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.     

H∞-optimal feedback controllers for linear multivariable systems

This paper treats the problem of designing, for a linear multivariable plant, a feedback controller which minimizes theH^{infty}-norm of a weighted sensitivity matrix. There exists a family of optimal improper feedbacks. This family is determined by application of a theory of Ball and Helton. A method for computing optimal feedbacks is described in detail and a numerical example is included. It is shown that an optimal improper feedback can be approximated by a proper one under certain conditions on the weighting matrices.     

$H_{infty}$ Controller Synthesis via Switched PDC Scheme for Discrete-Time T--S Fuzzy Systems

This paper is concerned with the problem of designing switched state feedback $H_{infty}$ controllers for discrete-time Takagi--Sugeno (T--S) fuzzy systems. New types of state feedback controllers, namely, switched parallel distributed compensation (PDC) controllers, are proposed, which are switched based on the values of membership functions. Switched quadratic Lyapunov functions are exploited to derive a new method for designing switched PDC controllers to guarantee the stability and $H_{infty}$ performances of closed-loop nonlinear systems. The design conditions are given in terms of solvability of a set of linear matrix inequalities. It is shown that the new method provides better or at least the same results of the existing design methods via the pure PDC scheme with a quadratic Lyapunov function or switched constant controller gain scheme. Numerical examples are given to illustrate the effectiveness of the proposed method.      

Robust Output Regulation of T--S Fuzzy Systems With Multiple Time-Varying State and Input Delays

This paper proposes a robust output regulator design for Takagi–Sugeno (T–S) fuzzy systems with uncertain time delays. For generalization of the control problem, we assume that there exist affine dynamics, unknown multiple time-varying delays in state and input, uncertain parameters, disturbance, and partial state feedback. Both continuous-time and discrete-time cases are considered in a unified theoretical derivation. Here, we introduce a memoryless fuzzy observer and a fuzzy integral compensator. In comparison with previous studies, the proposed scheme drops the need for coordinate transformation, calculation of the desired operational point, which is known state and input delays, and exact fuzzy modeling. The control result is asymptotic output regulation for systems without disturbance and guaranteed $H^{infty}$ performance for systems with disturbance. Moreover, a piecewise constant output regulation is achieved without controller redesign. In addition, the developed fuzzy regulator can be applied to both affine and nonaffine uncertain time-delay systems. Finally, numerical simulations are performed by using two typical time-delay systems to validate the expected performance.      

基于强化学习的一类具有输入约束非线性系统最优控制

针对部分系统存在输入约束和不可测状态的最优控制问题,本文将强化学习中基于执行–评价结构的近似最优算法与反步法相结合,提出了一种最优跟踪控制策略.首先,利用神经网络构造非线性观测器估计系统的不可测状态.然后,设计一种非二次型效用函数解决系统的输入约束问题.相比现有的最优方法,本文提出的最优跟踪控制方法不仅具有反步法在处理...     

Distributed Control: A Sequentially Semi-Separable Approach for Spatially Heterogeneous Linear Systems

We consider the problem of designing controllers for spatially-varying interconnected systems distributed in one spatial dimension. The matrix structure of such systems can be exploited to allow fast analysis and design of centralized controllers with simple distributed implementations. Iterative algorithms are provided for stability analysis, $H_{infty}$ analysis and sub-optimal controller synthesis. For practical implementation of the algorithms, approximations can be used, and the computational efficiency and accuracy are demonstrated on an example.      

On the minimum order of a robust servocompensator

In recent papers [1]-[4], Davison et al. have given the characterization of a minimal-order robust error-driven servocompensator which achieves asymptotic tracking and disturbance rejection. In this note, we establish this minimality property by frequency domain methods. We show that any right coprime factorization of the controller, sayN_{r}(S)D_{r}(S)^{-1}, must have all the elements ofD_{r}(s)divisible byPhi(s), the minimal polynomial of the tracking and disturbance signal generator. Hence, its order must be at leastn_{0}.d(phi)(n0=number of outputs,d(Phi)= degree ofPhi).     

Nonlinear Adaptive Tracking Of Surface Vessels With Exogenous Disturbances

Significant interaction disturbances in surface vessel maneuvering and position tracking often require high precision controllers. In this paper we develop a coupled nonlinear two‐vessel tracking model for addressing the problem of underway replenishment. Next, using this model we develop an inverse optimal adaptive controller that guarantees disturbance rejection to exogenous disturbances while maintaining a desired separation between the two vessels.     

Optimal Output Feedback Controllers for Spacecraft Attitude Tracking

This paper investigates the problem of output feedback attitude tracking control of a rigid spacecraft in the presence of external disturbances. Two optimal control laws with a disturbance estimator are developed to deal with this problem. An adapted extended state observer is used to estimate the angular velocity tracking errors and to allow for compensation for the total disturbances. The proposed control can be expressed as the sum of a nonlinear optimal controller and an estimated disturbance. For the optimal controller, the state‐dependent Riccati equation and optimal Lyapunov techniques are employed to solve the infinite‐time nonlinear optimal control problem. The developed controllers can minimize a performance index and ensure the stability of the closed‐loop system and external disturbance attenuation. On the other hand, using the adapted extended state observer, the asymptotic convergence of estimation error dynamics is proven. An example of multiaxial attitude manoeuvres is given and simulation results are included to demonstrate and verify the usefulness of the proposed controllers.     

基于有限时间预设性能的高超声速飞行器反演控制

针对存在参数不确定以及外界干扰的高超声速飞行器跟踪性能问题,提出一种基于有限时间预设性能的反演控制方案.首先,为便于控制器设计,将高超声速飞行器模型划分为速度和高度子系统,针对子系统分别设计预设性能控制器以提高系统的瞬态和稳态性能;然后,通过设计一种有限时间性能函数,使得跟踪误差能够在预设时间内收敛至稳态值;接着,考虑到反演设计中虚拟指令导数难以获取以及干扰项对系统的影响,基于干扰观测器提出一种扰动估计方法,目的是在取得良好的观测扰动效果的同时,使得控制器设计流程简化、复杂度降低;最后,基于Lyapunov稳定理论证明系统的跟踪误差最终一致有界,并通过仿真验证该方法的有效性.     

Some investigations on hybrid fuzzy IPD controllers for proportional and derivative kick suppression

Proportional and derivative kick i.e., a large change in control action of a proportional plus integral plus derivative (PID) controller due to a sudden change in reference set-point is generally undesired in process industry. Therefore, the structure of conventional parallel PID controller is modified to integral minus proportional derivative (I-PD) controller. In this paper, three hybrid fuzzy IPD controllers such as a fuzzy I-fuzzy PD (FI-FPD) controller and its hybrid combinations with its conventional counterpart such as fuzzy I-PD (FI-PD) and I-fuzzy PD (I-FPD) are presented in view of above industrial problem. These controllers are based upon the counterpart conventional I-PD controller and contains analytical formulae. Computer simulations are carried out to evaluate the performance of hybrid fuzzy controllers along with conventional I-PD and PID controllers for set-point tracking and disturbance rejection for an induction motor in closed loop using LabVIEW? environment. The gains of conventional and hybrid fuzzy controllers are tuned using genetic algorithm (GA) for minimum overshoot and settling time. It has been observed that hybrid fuzzy controllers along with the conventional I-PD controller significantly remove the kick from the control action in reference set-point tracking. However, in disturbance rejection, I-PD and FI-PD controllers fail to eliminate the kick from the control signal. In contrast, FI-FPD and I-FPD controllers considerably reduced spikes from the control action in disturbance rejection. Among the conventional and hybrid fuzzy IPD controllers, FI-FPD demonstrates much better set-point tracking and disturbance rejection response with spike free control action.     

On constrainedH^{∞}optimization problem for SISO systems

This note is concerned with a control problem of designing a cascade compensator which minimizes the effect of the disturbance inputs or the weighted sensitivityH^{infty}-norm on the plant output subject to the constraint of a sensor-noise characteristic or robust stability of the closed-loop system. Lower and upper bounds are presented.     

Neurodynamic Programming and Zero-Sum Games for Constrained Control Systems

In this paper, neural networks are used along with two-player policy iterations to solve for the feedback strategies of a continuous-time zero-sum game that appears in $L_{2}$ -gain optimal control, suboptimal $H_{infty}$ control, of nonlinear systems affine in input with the control policy having saturation constraints. The result is a closed-form representation, on a prescribed compact set chosen a priori, of the feedback strategies and the value function that solves the associated Hamilton–Jacobi–Isaacs (HJI) equation. The closed-loop stability, $L_{2}$-gain disturbance attenuation of the neural network saturated control feedback strategy, and uniform convergence results are proven. Finally, this approach is applied to the rotational/translational actuator (RTAC) nonlinear benchmark problem under actuator saturation, offering guaranteed stability and disturbance attenuation.      

Cancellations in multivariable continuous-time and discrete-time feedback systems treated by greatest common divisor extraction

This correspondence considers a multivariable system with proper rational matrix transfer functions G0and Gfin the forward and feedback branches, respectively. It develops a strictly algebraic procedure to obtain polynomials whose zeros are the poles of the matrix transfer functions from input to output (Hy), and from input to error (He). G0and Gfare given in the polynomial matrix factored formN_{0}D_{0}^{-1}andD_{f}^{-1}N_{f}. The role of the assumption det [I + G_{f}(infty)G_{0}(infty)] neq 0and the relation between the zeros of det [I + G_{f}G_{0}] and the poles of Hyand Heare indicated. The implications for stability analysis of continuous-time as well as discrete-time systems are stressed.     

A Sufficient Condition for Invalidation of Linear State-Space Systems With Uncertain Time-Varying Parameters

The model validation problem for linear systems with time-varying parameter uncertainty and additive disturbances is addressed. The disturbance are modelled using the window norm, which is a generalization of the ${rm l}_{infty}$-norm and is shown to be attractive for optimal control. An approximation of the nonlinear operator from parameters to output is found based on the FrÉchet derivative. Using this approximation, a sufficient condition for invalidation of a process model is formulated as a linear feasibility problem. In this condition, an upper bound for the approximation error is included. An overhead crane is used as an illustrative example to show that the model validation test is realistic to perform even with large data sets.      

Robust tracking and disturbance rejection of bounded rate signals for uncertain/non-linear systems

We consider the problem of designing controllers for non-linear/uncertain systems to achieve tracking of a reference output signal in the presence of a disturbance input signal. When the exogenous signal (combined reference and disturbance) is constant, we require that the tracking error eventually go to zero. When the exogenous signal has a bounded rate, we require that the tracking error be eventually bounded with a bound which only depends on the bound on the magnitude of the rate of the exogenous signal. We also require that the state and control input are bounded when the exogenous signal is bounded. We propose controllers which have a classical PI (proportional integral) structure using state feedback. For linear systems and specific classes of non-linear/uncertain systems we present conditions whose satisfaction guarantees the existence of controllers which achieve the desired behaviour. Satisfaction of these conditions also yields the controller gain matrices.     

The stable regulator problem and its inverse

This paper provides a detailed survey and extension of certain properties of the stable regulator problem: determinemininf{u} intmin{0}max{infty} x'Qx + u'u dtsubject todot{x} = Fx + Gu; x(0) = x_{0}; liminf{t rightarrow infty} x(t) = 0whereQis not necessarily sign definite. First, equivalence conditions recently given by Willems for the existence of the minimum are extended to include statements in terms of the Hamiltonian matrix and spectral factorization. This provides a precise relation between the time-domain and frequency-domain solutions to the problems. Second, the inverse problem of whether a given feedbacku = -Kxis optimal for someQis easily resolved, as is the redundancy problem of distinct Q1and Q2, resulting in the same optimal control.     

具有预期闭环极点区域的稳定控制器的H∞优化设计方法

本文从工程应用角度出发,提出了一种将闭环极点设置于预期稳定区域的稳定控制器的 H∞优化设计方法,即实参数优化求解控制器的方法.这种方法综合考虑了闭环动态性能、抗 干扰、鲁棒性以及控制器本身的稳定性.实例表明,与现有的H∞设计方法相比,用本文方法 设计的控制系统在不显著增大抗干扰和鲁棒性指标情况下,具有闭环动态性能良好及控制器 稳定等优点,因此具有工程应用价值.     

基于遗传算法的输出反馈动态面优化控制

针对一类只有输出信号可测且非线性项含不可测状态的不确定系统,基于输入信号置换思想构建了神经网络状态观测器,结合动态面理论设计了输出反馈自适应控制方案。通过理论分析确定了控制律参数选取范围,保证了闭环控制系统所有信号半全局一致终结有界; 利用遗传算法提出一种参数寻优策略,选取了最优的输入初始值和控制律参数,解决了控制冲击问题,提高了跟踪精度。     

Sub-optimal PID controller settings for FOPDT systems with long dead time

We propose a method for setting up PI and PID controllers based on stable FOPDT process model, where dead-time dynamics is manipulated without approximation. The main idea used is a partial compensation of the system dynamics, which makes possible obtaining simple tuning rules. Remaining unknown controller parameters are determined on the basis of the modulus optimum and the minimum ISE criterions. Besides the performance indices, quality of the settings is also evaluated by the stability margin. Although optimal values of the parameters are valid for the reference tracking problem, a compensation of the disturbance lag that preserves the stability margin is proposed for the disturbance rejection problem.