Two-degree-of-freedom dead-beat control system with robustness: multivariable case

A design procedure for two-degree-of-freedom (TDF) dead-beat controllers for multivariable systems is presented. Based on the parametrization of all stabilizing TDF controllers, a minimal-time dead-beat control system with optimal robustness is constructed for an arbitrary reference input. The optimal robustness is achieved under the constraint of robust tracking. A comparison of a TDF system with a one-degree-of-freedom (ODF) system reveals that, under the same robustness criterion, the optimal robustness of the TDF system is always superior to that of the ODF system irrespective of its settling time. It is also shown that the optimal robustness of the ODF system becomes identical to that of the TDF only when the settling time of the ODF system goes to infinity. Some numerical examples are given to illustrate the theoretical results.     

Dead-beat control of simple Hammerstein models

Dead-beat controllers for simple Hammerstein systems are investigated. Several designs for nonminimum-time state dead-beat controllers are given for certain classes of simple Hammerstein systems. A general minimum-time state dead-beat controller is presented for a class of simple Hammerstein systems. A design for a family of minimum-time control laws is provided. This enables, to a certain extent, shaping of transient response via choosing an appropriate control law. Finally, the authors design an output dead-beat controller for a class of Hammerstein systems that are not necessarily state dead-beat controllable     

Stabilizability and dead-beat controllers for two classes ofWiener-Hammerstein models

Two classes of block oriented models of the Wiener-Hammerstein type are considered. We prove that a generic condition is sufficient for a null controllable discrete-time system of this form to have a stabilizing minimum-time dead-beat controller. When the condition is violated, we show how to design a nonminimum time stabilizing (dynamic) dead-beat controller. The result is used to obtain stabilizability conditions for these systems     

Dead-beat control with robustness

A design procedure for dead-beat control systems with robustness is proposed for general unstable non-minimum-phase plants. Characterization of dead-beat controllers is given in terms of closed-loop error response, based on the YJB parameterization of all stabilizing controllers. The optimally robust design is formulated in terms of a robustness index that is essentially the same as the L2-norm of sensitivity. For a given number of dead-beat steps, a procedure for computing the optimally robust dead-beat controller is derived. The limit value of the robustness index as the number of dead-beat steps goes to infinity is also given. Some numerical examples are shown to illustrate the theoretical results.     

基于混合预测策略的改进型并联有源电力滤波器无差拍控制

针对传统的无差拍电流跟踪控制受时延影响实际上是差一拍控制,提出一种改进的无差拍控制.该方法提前两个采样周期预测出有源电力滤波器(APF)指令电流,提前一个采样周期预测出逆变器输出电流,从而实现真正意义上的无差拍控制.同时,提出一种综合考虑负载谐波电流稳态和动态过程的混合预测策略,使上述预测过程更加准确、快速.仿真实验结果表明,基于该方法的APF在负载稳态和变化时均具有良好的补偿效果.     

基于输入整形的时滞系统最小拍控制

基于Ｎｙｑｕｉｓｔ准则,按照给定的相位稳定裕度设计ＰＩ控制器使一阶时滞对象稳定,然后引入输入整形控制器对输入进行整形,实现了一阶时滞对象的最小拍控制。在确定采用周期后,整个控制系统的设计尺需按相位稳定裕度的需求解析算出ＰＩ控制器的比例增益即可,设计简单,性能良好。仿真结果表明,该方法相当有效,实现的最小拍控制无纹波。     

Optimization of control input for deadbeat control systems

The aim of this paper is to deal with the problem of excessive control magnitude with deadbeat control systems. By the use of the transfer-function factorization approach, all stabilizing deadbeat controls are characterized in terms of control input. A formula is derived for the optimal control that minimizes the control input error for the specified settling time. The design procedure is essentially trade-offs between settling time and control input properties. As the bound of such trade-offs, the limiting value of the optimal performance index, as the settling time goes to infinity, is derived. This limit value plays an important role in fixing the most appropriate settling time.     

A note on dead-beat controllability of generalised Hammerstein systems

Necessary and sufficient conditions for dead-beat and complete controllability for a class of generalised Hammerstein systems are presented. Since the system's structure is very close to linear, only linear algebra is used for the controllability test. The test is very simple and easy to use. A closed-loop minimum-time dead-beat controller can be designed for a subclass of generalised Hammerstein systems using the Gröbner basis method.     

最小能量有限拍鲁棒控制系统的设计

本文采用2自由度控制器,以传递函数分式分解理论为基础,提出了一种在保证系统内部稳定和最佳鲁棒性前提下,实现最小能量控制的有限拍系统设计法。设计过程本质上是控制能量与响应时间的折衷。本文导出了折衷的最终界限,并给出了确定最佳响应时间的方法。     

Optimal disturbance rejection controller design for integrating processes with dead time based on algebraic theory

In this paper, an H₂ optimal input-load disturbance rejection (ILDR) controller for integrating processes with dead time is proposed based on the internal model control principle. The main contribution of this work is that the optimal solution under ILDR criterion for integrating processes with dead time and input constant disturbances has been derived based on algebraic theory. To further improve the performance for both set-point tracking and input disturbance rejection, a two-degree-of-freedom (TDOF) control design method has also been developed. Compared with previous advanced control methods, the proposed design method has three main advantages. First, the optimal ILDR controller is derived systematically on the basis of algebraic theory. The designed controller is given in an analytical form. Second, a simple tune principle is developed. The set-point tracking performance specification and robustness stability specification can be quantitatively achieved by monotonously tuning the performance degree in the designed controller. Finally, both optimal set-point tracking performance and input disturbance rejection can be achieved by the proposed TDOF control structure. Numerical simulations are given to illustrate the effectiveness of the proposed method.     

Design of motion trajectory and tracking control for underactuated cart‐pendulum system

A cart‐pendulum system is a nonlinear underactuated mechanical system with two degrees of freedom. This paper addresses the motion trajectory design and tracking control problems for this underactuated system. First, a friction‐like control law is designed for the system. Then, the characteristics of the closed‐loop control system are analyzed. Second, a new method of constructing an optimal trajectory for the system is developed. Then, a tracking control law is designed to quickly track the constructed trajectory. It guarantees that the motion control of the cart‐pendulum system is achieved along a reference trajectory. Finally, a numerical example is presented to demonstrate the effectiveness of the theoretical results. This study constructs an optimal trajectory for the cart‐pendulum system in its whole motion space and solves the motion control objective by tracking the constructed trajectory. It has many advantages compared with other motion control methods, eg, the optimal motion control objective of the system is achieved by a single control law; and the motion process and transient characteristics (eg, the settling time) of the control system can be accurately predicted.     

Continuous gain scheduling control for a micro-positioning system: simple,robust and no overshoot response

Continuous gain scheduling control is proposed for a micro-positioning system. Controllers should be adapted according to the task. In fine positioning regions, the controller gain should be large enough to reject the disturbance and to maintain high-precision positioning. In coarse positioning regions, since the reference input is large, the controller gain should be small in order to avoid the controller saturation. The simple continuous function of gain versus displacement error is derived based on the robust controller. From the simulation and experimental results, continuous gain scheduling control provides a better response than fixed gain control in disturbance rejection and settling time. It also brings robustness to system uncertainty and prevents overshoot responses.     

加热炉网络控制系统的最少拍响应控制策略

研究加热炉网络控制系统的最少拍响应控制策略。推导了加热炉网络控制系统的频域和离散型状态方程的数学模型,并采用时间戳神经网络,对不确定、时变的网络信息传输延时进行预测。重点研究了具有最少拍响应的数字控制器设计方法,导出了数字控制器控制算法。仿真结果表明,提出的控制算法实现了加热炉精确的温度控制,无稳态偏差,并具有良好的动、静态特性。     

Guaranteed cost control for multi-inventory systems with uncertain demand

In this paper we consider the problem of controlling a multi-inventory system in the presence of uncertain demand. The demand is unknown but bounded in an assigned compact set. The control input is assumed to be also constrained in a compact set. We consider an integral cost function of the buffer levels and we face the problem of minimizing the worst-case cost. We show that the optimal cost of a suitable auxiliary problem with no uncertainties is always an upper bound for the original problem. In the special case of minimum-time control, this upper bound is tight, namely its optimal cost is equal to the worst-case cost for the original system. Furthermore, the result is constructive, since the optimal control law can be explicitly computed.     

Time-optimal control and high-gain linear state feedback

It is known that the fastest possible response of a linear system under input constraints is typically achieved using extreme control efforts at all times, or bang-bang control. However, closed-loop minimum-time control is very difficult to implement except for a few simple second-order systems, since a closed-form solution for the time-optimal switching hypersurface usually cannot be found for high-order systems. In this paper the connection between linear state feedback and time-optimal control is explored. It is shown that for a class of systems an equivalent time-optimal, linear, switching hypersurface exists corresponding to an initial condition. Based on these switching planes, a high-gain linear state feedback law can be used to achieve minimum-time control on systems of order higher than two, provided that the feedback coefficients are adjusted according to the initial conditions at the start of each operation. Three different cases are investigated in detail: a second-order DC servo drive, a third-order servo system including actuator dynamics, and a fourth-order flexible mechanism. Since the proposed algorithm resembles in form a sliding-mode controller, the similarities and differences between the two control algorithms are also discussed.     

The isopone method in optimal control

The minimum-time problem is a well known problem in optimal control and several methods are available to solve this problem. In this article, an extension of the minimum-time problem will be considered. A specific optimal control problem will be treated and the so-called Isopone method to determine the optimal control is proposed. In this Isopone method, multi dimensional reachable subsets are computed repeatedly. This method is similar to dynamic programming in that it is a recursive algorithm, but is designed to reduce the amount of calculation time. The current algorithm yields, as a degenerate case, also the time optimal route.     

Theoretical developments in discrete-time control

Significant theoretical developments in discrete-time control over the past 10–15 years are reviewed. Topics reviewed include optimal control, Riccati equations, controllability, stability, robustness, deadbeat control, minimum-time systems, sampling, quantization, microprocessor implementation, and stochastic systems. Emphasis is placed on topics that are peculiar to discrete-time systems and do not generalize from continuous-time theory.     

Time-optimal control of a single-DOF mechanical system withfriction

Presents the exact solution to the minimum-time optimal control problem of a single-degree-of-freedom (DOF) mechanical systems with friction. In particular, the optimal control input can be synthesized in feedback form. The effect of Coulomb friction, which has been ignored or precompensated in prior works, is taken into full account. As a result, the admissible range of control input can be maximized so as to achieve faster responses. A practical example using a direct-driven single-DOF robotic manipulator is discussed to demonstrate the practical use of the optimal solution     

执行器约束下基于数据驱动的参数化前馈控制器设计

针对执行器约束下非重复性点到点运动的轨迹跟踪问题, 提出了一种在执行器约束下基于数据驱动的参数化输入整形滤波器和前馈控制器优化设计算法. 首先对输入整形滤波器以及前馈控制器进行参数化, 然后在目标函数中加入控制信号变化量与控制信号能量的约束, 再采用基于数据驱动的迭代寻优算法得到最优参数, 在该参数下可以实现满足执行器约束条件下的运动控制系统轨迹最优跟踪性能. 并且由于采用了前馈参数化设计方法, 在点到点轨迹发生变化时所提出算法依然能够保持良好的轨迹跟踪性能. 仿真与实验结果表明在执行器约束下所提出算法能够实现最优点到点轨迹跟踪性能, 并且对非重复性点到点轨迹跟踪具有一定的鲁棒性.     

Minimum-time control for an inverted pendulum under force constraints

In order to numerically solve the minimum-time control problem of a linear system, the system is usually discretized with a fixed sampling period. Then the minimum count of control steps is searched to meet the constraints of the final state and the input variables. Since the count is a variable, there is no direct way for handling such problems except by exhaustive iteration. In contrast to the traditional methods, a new numerical technique was developed recently to avoid the exhaustive iteration. In this method, the control step is fixed and the sampling period is treated as a variable. Since this method requires only two iterations, it will reduce the computation time significantly. This paper applies this new numerical technique to generate the minimum-time trajectory between two end-points for an inverted pendulum under force constraints. Two main issues are addressed. The first one is the problem formulation in discrete-time domain and the second one is the generation of feasible solutions for the global search. Simulation examples are included for illustration.