Model algorithm control for path tracking of wheeled mobile robots

This paper proposes a model algorithm control (MAC) method for the path tracking control of differentially steered wheeled mobile robots (WMRs) subject to nonholonomic constraints. The continuous dynamic model of the wheeled mobile robot is presented and used as the model to be controlled. The MAC controller is designed based on the sampled-data representation of the system. In this paper the case that there exists time delay in the control input is also considered. A time discretization method using the Taylor series and the zero-order-hold (ZOH) assumption is proposed to discretize the continuous dynamic model of the WMR. This time discretization method is especially useful in the case of the time delayed system. It can provide finite dimensional and more accurate discretized form model of the mobile robot with input time delay and convert it into a general nonlinear time discretized form to which the MAC controller can be applied. Simulations are conducted to show the performance and feasibility of the proposed control strategy. In these simulations the WMR is controlled to track two difference reference paths such as the “8” shape path and the circular path. The bounded inertial parameters uncertainties and some disturbance are also considered in the model of the control system.     

Indirect predictive type-2 fuzzy neural network controller for a class of nonlinear input - delay systems

In this paper a new indirect type-2 fuzzy neural network predictive (T2FNNP) controller has been proposed for a class of nonlinear systems with input-delay in presence of unknown disturbance and uncertainties. In this method, the predictor has been utilized to estimate the future state variables of the controlled system to compensate for the time-varying delay. The T2FNN is used to estimate some unknown nonlinear functions to construct the controller. By introducing a new adaptive compensator for the predictor and controller, the effects of the external disturbance, estimation errors of the unknown nonlinear functions, and future sate estimation errors have been eliminated. In the proposed method, using an appropriate Lyapunov function, the stability analysis as well as the adaptation laws is carried out for the T2FNN parameters in a way that all the signals in the closed-loop system remain bounded and the tracking error converges to zero asymptotically. Moreover, compared to the related existence predictive controllers, as the number of T2FNN estimators are reduced, the computation time in the online applications decreases. In the proposed method, T2FNN is used due to its ability to effectively model uncertainties, which may exist in the rules and data measured by the sensors. The proposed T2FNNP controller is applied to a nonlinear inverted pendulum and single link robot manipulator systems with input time-varying delay and compared with a type-1 fuzzy sliding predictive (T1FSP) controller. Simulation results indicate the efficiency of the proposed T2FNNP controller.     

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。     

Discrete-time direct adaptive control for robotic systems based on model-free and if–then rules operation

An adaptive controller for a class of nonlinear discrete-time systems is proposed for robotic systems under the assumption that the parameters and structure of system dynamics are all unknown. This controller is designed with the concept of model-free adaptive control requiring only the input–output of the unknown plant. The robotic system has been generalized to be a nonaffine discrete-time system under reasonable assumptions. The adaptive scheme called fuzzy rules emulated network (FREN) is implemented as a direct controller. The IF–THEN rules for FREN have been defined by the knowledge according to the relation between input and output of the robotic system without any compensator for the unknown mathematical model or nonlinearities. The underlying physical specifications of robotic system such as the operating range, maximum joint velocity, and so on have been considered to initialize the membership functions and adjustable parameters of FREN. The adaptation scheme is developed according to convergence analysis established for both adjustable parameters and the tracking error. The performance of the proposed controller is validated by the experimental system with a 7-degrees-of-freedom robotic arm operated in velocity-mode control.     

Stability analysis and dynamic regulation of multi-dimensional Taylor network controller for SISO nonlinear systems with time-varying delay

Though many studies are focused on the stabilization of nonlinear systems with time-varying delay, they fail to involve the dynamic regulation without on-line optimization commonly. For this sake, feedback linearization, Lyapunov-Razumikhin theorem and polynomial approximation theorem are employed here to verify that the multi-dimensional Taylor network (MTN) controller can stabilize the single input single output (SISO) nonlinear time-varying delay systems through dynamic regulation of the system output with no need for on-line optimization. Here, the design of the controller is transformed into a convex optimization problem, which is tackled by means of the appropriate optimization method. Like its PD-like controller peers, the MTN controller functions well in eliminating the dependence on the system model. The effectiveness of the proposed approach is demonstrated and confirmed via two examples.     

A fast converging robust controller using adaptive second order sliding mode

This paper proposes an adaptive second order sliding mode (SOSM) controller with a nonlinear sliding surface. The nonlinear sliding surface consists of a gain matrix having a variable damping ratio. Initially the sliding surface uses a low value of damping ratio to get a quick system response. As the closed loop system approaches the desired reference, the value of the damping ratio gets increased with an aim to reducing the overshoot and the settling time. The time derivative of the control signal is used to design the controller. The actual control input obtained by integrating the derivative control signal is smooth and chattering free. The adaptive tuning law used by the proposed controller eliminates the need of prior knowledge about the upper bound of system uncertainties. Simulation results demonstrate the effectiveness of the proposed control strategy.     

含有测量时延摄动的冷轧机厚控系统控制器设计

针对冷带轧机液压厚控(Hydraulic automatic gauge control, HAGC)系统中带材厚度输出存在测量时延摄动以及系统存在不确定性的情况,提出一种新的控制器设计策略,以提高实际工作中冷带轧机板带材的板厚精度。基于轧机液压厚控系统各环节的方程式,给出具有测量时延摄动和不确定项的数学模型,并将该测量时延转化为时变输入时延考虑,建立最终的HAGC系统模型。针对该模型设计一种新的控制器,并利用Lyapunov稳定性理论对所设计的控制器进行严格的理论证明,得出系统的指数稳定性。针对1700单机架轧机进行Matlab仿真,将所提出的控制器与传统比例积分微分(Proportional integral derivative, PID)控制器的仿真结果进行对比,说明了该控制方法能够克服时延及不确定性的影响,比传统的PID控制器具有更加良好的效果,进一步验证了控制器的有效性和优越性。     

Memoryless disturbance-observer-based adaptive tracking of uncertain pure-feedback nonlinear time-delay systems with unmatched disturbances

This paper presents a delay-independent nonlinear disturbance observer (NDO) design methodology for adaptive tracking of uncertain pure-feedback nonlinear systems in the presence of unknown time delays and unmatched external disturbances. Compared with all existing NDO-based control results for uncertain lower-triangular nonlinear systems where unknown time delays have been not considered, the main contribution of this paper is to develop a delay-independent design strategy to construct an NDO-based adaptive tracking scheme in the presence of unknown time-delayed nonlinearities and non-affine nonlinearities unmatched in the control input. The proposed delay-independent scheme is constructed by employing the appropriate Lyapunov-Krasovskii functionals and the same function approximators for the NDO and the controller. It is shown that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to an adjustable neighborhood of the origin.     

Globally linearized control on diabatic continuous stirred tank reactor: a case study

This paper focuses on the promise of globally linearized control (GLC) structure in the realm of strongly nonlinear reactor system control. The proposed nonlinear control strategy is comprised of: (i) an input-output linearizing state feedback law (transformer), (ii) a state observer, and (iii) an external linear controller. The synthesis of discrete-time GLC controller for single-input single-output diabatic continuous stirred tank reactor (DCSTR) has been studied first, followed by the synthesis of feedforward/feedback controller for the same reactor having dead time in process as well as in disturbance. Subsequently, the multivariable GLC structure has been designed and then applied on multi-input multi-output DCSTR system. The simulation study shows high quality performance of the derived nonlinear controllers. The better-performed GLC in conjunction with reduced-order observer has been compared with the conventional proportional integral controller on the example reactor and superior performance has been achieved by the proposed GLC control scheme.     

Predictor-based control for an inverted pendulum subject to networked time delay

The inverted pendulum is considered as a special class of underactuated mechanical systems with two degrees of freedom and a single control input. This mechanical configuration allows to transform the underactuated system into a nonlinear system that is referred to as the normal form, whose control design techniques for stabilization are well known. In the presence of time delays, these control techniques may result in inadequate behavior and may even cause finite escape time in the controlled system. In this paper, a constructive method is presented to design a controller for an inverted pendulum characterized by a time-delayed balance control. First, the partial feedback linearization control for the inverted pendulum is modified and coupled with a state predictor to compensate for the delay. Several coordinate transformations are processed to transform the estimated partial linearized system into an upper-triangular form. Second, nested saturation and backstepping techniques are combined to derive the control law of the transformed system that would complete the design of the whole control input. The effectiveness of the proposed technique is illustrated by numerical simulations.     

Input/output linearization using time delay control and time delay observer

In this paper, input/output linearization (IOL) method using time delay control (TDC) and time delay observer (TOO) is presented. This method enables the IOL method to be applied to plants even when all the states of plant are not measurable or the measured plant output is very noisy. The designed control system requires neither an accurate plant model nor the real time computation of plant nonlinearity. Consequently, the proposed control algorithm turned out to be computationally efficient and easy to design for nonlinear plants. In a simulation for a second order nonlinear plant, the output followed desired response well and the control performance appeared to be superior to IOL using TDC and numerical differentiation. Finally, in an experiment with a pneumatic servo system, we obtained results consistent with those from the simulation, and it was confirmed that the proposed control algorithm can be effectively used in a real closed-loop system.     

Wiener model based GMVC design considering sensor noise and delay

Even though there is a plethora of literature available for assessing linear control loop performance, they cannot be applied to the nonlinear control loops. In this paper, a nonlinear generalized minimum variance (NGMV) controller based on a single input–single output (SISO) Wiener model is proposed. The NGMV controller’s performance is used as a benchmark for a class of nonlinear control loops. The advantage of the proposed method is ability of online parameter estimation of the nonlinear model using common recursive least squares (RLS) method. In real-world applications, sensor and measurement tools force noises and extra delay to the control loop which poses limitations on achievable control performance. Hence, the classic control performance assessment techniques, is not attainable anymore. To handle the limitation caused by sensor delay, the k-step ahead prediction method is utilized. Further, the exponential digital filter is used in order to attenuate impact of the measurement noise on the controller. To show the effectiveness of the proposed method, a simulation test on a pH neutralization process is carried out.     

A novel auto-tuning PID control mechanism for nonlinear systems

In this paper, a novel Runge–Kutta (RK) discretization-based model-predictive auto-tuning proportional-integral-derivative controller (RK-PID) is introduced for the control of continuous-time nonlinear systems. The parameters of the PID controller are tuned using RK model of the system through prediction error-square minimization where the predicted information of tracking error provides an enhanced tuning of the parameters. Based on the model-predictive control (MPC) approach, the proposed mechanism provides necessary PID parameter adaptations while generating additive correction terms to assist the initially inadequate PID controller. Efficiency of the proposed mechanism has been tested on two experimental real-time systems: an unstable single-input single-output (SISO) nonlinear magnetic-levitation system and a nonlinear multi-input multi-output (MIMO) liquid-level system. RK-PID has been compared to standard PID, standard nonlinear MPC (NMPC), RK-MPC and conventional sliding-mode control (SMC) methods in terms of control performance, robustness, computational complexity and design issue. The proposed mechanism exhibits acceptable tuning and control performance with very small steady-state tracking errors, and provides very short settling time for parameter convergence.     

Decentralized PID controller for TITO systems using characteristic ratio assignment with an experimental application

This paper presents a decentralized PID controller design method for two input two output (TITO) systems with time delay using characteristic ratio assignment (CRA) method. The ability of CRA method to design controller for desired transient response has been explored for TITO systems. The design methodology uses an ideal decoupler to reduce the interaction. Each decoupled subsystem is reduced to first order plus dead time (FOPDT) model to design independent diagonal controllers. Based on specified overshoot and settling time, the controller parameters are computed using CRA method. To verify performance of the proposed controller, two benchmark simulation examples are presented. To demonstrate applicability of the proposed controller, experimentation is performed on real life interacting coupled tank level system.     

电加热炉控制的免疫PID应用研究

温控系统在工业现场是一个大滞后、强耦合、非线性的系统,常规PID控制器很难取得优良的控制效果。文章依据免疫系统的自适应反馈调节作用,提出了免疫PID控制器的实现方法,并将其应用到常规温度控制系统中。仿真结果表明,免疫PID控制器具有良好的控制品质,当系统发生扰动时具有较强的鲁棒性和自适应能力。     

Dual-user nonlinear teleoperation subjected to varying time delay and bounded inputs

A novel trilateral control architecture for Dual-master/Single-slave teleoperation system with taking account of saturation in actuators, nonlinear dynamics for telemanipulators and bounded varying time delay which affects the transmitted signals in the communication channels, is proposed in this paper. In this research, we will address the stability and desired position coordination problem of trilateral teleoperation system by extension of (nP+D) controller that is used for Single-master/Single-slave teleoperation system. Our proposed controller is weighted summation of nonlinear Proportional plus Damping (nP+D) controller that incorporate gravity compensation and the weights are specified by the dominance factor, which determines the supremacy of each user over the slave robot and over the other user. The asymptotic stability of closed loop dynamics is studied using Lyapunov-Krasovskii functional under conditions on the controller parameters, the actuator saturation characteristics and the maximum values of varying time delays. It is shown that these controllers satisfy the desired position coordination problem in free motion condition. To show the effectiveness of the proposed method, a number of simulations have been conducted on a varying time delay Dual-master/Single-slave teleoperation system using 3-DOF planar robots for each telemanipulator subjected to actuator saturation.     

基于干扰观测器的电液伺服系统反馈线性化滑模控制

为抑制电液伺服系统中各种非线性因素及不确定干扰,提出了基于输入输出反馈线性化的滑模控制与非线性干扰观测器相结合的控制策略以提高其位置控制跟踪精度。以电液振动台为试验对象,建立其非线性控制模型,利用李雅普诺夫稳定性理论保证了位置闭环系统的全局稳定性。利用MATLAB/Simulink对设计的控制器进行了仿真验证,结果验证了提出的控制器的可行性。为了模拟实际环境下存在不确定干扰,在位置电液系统基础上增加了电液加载系统,开展了试验研究。结果表明,该控制器能有效的提高干扰下电液伺服系统的位置跟踪性能。     

Time-discretization of non-affine nonlinear system with delayed input using taylor-series

In this paper, we propose a new scheme for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption. This scheme is applied to the sampled-data representation of a non-affine nonlinear system with constant input time-delay. The mathematical expressions of the discretization scheme are presented and the ability of the algorithm is tested for some of the examples. The proposed scheme provides a finite-dimensional representation for nonlinear systems with time-delay enabling existing controller design techniques to be applied to them. For all the case studies, various sampling rates and time-delay values are considered.     

A new discrete-time robust adaptive time-delay control for a class of uncertain nonlinear strict-feedback systems using sliding mode

This paper presents a new discrete-time adaptive second-order sliding mode control with time delay estimation (TDE) for a class of uncertain nonlinear time-varying strict-feedback systems. The existing researches on time delay control (TDC) are conventionally established based on a stability criterion that is subject to the infinitesimal time delay assumption. Recently, this criterion was rejected and a new criterion was proposed for the development of a controller for systems with fully known dynamics. In this study, this approach is extended to uncertain systems. Specifically, a new criterion is developed for the stability of the TDE-error within an adaptive robust controller design without the infinitesimal time delay assumption. With the proposed adaptive robust control, there is no need for determination of uncertainties upper-bounds. Simulation results illustrate the efficacy of the proposed controller.     

Discretization of nonlinear systems with delayed multi-input via Taylor series and scaling and squaring technique

An input time delay always exists in practical systems. Analysis of the delay phenomenon in a continuous-time domain is sophisticated. It is appropriate to obtain its corresponding discrete-time model for implementation via digital computers. In this paper a new scheme for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption is proposed. The mathematical structure of the new discretization method is analyzed. On the basis of this structure the sampled-data representation of nonlinear systems with time-delayed multi-input is presented. The delayed multi-input general equation has been derived. In particular, the effect of the time-discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. Additionally, hybrid discretization schemes that result from a combination of the scaling and squaring technique (SST) with the Taylor series expansion are also proposed, especially under conditions of very low sampling rates. Practical issues associated with the selection of the method’s parameters to meet CPU time and accuracy requirements, are examined as well. A performance of the proposed method is evaluated using a nonlinear system with time delay: maneuvering an automobile.