Adaptive NN control for discrete-time pure-feedback systems with unknown control direction under amplitude and rate actuator constraints

This paper focuses on the problem of adaptive neural network tracking control for a class of discrete-time pure-feedback systems with unknown control direction under amplitude and rate actuator constraints. Two novel state-feedback and output-feedback dynamic control laws are established where the function tanh() is employed to solve the saturation constraint problem. Implicit function theorem and mean value theorem are exploited to deal with non-affine variables that are used as actual control. Radial basis function neural networks are used to approximate the desired input function. Discrete Nussbaum gain is used to estimate the unknown sign of control gain. The uniform boundedness of all closed-loop signals is guaranteed. The tracking error is proved to converge to a small residual set around the origin. A simulation example is provided to illustrate the effectiveness of control schemes proposed in this paper.     

Solution of low-dimensional constrained model predictive control problems

Large benefits are possible by utilizing the solution of the constrained optimization problem involved in model predictive control. For a special case of these problems, the solution can be obtained relatively easily from its relationship with the unconstrained optimum. In this paper, a visualization of the relationship between the constrained and unconstrained optimum is presented. Based upon this relationship, a method for finding the constrained optimum is proposed that is suitable for low-dimensional control systems. A comparison with a linear programming formulation on 2 × 2 and 3 × 3 problems shows that the computational effort can be 10–35 times lower. For such processes, the proposed approach may allow one to avail the benefits of optimization by using the small process control systems already present in many plants.     

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.     

Model predictive control of discrete-time hybrid systems with discrete inputs

This paper proposes and discusses a model predictive control approach to hybrid systems with discrete inputs only. The algorithm, which takes into account a model of a hybrid system, described as a mixed logical dynamical system, is based on a performance-driven reachability analysis. The algorithm abstracts the behavior of the hybrid system by building a "tree of evolution." The nodes of the tree represent the reachable states of a process, and the branches connect two nodes if a transition exists between the corresponding states. A cost-function value is associated with each node, and based on this value the exploration of the tree is driven. As soon as the exploration of the tree is finished, the corresponding input is applied to the system and the procedure is repeated.     

Static and low order anti-windup synthesis for cascade control systems with actuator saturation: An application to temperature-based process control

In this paper, a new framework for designing static and low order anti-windup compensator (AWC) for industrial cascade control systems with actuator saturation constraint is presented. Based on less conservative block diagonal quadratic Lyapunov function, sector boundedness, decoupled architecture, norm reduction and cascade loop compensation, linear matrix inequalities are developed which guarantee stability and suitable performance for overall closed-loop system. Static AWC parameters are obtained by comparing the full order AWC architecture with generalized architecture for cascade control system. Low order AWC is designed by sub-optimal approach in which AWC weights are tuned by designer. Anti-windup compensator is divided into inner and outer loop compensators which compensate the effect of saturation at each level. It is observed that the proposed methodology is less conservative than the traditional AWC schemes when applied to cascade control systems. The proposed scheme is successfully tested experimentally on a temperature-based process control system and results are outlined.     

Model predictive control helps to regulate slow processes--robust barrel temperature control

Slow temperature control is a challenging control problem. The problem becomes even more challenging when multiple zones are involved, such as in barrel temperature control for extruders. Often, strict closed-loop performance requirements (such as fast startup with no overshoot and maintaining tight temperature control during production) are given for such applications. When characteristics of the system are examined, it becomes clear that a commonly used proportional plus integral plus derivative (PID) controller cannot meet such performance specifications for this kind of system. The system either will overshoot or not maintain the temperature within the specified range during the production run. In order to achieve the required performance, a control strategy that utilizes techniques such as model predictive control, autotuning, and multiple parameter PID is formulated. This control strategy proves to be very effective in achieving the desired specifications, and is very robust.     

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.     

A PSO-based optimal tuning strategy for constrained multivariable predictive controllers with model uncertainty

This paper describes the development of a method to optimally tune constrained MPC algorithms with model uncertainty. The proposed method is formulated by using the worst-case control scenario, which is characterized by the Morari resiliency index and the condition number, and a given nonlinear multi-objective performance criterion. The resulting constrained mixed-integer nonlinear optimization problem is solved on the basis of a modified version of the particle swarm optimization technique, because of its effectiveness in dealing with this kind of problem. The performance of this PSO-based tuning method is evaluated through its application to the well-known Shell heavy oil fractionator process.     

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.     

液压机器人作动器建模及关节转角跟踪控制

针对液压四足机器人作动器伺服精度较差问题,分别推导电液伺服作动器在摆动相、刚性支撑相和弹性支撑相的等效模型,分析各作动器模型特点,提出比例内环自适应幅相控制外环的复合控制策略,应用比例控制器保证位置内环的稳定性,采用自适应幅相控制器进行幅值和相位补偿。通过机器人单腿测试平台进行控制策略验证,实验结果表明:所提控制策略可使系统幅值衰减小于2%,相位滞后小于4°,验证了此方法的有效性。     

Robust model predictive control design with input constraints

The paper addresses the problem of designing a robust output/state model predictive control for linear polytopic systems with input constraints. The new predictive and control horizon model is derived as a linear polytopic system. Lyapunov function approach guarantees the quadratic stability and guaranteed cost for closed-loop system. The invariant set and an algorithm approach similar to Soft Variable-Structure Control (SVSC), ensures input constraints for the model predictive plant control system. In the proposed control scheme, the required on-line computation load is significantly less than in MPC literature, which opens the possibility to use these control design schemes not only for plants with slow dynamics, but also for faster ones.     

机械臂执行器故障重构与容错控制

为了提高机械臂系统鲁棒性、使系统在故障情况下能够正常运行,提出了基于滑膜控制的故障重构与容错控制方法。建立了机械臂系统动力学方程和执行器故障模型;设计了准连续高阶滑膜观测器,结合等效输出误差注入法给出了故障重构方法;提出了非奇异快速终端滑膜控制方法,求解滑膜面得到了容错控制律。经仿真验证,准连续高阶滑膜观测器可以快速、高精度重构执行器故障,同时避免了滑膜控制抖振问题;非奇异快速终端滑膜控制器可以在系统故障情况下快速跟踪期望轨迹,有效提高了机械臂系统鲁棒性。     

基于广义预测控制算法的水槽液位控制系统

为提高液位系统控制的可靠性和安全性,引入了广义预测控制算法。首先介绍了广义预测控制的基本算法,包括其基本理论、算法的优点及一些重要参数的选取标准。然后以水槽液位控制装置为控制对象建立了一个控制系统的数学模型,并对应用广义预测控制算法的该模型进行了仿真验证。仿真结果表明,所提出的算法具有良好的动态响应性能和快速跟踪设定值,并具有较好的控制效果。无论系统是否存在模型失配,只要控制系统是稳定的,就不会有静差。     

叠堆式超磁致伸缩致动器的模型预测滑模控制

根据新型电液伺服阀的驱动要求,设计了叠堆式超磁致伸缩致动器(SGMA),为补偿其固有的非线性,提高位移输出精度,研究了SGMA的控制策略,并对控制策略进行了仿真和实验验证。首先,采用永磁体和GMM棒交替排布的结构形式设计了SGMA,有助于提高偏置磁场的均匀性;然后,根据SGMA的结构特点,将其视为多自由度振动系统,建立了系统的位移输出模型;接着,在输出模型的基础上,结合模型预测控制与滑模控制策略,设计了模型预测滑模控制器;最后,进行了控制策略仿真和实验验证。实验结果表明,模型预测滑模控制器能够实现SGMA的精密控制。在阶跃控制实验中,系统稳定时间低于1.5ms,无超调和稳态误差;在正弦控制实验中,系统最大控制误差约为0.83μm,相对值约为6.9%,证明了控制策略的有效性。     

饱和离散时间系统非保守输出反馈控制器设计

针对输入饱和离散系统由于采用输出反馈而导致的控制器设计存在很强保守性的问题,将凸多面体分析的方法应用于系统吸引域描述中,给出了基于状态的系统可控域的顶点描述和面描述形式,建立了系统输出反馈与基于状态的系统可控域之间的关系;为解决由于不稳定系统输出反馈第一步控制不施加任何控制作用而造成的系统状态可控域大大减小的保守性问题,提出了基于状态观测器的输出反馈非保守控制器设计方法;针对二阶不稳定系统,根据系统输出矩阵及输出初始值的不同情况,给出了输出反馈控制器第一步控制作用的具体形式,并证明了在该控制器作用下,系统的可控域达到最大,从而最大程度减小了控制器的保守性。最后通过Matlab进行了数值仿真实例研究。研究结果验证了所设计控制器的有效性。     

Iterative learning control scheme for manipulators including actuator dynamics

This paper presents the iterative learning control for the industrial robot manipulators including actuator dynamics. Motivated by human learning, the basic idea of iterative learning control is to use information from previous execution of a trial in order to improve performance from trial to trial. This is an advantage, when accurate model of the system is not available as friction and actuator dynamics, though present in the system, are not modeled to reduce the computational complexity. In this paper different aspects of ILC including the design schemes and control algorithms are covered. The learning control scheme comprises two types of control laws: a linear feedback law and a feed-forward control law. In the feedback loop, the fixed gain PD controller provides stability of the system and keeps its state errors within uniform bounds. In the feed-forward path, a learning control rule/strategy is exploited to track the entire span of a reference input over a sequence of iterations. Algorithms are verified through detailed simulation results on a two DOF robot manipulator.     

Embedded estimator in predictive feedback control

In this work, a new approach to design predictive feedback control for SISO systems is presented. The proposed formulation relies on the development of a single step predictor based on an autoregressive moving average with external input (ARMAX) model. Although no explicit observer is actually involved in the implementation, this predictor implicitly includes one since the input-output model subsumes an observer. Exploiting this idea the resulting ARMAX model is extended to include extra outputs to improve the quality of the prediction for systems with large time delay and nonmeasurable disturbances. The resulting predictor is used to develop a predictive feedback controller. This new formulation of predictive feedback control includes feedback and feedforward actions. Simulations of two linear systems illustrate the applicability of the control algorithm.     

Adaptive backstepping fault-tolerant control for flexible spacecraft with unknown bounded disturbances and actuator failures

In this paper, a robust adaptive fault-tolerant control approach to attitude tracking of flexible spacecraft is proposed for use in situations when there are reaction wheel/actuator failures, persistent bounded disturbances and unknown inertia parameter uncertainties. The controller is designed based on an adaptive backstepping sliding mode control scheme, and a sufficient condition under which this control law can render the system semi-globally input-to-state stable is also provided such that the closed-loop system is robust with respect to any disturbance within a quantifiable restriction on the amplitude, as well as the set of initial conditions, if the control gains are designed appropriately. Moreover, in the design, the control law does not need a fault detection and isolation mechanism even if the failure time instants, patterns and values on actuator failures are also unknown for the designers, as motivated from a practical spacecraft control application. In addition to detailed derivations of the new controller design and a rigorous sketch of all the associated stability and attitude error convergence proofs, illustrative simulation results of an application to flexible spacecraft show that high precise attitude control and vibration suppression are successfully achieved using various scenarios of controlling effective failures.     

Adaptive vibration control of micro-cantilever beam with piezoelectric actuator in MEMS

This paper proposes a dynamical model and the governing equations of motion of the micro-cantilever beams based MEMS with piezoelectric actuator (PZT). The Rayleigh–Ritz method is used to reduce the order of the system and the state equations are presented in modal space. The first ten mode frequencies and mode shapes of the micro-cantilever beam with and without PZT are studied. The effects of PZT on the modal frequencies and shapes of the beam system can be ignored for the reason that the beam holds larger nature frequencies and Q values in micro-scale. A rational linearizing feedback controller with a high gain observer is designed to eliminate the unwanted deflection of the micro-cantilever beam system. The open-loop step response and the effects of situated places of PZT on the frequency responses of the system are discussed. Various frequency responses of the beam system, subject to different applied control voltages and feedback gains, are illustrated. The four resonances are well controlled, while the anti-resonance has little change. Computer simulations are provided to demonstrate the performance of the designed control scheme.     

Optimal load of robotic manipulator with joint elasticity using accuracy and actuator constraints

A computational technique for obtaining the maximum load-carrying capacity for a robotic manipulator with joint elasticity, subject to accuracy and actuator constraints, is described. Full load motions and increased productivity are linked in the industrial applications of many robotic manipulators; the maximum load carrying capacity which can be achieved by a manipulator during a given trajectory is limited by a number of factors. The dynamic properties of a manipulator, its actuator limitations, and joint elasticity (transmissions, reducers, and servo drive system) are probably the most important factors. This paper presents a strategy for determining dynamic load carrying capacity (DLCC), subject to both accuracy and actuator constraints, where a series of cubical bounds centred at the desired trajectory is used in the end-effector oscillation constraint while a typical d.c. motor speed-torque characteristics curve is used in the actuator constraint. The technique which considers the full nonlinear manipulator dynamics, actuator constraints, and accuracy constraints permits the manipulator user to specify the trajectory completely. Finally, a numerical example involving a two-link manipulator with joint flexibility using this method is presented and the results are discussed.