Hybrid explicit model predictive control of a nonlinear process approximated with a piecewise affine model

The recently developed methods of explicit (multi-parametric) model predictive control (e-MPC) for hybrid systems provide an interesting opportunity for solving a class of nonlinear control problems. With this approach, the nonlinear process is approximated by a piecewise affine (PWA) hybrid model containing a set of local linear dynamics. Compared to linear-model-based MPC, a performance improvement is expected with the reduction of the plant-to-model mismatch; however at a cost of controller computation complexity. In order to reduce the computational load, so that desired horizon lengths may be used, we present an efficient sub-optimal solution. The feasibility of the approach for the application was evaluated in an experimental case study, where an output feedback, offset-free-tracking hybrid e-MPC controller was considered as a replacement for a PID-controller-based scheme for the control of the pressure in a wire-annealing machine.     

Neural network robust control of a 3-DOF hydraulic manipulator with asymptotic tracking

Multiaxial hydraulic manipulators are complicated systems with highly nonlinear dynamics and various modeling uncertainties, which hinders the development of high-performance controller. In this paper, a neural network feedforward with a robust integral of the sign of the error (RISE) feedback is proposed for high precise tracking control of hydraulic manipulator systems. The established nonlinear model takes three-axis dynamic coupling, hydraulic actuator dynamics, and nonlinear friction effects into consideration. A radial basis function neural network (RBFNN) is synthesized to approximate the uncertain system dynamics and external disturbance, which can greatly reduce the dependence on accurate system model. In addition, a continuous RISE feedback law is judiciously integrated to deal with the residual unknown dynamics. Since the major unknown dynamics can be estimated by the RBFNN and then compensated in the feedforward design, the high-gain feedback issue in RISE feedback control will be avoided. The proposed RISE-based neural network robust controller theoretically guarantees an excellent semi-global asymptotic stability. Comparative simulation is performed on a 3-DOF hydraulic manipulator, and the obtained results verify the effectiveness of the proposed controller.     

Robust stabilization of nonlinear interconnected systems with application to an industrial utility boiler

This paper presents a new scheme for robust stabilization of nonlinear interconnected systems, based on linear matrix inequalities (LMIs). The fact that the improvement in stability is significant and the controller uses only the output information of plant leads to the name robust output feedback control. The control design is formulated as a convex optimization problem, which makes it computationally tractable, when the problem size increases. The controller concept is then evaluated on a natural circulation drum boiler (utility boiler), where the nonlinear model describes the complicated dynamics of the drum, downcomer, and riser components. The linearized system is non-minimum phase and has two poles at the origin, which are major sources of interaction, bandwidth limitation and instability. Simulation results are presented which show the effectiveness of the proposed control against instabilities following sudden load variations. The control is also effective for steady state operation.     

Bridging the gap between designed and implemented controllers via adaptive robust discrete sliding mode control

Bridging the gap between designed and implemented model-based controllers is a major challenge in the design cycle of industrial controllers. This gap is created due to (i) digital implementation of controller software that introduces sampling and quantization uncertainties, and (ii) uncertainties in the modeled plant's dynamics. In this paper, a new adaptive and robust model-based control approach is developed based on a nonlinear discrete sliding mode controller (DSMC) formulation to mitigate implementation imprecisions and model uncertainties, that consequently minimizes the gap between designed and implemented controllers. The new control approach incorporates the predicted values of the implementation uncertainties into the controller structure. Moreover, a generic adaptation mechanism will be derived to remove the errors in the nonlinear modeled dynamics. The proposed control approach is illustrated on a nonlinear automotive engine control problem. The designed DSMC is tested in real-time in a processor-in-the-loop (PIL) setup using an actual electronic control unit (ECU). The verification test results show that the proposed controller design, under ADC and model uncertainties, can improve the tracking performance up to 60% compared to a conventional controller design.     

Experimental implementation and validation of a novel minimal control synthesis adaptive controller for continuous bimodal piecewise affine systems

This paper presents the first digital implementation of a novel model reference adaptive scheme for the control of continuous bimodal piecewise affine systems. The algorithm is based on the minimal control synthesis algorithm, originally developed as a MRAC for smooth systems. The resulting adaptive algorithm is a switched feedback controller able to cope with uncertain continuous PWA systems. The analogue continuous-time control law is implemented by using a digital low-cost commercial microcontroller. The aim is to control a piecewise-linear electrical circuit. The experimental validation process is made challenging by the presence of measure uncertainties, noise, quantization errors, unmodeled nonlinear dynamics and computational delays. Experiments confirm the effectiveness of the controller to cope with switching in the circuit dynamics, establishing the strategy as a viable control tool. Nevertheless, the experimental analysis provides a first insight into the robustness of the algorithm.     

非线性时滞系统的稳定自适应控制

针对模型不确定性的连续时间时滞系统，提出了一种新的神经网络自适应控制。系统的辨识模型是由神经网络和系统的已知信息组合构成，在此基础上，建立时滞系统的预测模型。基于神经网络预测模型的自适应控制器能够实现期望轨线的跟踪，理论上证明了闭环系统的稳定性。连续搅拌釜式反应器仿真结果表明了该控制方案的有效性。     

考虑侧倾的无人车NMPC轨迹跟踪控制

针对高速行驶工况下,无人车转弯时的侧倾易导致车辆模型非线性程度增加,引起轨迹跟踪精度下降和状态失稳的问题,设计一种考虑车辆侧倾因素,基于非线性模型预测控制(NMPC)的无人车轨迹跟踪控制器.根据拉格朗日分析力学和车辆运动学,考虑车辆侧倾几何学和载荷转移效应,建立考虑侧倾因素的非线性车辆模型,包括车体动力学模型和修正的“Magic Formula”轮胎模型;基于此车辆模型,构建非线性模型预测控制器(NMPC)的预测模型,并设定控制器的线性、非线性约束,以保证车辆的运动状态处于稳定区域内.在Carsim和Simulink联合仿真平台上,验证车辆高速蛇形工况和双移线工况下的轨迹跟踪控制效果,仿真结果显示,所设计的控制器可有效改善高速弯道工况下的跟踪精度和车辆状态稳定性.     

Design and Validation of an ${\mathcal{L}}_{1}$ Adaptive Controller for Mini-UAV Autopilot

The dynamics of Unmanned Aerial Vehicles (UAVs) is nonlinear and subject to external disturbances. The scope of this paper is the test of an \({\mathcal{L}_1}\) adaptive controller as autopilot inner loop controller candidate. The selected controller is based on piecewise constant adaptive laws and is applied to a mini-UAV. Navigation outer loop parameters are regulated via PID control. The main contribution of this paper is to demonstrate that the proposed control design can stabilize the nonlinear system, even if the controller parameters are selected starting from a decoupled linear model. The main advantages of this technique are: (1) the controller can be implemented for both linear and nonlinear systems without parameter adjustment or tuning procedure, (2) the controller is robust to unmodeled dynamics and parametric model uncertainties. The design scheme of a customized autopilot is illustrated and different configurations (in terms of mass, inertia and airspeed variations) are analyzed to validate the presented approach.     

Adaptive sliding mode control of interleaved parallel boost converter for fuel cell energy generation system

This paper deals with the problem of controlling energy generation systems including fuel cells (FCs) and interleaved boost power converters. The proposed nonlinear adaptive controller is designed using sliding mode control (SMC) technique based on the system nonlinear model. The latter accounts for the boost converter large-signal dynamics as well as for the fuel-cell nonlinear characteristics. The adaptive nonlinear controller involves online estimation of the DC bus impedance ‘seen’ by the converter. The control objective is threefold: (i) asymptotic stability of the closed loop system, (ii) output voltage regulation under bus impedance uncertainties and (iii) equal current sharing between modules. It is formally shown, using theoretical analysis and simulations, that the developed adaptive controller actually meets its control objectives.     

Reinforcement Learning Based Controller Synthesis for Flexible Aircraft Wings

Aeroelastic study of flight vehicles has been a subject of great interest and research in the last several years. Aileron reversal and flutter related problems are due in part to the elasticity of a typical airplane. Structural dynamics of an aircraft wing due to its aeroelastic nature are characterized by partial differential equations. Controller design for these systems is very complex as compared to lumped parameter systems defined by ordinary differential equations. In this paper, a stabilizing statefeedback controller design approach is presented for the heave dynamics of a wing-fuselage model. In this study, a continuous actuator in the spatial domain is assumed. A control methodology is developed by combining the technique of "proper orthogonal decomposition" and approximate dynamic programming. The proper orthogonal decomposition technique is used to obtain a low-order nonlinear lumped parameter model of the infinite dimensional system. Then a near optimal controller is designed using the single-network-adaptive-critic technique. Furthermore, to add robustness to the nominal single-network-adaptive-critic controller against matched uncertainties, an identifier based adaptive controller is proposed. Simulation results demonstrate the effectiveness of the single-network-adaptive-critic controller augmented with adaptive controller for infinite dimensional systems.      

Adaptive robust control for servo manipulators

In this paper, an adaptive robust control scheme is developed which is suitable for the control of a class of uncertain nonlinear systems, typical of many servo manipulators. The control scheme is comprised of a model reference adaptive controller (MRAC) augmented with a nonlinear compensator based on an adaptive radial basis function (RBF). The RBF compensator is used to neutralise the effects of uncertain and possibly nonlinear dynamics, so that the equivalent system as seen by the MRAC is reduced to one without significant unstructured modelling errors. A stability analysis is provided to show the uniform stability and the asymptotic tracking capabilities of the proposed control system. Real-time experiment results verify the effectiveness of the control scheme.     

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.     

Adaptive control for uncertain nonlinear systems based on multiple neural networks.

A new adaptive multiple neural network controller (AMNNC) with a supervisory controller for a class of uncertain nonlinear dynamic systems was developed in this paper. The AMNNC is a kind of adaptive feedback linearizing controller where nonlinearity terms are approximated with multiple neural networks. The weighted sum of the multiple neural networks was used to approximate system nonlinearity for the given task. Each neural network represents the system dynamics for each task. For a job where some tasks are repeated but information on the load is not defined and unknown or varying, the proposed controller is effective because of its capability to memorize control skill for each task with each neural network. For a new task, most similar existing control skills may be used as a starting point of adaptation. With the help of a supervisory controller, the resulting closed-loop system is globally stable in the sense that all signals involved are uniformly bounded. Simulation results on a cartpole system for the changing mass of the pole were illustrated to show the effectiveness of the proposed control scheme for the comparison with the conventional adaptive neural network controller (ANNC).     

Sliding mode control of singularly perturbed systems and its application in quad-rotors

This paper presents a sliding mode control scheme for tracking control of nonlinear singularly perturbed systems in the presence of model errors and external disturbances. A dual-loop feedback control is developed to provide accurate tracking capability and sufficient robustness to system uncertainties. A sliding mode controller is proposed in the outer-loop feedback design such that the plant states are stabilised for given reference trajectories, while an additional robust controller is designed in the inner loop to increase the adaptability to uncertainties, and reduce the effect of unmodelled high-frequency dynamics on plant dynamics. An appealing feature of the control scheme is the attenuation of chattering. The effectiveness and merits of the new control scheme developed are shown via a verification example of velocity control of a quad-rotor.     

Model-based periodic event-triggered stabilization for continuous-time stochastic nonlinear systems

In this paper, we investigate a model-based periodic event-triggered control framework for continuous-time stochastic nonlinear systems. In this framework, an auxiliary approximate discrete-time model of stochastic nonlinear systems is constructed in the controller module, which is utilized not only to design a discrete-time controller but also as a state predictor within trigger intervals. This discrete controller design approach, the strategy of state prediction, and the periodic detection strategy for the trigger rule not only provide a manner of more direct and easier implementation on the digital platform but also effectively reduce the communication load while a satisfactory control performance is maintained. Additionally, the mean-square exponentially stabilization for continuous-time stochastic nonlinear systems is achieved, in which a guideline for determining the maximum admissible sampling period is provided and the periodic event trigger rule is designed. The final numerical simulation also supports the effectiveness of our proposed framework.     

Adaptive backstepping‐based control design for uncertain nonlinear active suspension system with input delay

This paper addresses the control problem of adaptive backstepping control for a class of nonlinear active suspension systems considering the model uncertainties and actuator input delays and presents a novel adaptive backstepping‐based controller design method. Based on the established nonlinear active suspension model, a projector operator–based adaptive control law is first developed to estimate the uncertain sprung‐mass online, and then the desirable controller design and stability analysis are conducted by combining backstepping technique and Lyapunov stability theory, which can not only deal with the actuator input delay but also achieve better dynamics performances and safety constraints requirements of the closed‐loop control system. Furthermore, the relationship between the input delay and the state variables of this vehicle suspension system is derived to present a simple and effective method of calculating the critical input delay. Finally, a numerical simulation investigation is provided to illustrate the effectiveness of the proposed controller.     

Model free control based on GIMC structure

Many control researches for complicated and uncertain system are model-dependent and therefore require some prior knowledge for the complex systems. To avoid this problem, a number of model-free controllers are proposed. However, it is difficult to determine the control performance as the controller is not designed according certain system model especially when there are uncertainties and/or nonlinear dynamics in the system. To get over this problem, the model free controller (MFC) based on generalized internal model control (GIMC) structure is proposed in this paper. The MFC is used to attenuate the disturbance or uncertainty, and the system performance is determined by the nominal model and the nominal model controller. The parameters of nominal-model controller can be easily changed for meeting the change of the desired requirements. Moreover, the robust controller in the original GIMC is disassembled and rearranged to make the proposed methods easier to use, and the proposed method makes the controller be more flexible and greatly improves the system performance. Finally, the experiment results show that the MFC can be used to control the nonlinear systems and get the expected performance. The statistical analysis of performance for servo and regulatory behaviors also shows that the proposed method can achieve a better control performance than just using model free controller.     

Adaptive neural/fuzzy control for interpolated nonlinear systems

Adaptive control for nonlinear time-varying systems is of both theoretical and practical importance. We propose an adaptive control methodology for a class of nonlinear systems with a time-varying structure. This class of systems is composed of interpolations of nonlinear subsystems which are input-output feedback linearizable. Both indirect and direct adaptive control methods are developed, where the spatially localized models (in the form of Takagi-Sugeno fuzzy systems or radial basis function neural networks) are used as online approximators to learn the unknown dynamics of the system. Without assumptions on rate of change of system dynamics, the proposed adaptive control methods guarantee that all internal signals of the system are bounded and the tracking error is asymptotically stable. The performance of the adaptive controller is demonstrated using a jet engine control problem.     

An approximated scalar sign function approach to optimal anti-windup digital controller design for continuous-time nonlinear systems with input constraints

This article presents an approximated scalar sign function-based digital design methodology to develop an optimal anti-windup digital controller for analogue nonlinear systems with input constraints. The approximated scalar sign function, a mathematically smooth nonlinear function, is utilised to represent the constrained input functions, which are often expressed by mathematically non-smooth nonlinear functions. Then, an optimal linearisation technique is applied to the resulting nonlinear system (with smooth nonlinear input functions) for finding an optimal linear model, which has the exact dynamics of the original nonlinear system at the operating point of interest. This optimal linear model is used to design an optimal anti-windup LQR, and an iterative procedure is developed to systematically adjust the weighting matrices in the performance index as the actuator saturation occurs. Hence, the designed optimal anti-windup controller would lie within the desired saturation range. In addition, the designed optimal analogue controller is digitally implemented using the prediction-based digital redesign technique for the effective digital control of stable and unstable multivariable nonlinear systems with input constraints.     

Two-degree-of-freedom H-infinity control of combustion in diesel engine using a discrete dynamics model

This paper proposes an H-infinity combustion control method for diesel engines. The plant model is the discrete dynamics model developed by Yasuda et al., which is implementable on a real engine control unit. We introduce a two-degree-of-freedom control scheme with a feedback controller and a feedforward controller. This scheme achieves both good feedback properties, such as disturbance suppression and robust stability, and a good transient response. The feedforward controller is designed by taking the inverse of the static plant model, and the feedback controller is designed by the H-infinity control method, which reduces the effect of the trubocharger lag. The effectiveness of the proposed method is evaluated in simulations using the nonlinear discrete dynamics model.