speed control of electrical vehicles

This paper proposes a novel nonlinear model predictive controller (MPC) in terms of linear matrix inequalities (LMIs). The proposed MPC is based on Takagi–Sugeno (TS) fuzzy model, a non-parallel distributed compensation (non-PDC) fuzzy controller and a non-quadratic Lyapunov function (NQLF). Utilizing the non-PDC controller together with the Lyapunov theorem guarantees the stabilization issue of this MPC. In this approach, at each sampling time a quadratic cost function with an infinite prediction and control horizon is minimized such that constraints on the control input Euclidean norm are satisfied. To show the merits of the proposed approach, a nonlinear electric vehicle (EV) system with parameter uncertainty is considered as a case study. Indeed, the main goal of this study is to force the speed of EV to track a desired value. The experimental data, a new European driving cycle (NEDC), is used in order to examine the performance of the proposed controller. First, the equivalent TS model of the original nonlinear system is derived. After that, in order to evaluate the proficiency of the proposed controller, the achieved results of the proposed approach are compared with those of the conventional MPC controller and the optimal Fuzzy PI controller (OFPI), which are the latest research on the problem in hand.     

RBF-ARX model-based fast robust MPC approach to an inverted pendulum

In general, the online computation burden of robust model predictive control (RMPC) is very heavy, and the mechanical model of a plant, which is used in RMPC, is hard to obtain precisely in real industry. These issues may largely restrict the applicability of RMPC in real applications. This paper proposes a RBF-ARX (state-dependent Auto-Regressive model with eXogenous input and Radial Basis Function network type coefficients) model-based efficient robust predictive control (RBF-ARX-ERPC) approach to an inverted pendulum system, which is a complete and systematic method for designing robust MPC controller because it integrates the RBF-ARX modeling method and a fast RMPC approach. First, based on the offline identified RBF-ARX model without offset term, two convex polytopic sets are constructed to wrap the globally nonlinear behavior of the system. Then, the optimization problem of implementing a quasi-min–max MPC algorithm including several linear matrix inequalities (LMIs) is formulated, and it is solved offline to synthesize a sequence of explicit control laws that correspond to a sequence of asymptotically stable invariant ellipsoids, of which all the optimization results are stored in a look-up table. During the online real-time control, the controller only needs to carry out a simple state-vector computation and bisection search. The proposed approach is applied to an actual linear one-stage inverted pendulum (LOSIP), which is a fast-responding and nonlinear plant. The real-time control experiments demonstrate the effectiveness of the proposed RBF-ARX model-based efficient RMPC approach.     

Robust control of speed and temperature in a power plant gas turbine

In this paper, an H(∞) robust controller has been designed for an identified model of MONTAZER GHAEM power plant gas turbine (GE9001E). In design phase, a linear model (ARX model) which is obtained using real data has been applied. Since the turbine has been used in a combined cycle power plant, its speed and also the exhaust gas temperature should be adjusted simultaneously by controlling fuel signals and compressor inlet guide vane (IGV) position. Considering the limitations on the system inputs, the aim of the control is to maintain the turbine speed and the exhaust gas temperature within desired interval under uncertainties and load demand disturbances. Simulation results of applying the proposed robust controller on the nonlinear model of the system (NARX model), fairly fulfilled the predefined aims. Simulations also show the improvement in the performance compared to MPC and PID controllers for the same conditions.     

A nonlinear regression model-based predictive control algorithm

This paper presents a unique approach for designing a nonlinear regression model-based predictive controller (NRPC) for single-input-single-output (SISO) and multi-input-multi-output (MIMO) processes that are common in industrial applications. The innovation of this strategy is that the controller structure allows nonlinear open-loop modeling to be conducted while closed-loop control is executed every sampling instant. Consequently, the system matrix is regenerated every sampling instant using a continuous function providing a more accurate prediction of the plant. Computer simulations are carried out on nonlinear plants, demonstrating that the new approach is easily implemented and provides tight control. Also, the proposed algorithm is implemented on two real time SISO applications; a DC motor, a plastic injection molding machine and a nonlinear MIMO thermal system comprising three temperature zones to be controlled with interacting effects. The experimental closed-loop responses of the proposed algorithm were compared to a multi-model dynamic matrix controller (MPC) with improved results for various set point trajectories. Good disturbance rejection was attained, resulting in improved tracking of multi-set point profiles in comparison to multi-model MPC.     

永磁直线伺服系统模糊PI速度控制器研究

针对永磁直线同步电机伺服系统常规PI速度调节器动态响应慢、输出超调大等问题,提出了模糊自适应PI速度控制器,对比常规PI速度控制器进行了仿真和实验。基于永磁直线同步电机矢量速度闭环控制,分析了模糊PI速度控制器和基于模糊PI控制器的伺服矢量控制系统的结构,设计了模糊PI速度控制器,在Matlab/Simulink仿真环境下,建立了基于模糊PI速度控制器的永磁直线同步电机伺服系统仿真模型,并通过实际永磁同步直线电机伺服系统实验对仿真结果进行了实验验证。研究结果表明,模糊PI速度控制器,相对于常规PI控制器,可以明显降低超调量和调节时间。将仿真结果和试验结果对比,两者基本吻合,说明模糊PI速度控制确实可以较好地改善永磁直线同步电机伺服系统的动态性能。     

Modeling a multivariable reactor and on-line model predictive control

A nonlinear first principle model is developed for a laboratory-scaled multivariable chemical reactor rig in this paper and the on-line model predictive control (MPC) is implemented to the rig. The reactor has three variables-temperature, pH, and dissolved oxygen with nonlinear dynamics-and is therefore used as a pilot system for the biochemical industry. A nonlinear discrete-time model is derived for each of the three output variables and their model parameters are estimated from the real data using an adaptive optimization method. The developed model is used in a nonlinear MPC scheme. An accurate multistep-ahead prediction is obtained for MPC, where the extended Kalman filter is used to estimate system unknown states. The on-line control is implemented and a satisfactory tracking performance is achieved. The MPC is compared with three decentralized PID controllers and the advantage of the nonlinear MPC over the PID is clearly shown.     

Real time linear simulation and control for small aircraft turbojet engine

The performance of the aircraft gas turbine engine requires optimization because it is directly related to overall aircraft performance. In this study, a modified DYNGEN, a nolinear dynamic simulation program with component maps of the small aircraft turbojet engine, was used to predict the overall engine performance. Response characteristics of various cases, such as 6%, 5% and 3% rpm step models and the real-time linear model of the interpolation scheme within the operating range were compared. Among them, the real time linear model was selected for the turbojet engine with nonlinear characteristics. Finally control schemes such as PI (Proportional-Integral Controller) and LQR (Linear Quadratic Regulator) were applied to optimize the engine performance. The overshoot of the turbine inlet temperature was effectively eliminated by LQR controller with the proper control gain K.     

Distributed model predictive control for constrained nonlinear systems with decoupled local dynamics

This paper considers the distributed model predictive control (MPC) of nonlinear large-scale systems with dynamically decoupled subsystems. According to the coupled state in the overall cost function of centralized MPC, the neighbors are confirmed and fixed for each subsystem, and the overall objective function is disassembled into each local optimization. In order to guarantee the closed-loop stability of distributed MPC algorithm, the overall compatibility constraint for centralized MPC algorithm is decomposed into each local controller. The communication between each subsystem and its neighbors is relatively low, only the current states before optimization and the optimized input variables after optimization are being transferred. For each local controller, the quasi-infinite horizon MPC algorithm is adopted, and the global closed-loop system is proven to be exponentially stable.     

基于状态反馈线性化的阀控非对称缸系统模型预测控制

针对使用PID方法对阀控非对称液压缸位置控制中出现的超调问题,以及传统非线性模型预测控制优化求解计算时间较长的问题,提出了一种基于状态反馈线性化的阀控非对称缸模型预测控制方案。首先建立了阀控系统状态空间模型,运用微分几何理论讨论系统可反馈线性化的充要条件,并将非线性系统映射为新坐标空间内的线性系统模型;设计了反馈线性化模型预测控制器(Feedback Linearization Model Predictive Controller, FLMPC),讨论了线性系统下的约束问题,其中由于系统仿真预测时域远小于系统响应时间,对模型预测控制的损失函数加以修正。结果证明,在相同输入情况下,反馈线性化系统与原系统的位置误差满足控制需要,且在保证被控对象快速稳定控制的条件下,对比该算法与非线性模型预测控制的单步计算时间,证明该算法能够缩短计算时间。     

A simple method of tuning parallel cascade controllers for unstable FOPTD systems

A simple method is proposed to design parallel cascade controllers for open loop unstable processes. A proportional (P)controller is considered for the secondary loop and a proportional integral (PI) controller is considered for the primary loop (P/PI control configuration). Coefficients of the corresponding powers of s (Laplace variable), in the numerator is matched with the coefficients of the corresponding powers of s in the denominator of a closed loop transfer function for a servo problem. Three simulation case studies are considered in this paper. The first case involves a stable secondary loop process and an unstable primary process, the second case involves both unstable primary and secondary processes and the third one, a simulation application to a nonlinear bioreactor model equations. For comparison purposes, P/PI controller design is also carried out by improved simultaneous relay autotuning method, synthesis method and minimizing ISE criterion method. It is found that the proposed method gives a better performance. Robust stability analysis using the complimentary sensitivity function is carried out. The present method is found to be more robust.     

Stable modeling based control methods using a new RBF network

This paper presents a novel model with radial basis functions (RBFs), which is applied successively for online stable identification and control of nonlinear discrete-time systems. First, the proposed model is utilized for direct inverse modeling of the plant to generate the control input where it is assumed that inverse plant dynamics exist. Second, it is employed for system identification to generate a sliding-mode control input. Finally, the network is employed to tune PID (proportional + integrative + derivative) controller parameters automatically. The adaptive learning rate (ALR), which is employed in the gradient descent (GD) method, provides the global convergence of the modeling errors. Using the Lyapunov stability approach, the boundedness of the tracking errors and the system parameters are shown both theoretically and in real time. To show the superiority of the new model with RBFs, its tracking results are compared with the results of a conventional sigmoidal multi-layer perceptron (MLP) neural network and the new model with sigmoid activation functions. To see the real-time capability of the new model, the proposed network is employed for online identification and control of a cascaded parallel two-tank liquid-level system. Even though there exist large disturbances, the proposed model with RBFs generates a suitable control input to track the reference signal better than other methods in both simulations and real time.     

Nonlinear predictive control of a boiler-turbine unit: A state-space approach with successive on-line model linearisation and quadratic optimisation

This paper details development of a Model Predictive Control (MPC) algorithm for a boiler-turbine unit, which is a nonlinear multiple-input multiple-output process. The control objective is to follow set-point changes imposed on two state (output) variables and to satisfy constraints imposed on three inputs and one output. In order to obtain a computationally efficient control scheme, the state-space model is successively linearised on-line for the current operating point and used for prediction. In consequence, the future control policy is easily calculated from a quadratic optimisation problem. For state estimation the extended Kalman filter is used. It is demonstrated that the MPC strategy based on constant linear models does not work satisfactorily for the boiler-turbine unit whereas the discussed algorithm with on-line successive model linearisation gives practically the same trajectories as the truly nonlinear MPC controller with nonlinear optimisation repeated at each sampling instant.     

Model predictive control of non-linear systems over networks with data quantization and packet loss

This paper studies the approach of model predictive control (MPC) for the non-linear systems under networked environment where both data quantization and packet loss may occur. The non-linear controlled plant in the networked control system (NCS) is represented by a Tagaki-Sugeno (T-S) model. The sensed data and control signal are quantized in both links and described as sector bound uncertainties by applying sector bound approach. Then, the quantized data are transmitted in the communication networks and may suffer from the effect of packet losses, which are modeled as Bernoulli process. A fuzzy predictive controller which guarantees the stability of the closed-loop system is obtained by solving a set of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed method.     

Fuel cell starvation control using model predictive technique with Laguerre and exponential weight functions

Fuel cell system is a complicated system that requires an efficient controller. Model predictive control is a prime candidate for its optimization and constraint handling features. In this work, an improved model predictive control (MPC) with Laguerre and exponential weight functions is proposed to control fuel cell oxygen starvation problem. To get the best performance of MPC, the control and prediction horizons are selected as large as possible within the computation limit. An exponential weight function is applied to place more emphasis on the current time and less emphasis on the future time in the optimization process. This leads to stable numerical solution for large prediction horizons. Laguerre functions are used to capture most of the control trajectory, while reducing the controller computation time and memory for large prediction horizons. Robustness and stability of the proposed controller are assessed using Monte-Carlo simulations. Results verify that the modified MPC is able to mimic the performance of the infinite horizon controller, discrete linear quadratic regulator (DLQR). The controller computation time is reduced approximately by one order of magnitude compared to traditional MPC scheme. Results from Monte-Carlo simulations prove that the proposed controller is robust and stable up to system parameters uncertainty of 40%.     

Application of Gaussian processes for black-box modelling of biosystems

Different models can be used for nonlinear dynamic system identification and the Gaussian process model is a relatively new option with several interesting features: model predictions contain the measure of confidence, the model has a small number of training parameters and facilitated structure determination, and different possibilities of including prior knowledge exist. In this paper the framework for the identification of a dynamic system model based on Gaussian processes is shown, illustrated on a simulated bioreactor example and then applied to two case studies. The first one addresses modelling of the nitrification process in a wastewater treatment plant and the second models biomass growth in the Lagoon of Venice. Special emphasis is placed on model validation, an often underemphasised part of the identification procedure, where the Gaussian model prediction variance can be utilised.     

Predictive IP controller for robust position control of linear servo system

Position control is a typical application of linear servo system. In this paper, to reduce the system overshoot, an integral plus proportional (IP) controller is used in the position control implementation. To further improve the control performance, a gain-tuning IP controller based on a generalized predictive control (GPC) law is proposed. Firstly, to represent the dynamics of the position loop, a second-order linear model is used and its model parameters are estimated on-line by using a recursive least squares method. Secondly, based on the GPC law, an optimal control sequence is obtained by using receding horizon, then directly supplies the IP controller with the corresponding control parameters in the real operations. Finally, simulation and experimental results are presented to show the efficiency of proposed scheme.     

汽车线性与非线性乘坐动力学建模与仿真研究

在建立4自由度半车线性与非线性数学模型的基础上,选择半圆形凸起、波形路面为离散事件激励进行仿真。结果表明,两者的误差在较大的范围内变化,只有当路面激励状况在特定的工作点附近变化时,线性模型才可较精确地代替非线性模型。国内路面状况比较复杂,如果采用线性模型进行乘坐动力学系统的参数设计,采用非线性模型在不同路况下进行仿真是必要的。