Modified Smith predictor based cascade control of unstable time delay processes

An improved cascade control structure with a modified Smith predictor is proposed for controlling open-loop unstable time delay processes. The proposed structure has three controllers of which one is meant for servo response and the other two are for regulatory responses. An analytical design method is derived for the two disturbance rejection controllers by proposing the desired closed-loop complementary sensitivity functions. These two closed-loop controllers are considered in the form of proportional-integral-derivative (PID) controller cascaded with a second order lead/lag filter. The direct synthesis method is used to design the setpoint tracking controller. By virtue of the enhanced structure, the proposed control scheme decouples the servo response from the regulatory response in case of nominal systems i.e., the setpoint tracking controller and the disturbance rejection controller can be tuned independently. Internal stability of the proposed cascade structure is analyzed. Kharitonov's theorem is used for the robustness analysis. The disturbance rejection capability of the proposed scheme is superior as compared to existing methods. Examples are also included to illustrate the simplicity and usefulness of the proposed method.     

Generalized predictor based active disturbance rejection control for non-minimum phase systems

In this paper, a generalized predictor based control scheme is proposed to improve system performance of set-point tracking and disturbance rejection for non-minimum phase (NMP) systems. By using a generalized predictor to estimate the system output without time delay, a model-based extended state observer (MESO) is designed to simultaneously estimate the system state and disturbance. Accordingly, an active disturbance rejection control design is developed which consists of a state feedback control and a feedforward control for the disturbance rejection. The MESO and feedback controllers are analytically derived by specifying the desired characteristic roots of MESO and closed-loop system poles, respectively. To improve the output tracking performance, a pre-filter is designed based on a desired closed-loop transfer function for the set-point tracking. A sufficient condition guaranteeing robust stability of the closed-loop system against time-varying uncertainties is established in terms of linear matrix inequalities (LMIs). Three illustrative examples from the literature are used to demonstrate the effectiveness and merit of the proposed control scheme.     

Modified Smith predictor for frequency identification and disturbance rejection of single sinusoidal signal

This paper presents a frequency identification and disturbance rejection scheme for open loop stable time delay systems with disturbance containing a constant signal and a single sinusoidal signal. Astrom’s modified Smith predictor is employed to maintain good setpoint tracking performance. Disturbance rejection controller is designed via internal model control principle and functions as a finite dimensional repetitive controller. Extended Kalman filter is designed to track the frequency of unknown periodic disturbance. The simulation results demonstrate the successful performance of the proposed disturbance rejection method for controlling a linear system with time delays, subjected to both step and sinusoidal disturbances.     

Multi-loop nonlinear control design for performance improvement of LTI systems

This paper puts forward a multi-loop nonlinear control (MLNC) strategy to overcome the limited performance of LTI controllers due to the so-called “waterbed” effect. According to “Bode's sensitivity integral”, increasing the bandwidth or additional integral gain of LTI controller to improve the low-frequency disturbance attenuation irrefutably increases the sensitivity to high-frequency disturbances or measurement noise. Hence, it is impossible to attain the best of both worlds in the case of linear controllers. Therefore, with an aim to improve the transient and steady state performance of linear controllers, in this paper, a nonlinear control framework using circle criterion method and saturation nonlinearity, which adjusts the integral gain based on the error threshold, is discussed. The global asymptotic stability (GAS) of the MLNC strategy is theoretically proved using LaSalle's invariance principle and experimentally validated using measured frequency response function (FRF). Moreover, the performance of the MLNC strategy is compared with that of the multi-loop linear control (MLLC) strategy on a benchmark magnetic levitation system for tracking application. The cumulative power spectral density (CPSD) of tracking error, which is used as the performance index to assess the overall closed loop performance, accentuates that MLNC can yield better steady state and transient performance compared to MLLC scheme.     

Enhanced IMC design of load disturbance rejection for integrating and unstable processes with slow dynamics

In view of the deficiencies in existing internal model control (IMC)-based methods for load disturbance rejection for integrating and unstable processes with slow dynamics, a modified IMC-based controller design is proposed to deal with step- or ramp-type load disturbance that is often encountered in engineering practices. By classifying the ways through which such load disturbance enters into the process, analytical controller formulae are correspondingly developed, based on a two-degree-of-freedom (2DOF) control structure that allows for separate optimization of load disturbance rejection from setpoint tracking. An obvious merit is that there is only a single adjustable parameter in the proposed controller, which in essence corresponds to the time constant of the closed-loop transfer function for load disturbance rejection, and can be monotonically tuned to meet a good trade-off between disturbance rejection performance and closed-loop robust stability. At the same time, robust tuning constraints are given to accommodate process uncertainties in practice. Illustrative examples from the recent literature are used to show effectiveness and merits of the proposed method for different cases of load disturbance.     

Improving disturbance rejection of PI controllers by means of the magnitude optimum method

The magnitude optimum (MO) method provides a relatively fast and nonoscillatory closed-loop tracking response for a large class of process models frequently encountered in the process and chemical industries. However, the deficiency of the method is poor disturbance rejection when controlling low-order processes. In this paper, the MO criterion is modified in order to optimize disturbance rejection performance, while the tracking performance has been improved by an integral set-point filtering PI controller structure. The new tuning rules, referred to as the disturbance rejection magnitude optimum (DRMO) method, were applied to several different two-degrees-of-freedom PI controllers. The DRMO method has also been tested on several different representatives of process models. The results of experiments have shown that the proposed tuning method with the integral set-point filtering PI controller is quite efficient in improving disturbance rejection performance, while retaining tracking performance comparable to the original MO method.     

Estimation and disturbance rejection performance for fractional order fuzzy systems

This paper gives attention to the issues of output tracking and disturbance rejection performance for a class of fractional order Takagi–Sugeno fuzzy systems in the presence of time-varying delay and unknown external disturbances. More specifically, a new configuration of a fractional order modified repetitive controller that incorporates an improved equivalent-input-disturbance estimator and gain fluctuations in its design is proposed to perform disturbance rejection for the addressed system. By introducing a continuous frequency distributed equivalent model and using the Lyapunov–Krasovskii stability theory, a new set of sufficient conditions ensuring robust asymptotic stability of the resulting closed-loop system is obtained in the framework of linear matrix inequalities. Finally, a numerical example is presented to validate the developed theoretical results, where it is shown that the obtained conditions could force the considered system output to exactly track the given any kind of reference signal by compensating the unknown external disturbance.     

Path following control for towing system of cylindrical drilling platform in presence of disturbances and uncertainties

Towing is a critical process to deploy a cylindrical drilling platform. However, the towing process faces a great variety of risks from a complex nautical environment, the dynamics in towing and maneuvering, to unexpected events. Therefore, safely navigating the towing system following a planned route to a target sea area is essential. To tackle the time-varying disturbances induced by wind, current and system parametric uncertainties, a path following control method for a towing system of cylindrical drilling platform is designed based on linear active disturbance rejection control. By utilizing Maneuvering Modeling Group model as well as a catenary model, we develop a three degree-of-freedom dynamic mathematical model of the towing system under external environmental disturbances and internal uncertainties. Furthermore, we design a linear active disturbance rejection control path following controller for real-time tracking error correction based on a guidance method combining cross-track error and parallax. Finally, the path following performance of the towing system is evaluated in a simulation environment under various disturbances and internal uncertainties, where the corresponding tracking error is analyzed. The results show that the linear active disturbance rejection control performs well under both the external disturbance and inherent uncertainties, and better satisfy the tracking performance criteria than a traditional proportional–integral–derivative controller.     

Discrete-time domain two-degree-of-freedom control design for integrating and unstable processes with time delay

A discrete-time domain two-degree-of-freedom (2DOF) design method is proposed for integrating and unstable processes with time delay. Based on a 2DOF control structure recently developed, a controller is analytically designed in terms of the H₂ optimal control performance specification for the set-point tracking, and another controller is derived by proposing the desired closed-loop transfer function for load disturbance rejection. Both controllers can be tuned relatively independent to realize control optimization. Analytical expression of the set-point response is given for quantitatively tuning the single adjustable parameter in the set-point tracking controller. At the meantime, sufficient and necessary conditions for holding robust stability of the closed-loop control system are established for tuning another adjustable parameter in the disturbance rejection controller, along with numerical tuning guidelines. Illustrative examples from the literature are used to demonstrate the effectiveness of the proposed method.     

Improving disturbance rejection of PID controllers by means of the magnitude optimum method

The magnitude optimum (MO) method provides a relatively fast and non-oscillatory closed-loop tracking response for a large class of process models frequently encountered in the process and chemical industries. However, the deficiency of the method is poor disturbance rejection performance of some processes. In this paper, disturbance rejection performance of the PID controller is improved by applying the“disturbance rejection magnitude optimum” (DRMO) optimisation method, while the tracking performance has been improved by a set-point weighting and set-point filtering PID controller structure. The DRMO tuning method requires numerical optimisation for the calculation of PID controller parameters. The method was applied to two different 2-degrees-of-freedom PID controllers and has been tested on several different representatives of process models and one laboratory set-up. A comparison with some other tuning methods has shown that the proposed tuning method, with a set-point filtering PID controller, is quite efficient in improving disturbance rejection performance, while retaining tracking performance comparable with the original MO method.     

Extended observer based on adaptive second order sliding mode control for a fixed wing UAV

This paper addresses the design of attitude and airspeed controllers for a fixed wing unmanned aerial vehicle. An adaptive second order sliding mode control is proposed for improving performance under different operating conditions and is robust in presence of external disturbances. Moreover, this control does not require the knowledge of disturbance bounds and avoids overestimation of the control gains. Furthermore, in order to implement this controller, an extended observer is designed to estimate unmeasurable states as well as external disturbances. Additionally, sufficient conditions are given to guarantee the closed-loop stability of the observer based control. Finally, using a full 6 degree of freedom model, simulation results are obtained where the performance of the proposed method is compared against active disturbance rejection based on sliding mode control.     

串级时滞过程的解耦控制设计

针对化工串级过程提出了两种新颖的两自由度解耦控制结构。基于鲁棒控制H2最优性能指标设计给定值响应控制器。根据系统运行抗负载干扰要求,在中间级可测量过程的输入和输出端之间设计抑制负载干扰信号的闭环,通过提出期望闭环余灵敏度函数的方法来确定其反馈通道中的扰动观测器,同时给出了该闭环保证鲁棒稳定性的充要条件。最后通过实验显示了该方法相对于其它方法的优越性。     

Real-time comparison of a number of predictive controllers

Many model predictive control (MPC) algorithms have been proposed in the literature depending on the conditionality of the system matrix and the choice of its cost-function. This paper presents the newer MPC schemes such as extended predictive control (EPC) and shifted MPC as well as other well known forms. The control performance of these controllers are compared using two systems that are slow and fast reacting. The closed-loop responses are compared and the differences and similarities are explained on the basis of the structure of the control schemes. Disturbance rejection and the tracking of various setpoint trajectories are performed with good closed-loop results from all the controllers. It was found that the controllers that were specifically designed to reduce the system matrix ill-conditionality such as EPC and generalized predictive control provided better control performance when compared to other MPC methods.     

基于降阶双环自抗扰的永磁同步直线电机电流谐波抑制

永磁同步直线电机由于反电势和逆变器频繁切换导致电流谐波分量较大,同时参数时变以及负载突变等扰动严重影响伺服系统的控制精度。本文采用一种基于降阶状态观测器的双环自抗扰伺服控制算法,以降低控制系统的谐波抑制从而提高控制精度。首先,构造了位置速度环级联的二阶自抗扰控制器。运用极点配置法对三阶线性状态观测器进行降阶,减小了相位滞后的影响,提高了伺服系统的控制精度;其次,电流环采用一阶非线性自抗扰控制器,消除了积分饱和的影响,降低了三相电流的谐波含量。最后,与基于自抗扰控制的其他优化算法进行对比,实验表明在多工况下降阶双环自抗扰控制的总谐波失真不超过2.13%,推力波动可减小至1.49%,稳态误差不大于15μm。     

Trajectory tracking for two-degree of freedom helicopter system using a controller-disturbance observer integrated design

Trajectory tracking control for helicopters, which are widely used in severe situations such as military and rescue missions, is a challenging field of research. In helicopter system, the stability problem and predefined trajectories tracking are main challenges, especially in the presence of external disturbances and dynamic model uncertainties. Hence, a robust control design is needed for tracking the desired references. There has been a lot of motivation for solving these problems with simpler methods and also reducing the couplings in the helicopter system to achieve better performance, as the presented paper attempts to fill these gaps. This paper focuses on designing control laws for two-degree of freedom helicopter system while assuring the closed-loop stability. A nonlinear disturbance observer-based control (NDOBC) is designed for attenuating the effects of exogenous disturbances. Trajectory tracking controller and nonlinear disturbance observer are formulated in the form of two linear matrix inequality (LMI) problems. The closed-loop system stability, including controller and observer, is investigated by Lyapunov theorem. The effectiveness of the proposed design for tracking the trajectories (vertical flight and pitch angle rotor blade) and disturbance estimation is verified by simulation results.     

Performance analysis of active disturbance rejection tracking control for a class of uncertain LTI systems

The paper considers the tracking problem for a class of uncertain linear time invariant (LTI) systems with both uncertain parameters and external disturbances. The active disturbance rejection tracking controller is designed and the resulting closed-loop system׳s characteristics are comprehensively studied. In the time-domain, it is proven that the output of closed-loop system can approach its ideal trajectory in the transient process against different kinds of uncertainties by tuning the bandwidth of extended state observer (ESO). In the frequency-domain, different kinds of parameters׳ influences on the phase margin and the crossover frequency of the resulting control system are illuminated. Finally, the effectiveness and robustness of the controller are verified through the actuator position control system with uncertain parameters and load disturbances in the simulations.     

机带海水冷却电液伺服系统反步抗扰控制研究

针对船舶传动装置机带海水冷却系统的电液伺服系统,通过详细建立阀控液压马达系统的数学模型,提出反步抗扰控制策略。该方法利用反步设计方法将系统分为3个子系统,分别设计相应的控制率;考虑系统中的非匹配干扰和匹配干扰,结合不确定性和干扰估计器以及观测器设计方法,提出一种状态和干扰估计器,估计系统状态、非匹配干扰和匹配干扰,并将估计值带入反步法设计的控制率,获得最终的反步抗扰控制率。分析状态和干扰估计器的稳定性,证明闭环系统跟踪误差最终一致有界。采用PID控制和反步控制作为对比,仿真验证反步抗扰控制的跟踪性能。结果表明:所提出的反步抗扰控制方法具有较强的抗扰鲁棒性,能够有效补偿干扰,进而获得快速准确的跟踪效果。     

An enhanced tracking control of marine surface vessels based on adaptive integral sliding mode control and disturbance observer

In this paper, a new control methodology is developed to enhance the tracking performance of fully actuated surface vessels based on an integrating between an adaptive integral sliding mode control (AISMC) and a disturbance observer (DO). First, an integral sliding mode control (ISMC), in which the backstepping control technique is used as the nominal controller, is designed for the system. The major features, i.e., benefits and drawbacks, of the ISMC are discussed thoroughly. Then, to enhance the tracking performance of the system, an adaptive technique and a new disturbance observer based on sliding mode technique are developed and integrated into the ISMC. The stability of the closed-loop system is proved based on Lyapunov criteria. Computer simulation is performed to illustrate the tracking performance of the proposed controller and compare with the existing controllers for the tracking control of a surface vessel. The simulation results demonstrate the superior performance of the proposed strategy.     

Set point weighted modified Smith predictor for integrating and double integrating processes with time delay

A simple method of designing the controllers for a modified form of Smith predictor is proposed for integrating and double integrating processes with time delay. The modified Smith predictor has two controllers, namely, a set point tracking controller and a load disturbance rejection controller for obtaining good set point tracking and load disturbance rejection, respectively. The set point tracking controller is designed using the classical direct synthesis method based on the process model without considering the time delay. The disturbance rejection controller is considered as a proportional-derivative (PD) controller and is designed using optimal gain and phase margin approaches. Set point weighting is considered for reducing undesirable overshoots and settling times in the modified Smith predictor. Guidelines are provided for selection of the desired closed loop tuning parameter in the direct synthesis method and the set point weighting parameter. The method gives significant load disturbance rejection performances. Illustrative examples are considered to show the performances of the proposed method. A significant improvement in control performance is obtained when compared to recently reported methods.     

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.