NARMAX modelling and robust control of internal combustion engines

Detailed in this paper is a SISO non-linear modelling and robust controller design methodology experimentally verified on an internal combustion engine. The methodology begins with the identification of a NARMAX model that captures the non-linear dynamics relating the input to the output of a system. This model is converted to a describing function representation for the purpose of robust feedback controller design. The ideology for the describing function recovery is developed in the form of an algorithm which can be extended to other NARMAX model structures not considered here. The controller design is executed in the frequency domain where the output performance specification is |y(t)|≤β?t>0 and the actuator saturation constraint is |u(t)|≤K?t>0. For the engine idle speed control application of this study, a SISO NARMAX model of the engine is developed between the by-pass idle air valve (BPAV) and engine speed. The performance objective for the controller design is the time domain tolerance of |Δ rpm| ≤ 100 rpm on idle speed perturbations despite a non-measurable 20 N m external torque disturbance. The controller is validated through numerical simulations as well as experimental verification.     

Identification and idle speed control of internal combustion engines

This paper presents an integrated approach for the identification and control of internal combustion engines in idle-speed conditions. The inputs of the nonlinear identification model are the position of the idle speed air actuation system and the spark advance, while its outputs are the pressure inside the air intake manifold and the crank shaft speed. The estimated model is then used to synthesize an idle speed controller with the linear quadratic technique. The design procedure outlined here is currently being used by Magneti Marelli for the synthesis of commercial idle-speed regulators. Some identification and control results obtained by applying this method to a 1400 cm³ commercial engine are reported to witness the effectiveness of the proposed approach.     

Frequency‐based nonlinear controller design for regulating systems subjected to time‐domain constraints

Presented is a nonlinear controller design methodology for a class of linear regulating systems subjected to quantitative time‐domain constraints. The design objective is to satisfy an output time‐domain tolerance given an actuator saturation constraint despite an external step disturbance. The goal is to increase the allowable magnitude of the external disturbance beyond that achievable via linear control subject to the time‐domain specifications. The controller design process is comprised of two phases. In the first phase, a linear controller is designed that balances the trade‐off between output regulation and required actuation. To realize the linear design, the time‐domain performance specifications are mapped into amplitude and phase constraints which are in turn imposed on the frequency response of the linear open‐loop transfer function. In the second phase, the linear controller is then augmented with an odd nonlinearity. The coefficient for the nonlinear term is designed such that the gain and phase distortions (in the sense of describing functions) meet the frequency‐domain constraints. The describing function calculation is automated by a recursive Volterra Series relationship. The nonlinear controller design methodology is experimentally verified on the idle speed control of a Ford 4.6L V‐8 fuel injected engine. Copyright © 2000 John Wiley & Sons, Ltd.     

Delay-dependent guaranteed cost control for state-delayed system with disturbance and its application to engine idle speed control

This paper proposes a delay-dependent guaranteed cost control scheme for engine idle speed control （ISC） with induction-to-torque delay and external load disturbance. An augmented linearization model of engine at idle speed operating mode was developed based on physical principle and experiment data. To provide a compromise between disturbance rejection and other performance requirements of ISC, a multi-objective cost function upper bound was given, which can help us to take into account the fuel economy and disturbance rejection performance together in ISC. Poles constraint was added to the closed-loop system to guarantee convergence rates of state. The whole optimization solution to ISC can be solved under the framework of LMI. A commercial engine model was utilized to assess the performance of the controller. Simulation results on this model show us that designed controller can achieve desired performance.     

Dynamic control of a SI engine with variable intake valve timing

Engines equipped with a means to actuate air flow at the intake valve can achieve superior fuel economy performance in steady state. This paper shows how modern nonlinear design techniques can be used to control such an engine over a wide range of dynamic conditions. The problem is challenging due to the nonlinearities and delays inherent in the engine model, and the constraint on the air flow actuator. The controller is designed on the basis of a mean‐value model, which is derived from a detailed intake stroke model. The control solution has two novel features. Firstly, a recovery scheme for integrator wind‐up due to input constraints is directly integrated into the nonlinear control design. The second novel feature is that the control Lyapunov function methodology is applied to a discrete‐time model. The performance of the controller is evaluated and compared with a conventionally controlled engine through simulation on the detailed engine model. Copyright © 2003 John Wiley & Sons, Ltd.     

Multivariable PI tuning for disturbance rejection and application to engine idle speed control simulation

In this paper, a new multivariable proportional-integral (PI) tuning strategy is developed and the advantage of the new design is illustrated in simulation on an internal combustion engine model. The multivariable control design technique developed here has disturbance rejection as its main objective rather than set-point tracking, which is the focus of most of the multivariable PI tuning techniques so far in the literature. The benefit of the new design is that it does not try to minimize cross couplings in the multivariable plant; instead it uses the cross couplings to achieve better disturbance rejection. The application of the control design method is in multivariable speed and air/fuel ratio control of a lean-burn natural gas engine to achieve smooth and effective idle speed regulation. When applied to a simulation model of the engine, the new PI tuning strategy effectively reduces speed undershoot during the application of a transient torque load during idle.     

Composite nonlinear feedback design for discrete-time switching systems with disturbances and input saturation

This paper addresses the problem of robust controller design for a class of discrete-time switching systems with input saturation. To this aim, the composite nonlinear feedback method is extended to design a robust controller with improved performances in terms of the response speed and overshoot in the presence of disturbances and input saturation. The proposed approach is theoretically analysed and its closed-loop stability is proved. Then, the performance of the proposed method is verified using numerical simulations.     

含有时滞的怠速控制与输出扭矩估计器设计

发动机由怠速工况向启动工况转换时的输出扭矩信息直接影响离合器接合过程的平顺特性。针对发动机自身和控制环节带来的时间滞后对系统性能的影响,研究了含有时滞信息的鲁棒H_∞状态反馈控制规律,使干扰信息作用下的发动机怠速工况的转速恒定且满足H_∞性能要求。进一步设计了H_∞滤波器在线估计发动机怠速时输出扭矩,为离合器的接合控制提供力矩信息。基于Simulink搭建发动机怠速系统仿真验证估计器的有效性,结果表明在扰动量出现和消失瞬间,提出的算法能保证电子节气门开度切换小,控制转速能快速稳定,且有效估计了发动机怠速时的输出扭矩,克服了时间滞后带来的性能下降的问题。     

Robust adaptive path-following control of underactuated marine vessel with off-track error constraint

In this paper, a new robust adaptive controller is investigated to force an underactuated surface marine vessel to follow a predefined parameterised path at a desired speed, despite actuator saturation and the presence of model uncertainties as well as environmental disturbances induced by waves, wind and sea-currents. To ensure robustness of the path-following controller, time-varying constraint on the off-track error (i.e. the maximal distance from the ship to the reference path) is considered. To address the off-track error constraint the tan-barrier Lyapunov function is incorporated with the control scheme, where the idea of auxiliary design system introduced in Chen, Sam, and Ren (2011) is adopted and its states are used in combination with backstepping and Lyapunov synthesis to adaptive tracking control design with guaranteed stability. Furthermore, the command filters are adopted to implement physical constraints on the virtual control laws so that analytic differentiation of the virtual control laws is avoided. We show that the proposed robust adaptive control law is able to guarantee semi-global uniform ultimate bounded stability of the closed-loop system. Numerical simulations and experimental results are carried out to demonstrate the effectiveness of the proposed algorithm.     

大功率天然气发动机怠速控制策略研究

为提高大功率天然气发动机怠速时的稳态和动态效果,以V模式为研究手段,基于一款六缸天然气多点电喷发动机,实现了发动机怠速控制策。首先针对不同的怠速工况设计了不同的目标怠速转速值的计算,并根据发动机特性确定了PI控制模式。利用目标怠速转速和瞬时转速的差值确定不同PI控制参数,通过PI控制调节电子节气门的开度,从而实现对发动机怠速转速的控制。然后根据实际发动机参数搭建了发动机MATLAB/SIMULINK仿真模型,用于对怠速控制策略进行软件在环仿真测试以及PI控制参数预标定。最后在天然气发动机试验台架上对控制策略进行了进一步的试验和标定。试验结果表明：该怠速控制策略,可让发动机转速响应时间控制在1秒左右,转速稳定时间在2秒左右,发动机转速稳态误差控制在±5rpm范围之内,实现了对怠速的良好稳定控制。     

鲁棒组合非线性反馈技术在直流电机速度控制中的应用

针对带有常量干扰和具有输入饱和约束的直流电机模型,本文通过设计鲁棒组合非线性反馈控制器,来提高电机速度控制的快速性和精确度。基本思想是在组合非线性反馈（Composite Nonlinear Feedback（CNF））控制的基础上加入干扰估计项和补偿项,在消除系统由于干扰产生的稳态误差的同时,保证了原组合非线性反馈控制响应快速及超调小的瞬态性能。     

Robust PID controller for flexible satellite attitude control under angular velocity and control torque constraint

A PID controller for flexible satellite attitude control with unknown perturbation is proposed in this paper. System inertia uncertainty, stochastic disturbance torque, and perturbation of flexible deformation are discussed, and the controller proposed in this paper is robust to these perturbations. A novel integral term is designed; hence the Lyapunov function structure is modified and the stability proof is simplified. The angular velocity constraint is discussed and a novel method to solve the angular velocity saturation issue is given. The control torque saturation issue is also taken into consideration. Stability for all conditions considered in this paper is proved by the Lyapunov method. The performance of the controller is demonstrated by numerical simulation.     

磁悬浮储能飞轮线性变参数鲁棒增益调度控制

针对强陀螺效应的磁悬浮储能飞轮转速快变引起的模型变化而带来的控制问题,设计了线性变参数增益调度鲁棒控制器.根据飞轮的线性变参数模型,设计的鲁棒增益调度控制器,能够保证其全转速范围内的鲁棒稳定性和性能.为降低控制器设计的保守性,在设计控制器时,可缩小转速区间,使控制性能得到提高.与按照非时变模型设计的鲁棒控制器相比,线性变参数鲁棒增益调度控制器可以实现以转速为参数的自适应调节,在全转速范围内,其鲁棒稳定性和性能均具有显著优势.仿真结果验证了此控制器的有效性和先进性.     

Variable‐Structure Control with Complementarity‐Inputs for a Lean‐Burn IC Engine of a Series Hybrid Vehicle

This paper presents a robust controller for an internal combustion (IC) engine, as the first stage of a project to develop a hybrid light urban vehicle, running on ethanol in lean burn. In particular, this work focuses on the design of a sliding mode control for an IC engine of a series hybrid power train. The controller must allow for optimal speed regulation and high fuel efficiency. To attain the latter, a complementary operation mode is proposed for the system inputs. Simulation results are presented and discussed showing the viability and advantages of the control strategy employed.     

Fixed-Order Robust H∞ Controller Design With Regional Pole Assignment

In this technical note, the problem of designing fixed-order robust H_infin controllers is considered for linear systems affected by polytopic uncertainty. A polynomial method is employed to design a fixed-order controller that guarantees that all the closed-loop poles reside within a given region of the complex plane. In order to utilize the freedom of the controller design, an H_infin performance specification is also enforced by using the equivalence between robust stability and H_infin norm constraint. The design problem is formulated as a linear matrix inequality (LMI) constraint whose decision variables are controller parameters. An illustrative example demonstrates the feasibility of the proposed design methods.     

Engine performance and optimum injection timing for 4-cylinder direct injection hydrogen fueled engine

This paper presents the engine performance and optimum injection timing for 4-cylinder direct injection hydrogen fueled engine. The 4-cylinder direct injection hydrogen engine model was developed utilizing the GT-Power commercial software. This model employed one dimensional gas dynamics to represent the flow and heat transfer in the components of engine model. Sequential pulse injectors are adopted to inject hydrogen gas fuel within the compression stroke. Injection timing was varied from 110° before top dead center (BTDC) until top dead center (TDC) timing. Engine speed was varied from 2000 rpm to 6000 rpm, while the equivalence ratio was varied from 0.2 to 1.0. The validation was performed with the existing previous experimental results. The negative effects of the interaction between ignition timing and injection duration was highlighted and clarified. The results showed that optimum injection timing and engine performance are related strongly to the air fuel ratio and engine speed. The acquired results show that the air fuel ratio and engine speed are strongly influence on the optimum injection timing and engine performance. It can be seen that the indicated efficiency increases with increases of AFR while decreases of engine speed. The power and torque increases with the decreases of AFR and engine speed. The indicated specific fuel consumption (ISFC) decreases with increases of AFR from rich conditions to lean while decreases of engine speed. The injection timing of 60° BTDC was the overall optimum injection timing with a compromise.     

By-pass valve control to improve energy efficiency of pneumatic drive system

In order to improve the performance and energy efficiency of the pneumatic drive, the by-pass valve control scheme is designed and studied. For pneumatic positioning application, in the constant speed phase, the inlet and outlet chambers will be connected via by-pass valve to reduce the overshoot and allow some exhaust compressed air to be reused. Therefore, compared with the traditional control of the motion of the asymmetric cylinder, a 12–28% saving in energy use can be acquired and meanwhile the position accuracy is maintained. Preliminary results from the simulation and experiment studies will be reported.     

Design and analysis of optimal controller for fuzzy systems with input constraint

In this paper, we present a design method of the optimal and robust controller subject to the constraint on control inputs for continuous-time Takagi-Sugeno (TS) fuzzy systems. In order to establish this design method, we consider an optimal and robust control problem for nonlinear dynamic systems. For this problem, we present an analytic way which can provide the optimal controller for nonlinear dynamic systems by the dynamic programming approach and the inverse optimal approach. Moreover, we analyze the robustness property of the proposed optimal controller with respect to a class of input uncertainties by the passivity approach. Then, based on the theoretical results presented in this paper, we formulate the design problem of the optimal and robust controller with input constraint for continuous-time TS fuzzy systems as the semidefinite programming problem, and find the controller by solving it. The usefulness of the proposed approach is illustrated by considering the three-axis attitude stabilization problem of rigid spacecraft.     

Adaptive CMAC-based supervisory control for uncertain nonlinear systems.

An adaptive cerebellar-model-articulation-controller (CMAC)-based supervisory control system is developed for uncertain nonlinear systems. This adaptive CMAC-based supervisory control system consists of an adaptive CMAC and a supervisory controller. In the adaptive CMAC, a CMAC is used to mimic an ideal control law and a compensated controller is designed to recover the residual of the approximation error. The supervisory controller is appended to the adaptive CMAC to force the system states within a predefined constraint set. In this design, if the adaptive CMAC can maintain the system states within the constraint set, the supervisory controller will be idle. Otherwise, the supervisory controller starts working to pull the states back to the constraint set. In addition, the adaptive laws of the control system are derived in the sense of Lyapunov function, so that the stability of the system can be guaranteed. Furthermore, to relax the requirement of approximation error bound, an estimation law is derived to estimate the error bound. Finally, the proposed control system is applied to control a robotic manipulator, a chaotic circuit and a linear piezoelectric ceramic motor (LPCM). Simulation and experimental results demonstrate the effectiveness of the proposed control scheme for uncertain nonlinear systems.