Optimal control of the linear regulator subject to disturbances

An optimal control problem for linear regulators with external disturbances is formulated. It is shown that if some a priori knowledge of the disturbance is incorporated into the design procedure the optimal control is not an explicit function of the disturbance and, for polynomial disturbances, can be implemented as a linear function of the state of the system.     

Optimal decentralized controller design for multivariable plants†

The most commonly employed feedback algorithms for the control of industrial plants are those of the P, PI and PID regulators. In this paper, the procedure for decentralized (local) P, PI and PID regulators for multivariable plants optimal with respect to the overall system performance is developed. It is assumed that the type of each regulator is defined a priori and, in the case of PI and PID control laws, the state space of the corresponding subsystem is extended to include the dynamics of the local feedback regulator. The implementation of the procedure is based on optimal structurally constrained state feedback design with respect to the extended quadratic performance criterion.     

一种次最优鲁棒调节器的设计方法

本文基于最优控制和极点配置理论,提出一种灵敏度低、动特性好的次最优鲁棒调节器设计法。它具有计算方便、结构简单的特点。     

不确定时滞系统的全局鲁棒最优滑模控制

针对一类不确定性时滞系统, 研究线性二次型最优调节器的鲁棒性设计问题. 首先基于级数近似方法, 将原标称时滞系统的最优调节器问题转化为迭代求解一族不含时滞的两点边值问题, 从而获得标称时滞系统最优控制的近似解. 然后将滑模控制理论应用于最优调节器的设计, 使得系统对于不确定性具有全局的鲁棒性, 并且其理想滑动模态与标称系统的最优闭环控制系统相一致, 从而实现了全局鲁棒最优滑模控制. 仿真示例将所提出的方法与相应的二次型最优控制进行比较, 验证了该方法的有效性和优越性.     

Comments on "The design of linear regulators optimal for time multiplied performance indices"

A procedure for the design of linear regulators optimal with respect to a time-multiplied performance index was suggested in a recent paper by Man and Smith. A counterexample, presented subsequently [2], indicated that the procedure was in error. It is shown that the optimal feedback control law must contain time-varying gains as opposed to the time-invariant gains as suggested by Man and Smith. This fact was also overlooked in [2].     

Optimal digital feedback control systems counting computation time of control laws

Since microprocessors are easily obtained, multivariable control theory can be applied to many practical control problems, for example control of robots. However, when the time constant of the plant is short and the dynamic order of the plant is high, the time delay due to the computation time of the control law cannot be neglected. In this paper, the author proposes design methods for linear optimal regulators and linear optimal servosystems in which the delay arising from the computation time of the processors is counted properly. From the theoretical point of view, the results are interesting since all the control laws derived in this paper are obtained using only conventional results of optimal regulator theory.     

Control of randomly varying systems with prescribed degree ofstability

The control of linear discrete-time systems with stochastic parameter matrices is discussed. Two control techniques are particularly used: infinite-horizon and finite-moving-horizon optimal regulators. It is shown that it is possible to design controllers with a guaranteed degree of exponential stochastic stability by properly modifying the performance indexes. In this way, the deterministic regulator problem with a prescribed degree of stability is extended to the case of stochastic parameter systems     

New results in state estimation and regulation

An alternative technique to design linear state estimators and regulators is presented. This technique is based on transfer matrix considerations. The optimal regulator or estimator gain is obtained via spectral factorization and the solution of a simple equation in polynomial matrices.This approach provides further insight, displays the duality of estimation and control nicely, and bridges the state-space and frequency-domain techniques. The resulting design procedure is computationally attractive and particularly simple for system matrices in the observer or controller canonical form.     

Optimal discrete systems using time-weighted performance index withprespecified closed-loop eigenvalues

A design problem of optimal regulators for discrete-time linear multi-input systems is investigated for the prespecified closed-loop eigenvalues. Then the design freedom, which remains after the prespecified closed-loop eigenvalues are assigned, is used to minimize a time-weighted performance index. Necessary conditions for the optimality of the controller that satisfies the prespecified closed-loop eigenvalues are derived and an algorithm for computing the optimal constant feedback gain is presented     

Minimax指标最优定常输出反馈调节器设计方法

本文在T. Yahagia工作的基础上进一步讨论了minimax指标最优输出反馈设计方法,并将该方法推广到离散系统。给出了计算方法,研制了适用于多种指标函数的CSCAD应用软件。     

Design of regulators using time-multiplied quadratic performance indices

The design of linear regulators, optimal with respect to a time-multiplied quadratic performance index, is considered. Since it is not possible to minimize the normal form of the index with constant feedback gains, a suitably modified index is used and a design which is optimal in an average sense is obtained.     

轨道摄动对航天器角动量管理的影响和补偿

三轴主惯量接近的航天器长期在轨采用惯性系的角动量管理,使用垂直于轨道面的某一主惯性轴为Y轴,建立参考的惯性系进行控制器设计,轨道摄动使轨道长周期项与时间呈近似线性关系,导致控制器输出线性累加.针对此问题,分析轨道摄动导致控制律失效的原因,参考内模原理扩维方程,重新设计最优控制方法进行惯性系的角动量管理.通过半物理仿真表明了摄动补偿方法的可行性,且角动量和姿态长期稳定性均优于补偿前.     

Sequential tuning methods of LQ/LQI controllers for multivariable systems and their application to hot strip mills

In this study, we propose such sequential tuning methods of multivariable optimal regulators that can be applied to the tuning of control systems under operation. In such tuning, it is desirable to change feedback gains only step by step, confirming that the control performance is actually improved in each step. The first method we propose is such that we design an optimal single-input regulator in each step, by paying attention to only one input of the plant while the feedback laws to other inputs are fixed to those obtained in the previous sequential tuning steps. On the other hand, the second method is such that all elements of the feedback gain are changed at once, while we are given the design freedom about how much we are to change the gain. These two methods as well as their combined use are shown to lead to the optimal gain as a multivariable control system eventually, provided that the sequential tuning steps are repeated sufficiently many times. We apply these methods to the tuning of LQI servo systems, and carry out the simulation study of the control of a hot strip mill to illustrate the tuning law and show its effectiveness.     

Lower bounds on the quadratic cost of optimal regulators

Lower bounds for linear optimal regulators with quadratic cost functional are derived, explicitly containing information pertaining to some parameters of the system, e.g. the weighting matrices of the quadratic cost. If the optimal solution is not available, but rather a sub-optimal design is known, these bounds provide a means for estimating how close a sub-optimal design is to the optimal one, without having to actually calculate the latter. Being explicit in terms of the system parameters, these bounds enable the ranking of the various sub-optimal designs in terms of these parameters.     

Design of stochastic discrete time linear optimal regulators Part II. Extension and computational procedures

Using the relationship established in Part I, computational procedures are formulated for implementing stochastic optimal regulators based on the CARMA model. The state space configurations (including both the implicit delay and explicit delay models) allow the consideration of general quadratic cost functions, in particular the receding horizon N-stage cost function ; a simple example is used to illustrate various design steps required. The characteristics of the implicit delay and explicit delay models are exploited to give a computationally efficient scheme for system with large control delay     

A wide area measurement based neurocontrol for generation excitation systems

Power system is a highly interconnected nonlinear system that needs optimal and accurate control for continuous operation. Large power transfer through long transmission line between different electrical areas, stressed system and adverse interaction between local controllers, may give rise to slow frequency inter-area oscillations. The inter-area modes may not be visible from local measurements and hence it is useful to use remote measurement based centralized supplementary control. Wide area control systems (WACSs) using wide-area or global signals can provide remote auxiliary control to local controllers such as automatic voltage regulators, power system stabilizers, etc. to damp out inter-area oscillations. This paper presents a design and real time implementation of a nonlinear neural network based optimal wide area controller using adaptive critic design (ACD). The real time implementation of a power system model is carried out on a real time digital simulator (RTDS). The performance of the WACS as a power system stability agent is studied using a two-area power system under different operating conditions and contingencies. The WACS shows improvement in the damping of inter-area mode with the use of supplementary excitation control. In addition, results show that the designed controller can provide robust performance under small communication delay in remote signal transmission.     

On the definition of ‘transfer function’†

The optimal asymptotically stabilizing control problem is formulated, and the theorem for the sufficient condition that guarantees its existence and uniqueness is stated and proved. The close relationship with Pontryagin's equations is discussed. It is shown that the control problem falls into the framework of optimal linear regulators with quadratic cost functionals. Furthermore, an alternate approach is presented that, for the problem solved, leads to the same optimal control.     

设计最优调节器的混合法

本文根据Kalman最优调节器理论和Wonham极点配置理论,提出了设计最优调节器的 一种方法.文中提出了等价权阵的概念,研究了权阵与闭环极点的关系以及最优调节器综合 评价问题,从而改进了以往工程中常用的试探法.     

Fuzzy regulators and fuzzy observers: relaxed stability conditionsand LMI-based designs

This paper presents new relaxed stability conditions and LMI- (linear matrix inequality) based designs for both continuous and discrete fuzzy control systems. They are applied to design problems of fuzzy regulators and fuzzy observers. First, Takagi and Sugeno's fuzzy models and some stability results are recalled. To design fuzzy regulators and fuzzy observers, nonlinear systems are represented by Takagi-Sugeno's (TS) fuzzy models. The concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the TS fuzzy models. New stability conditions are obtained by relaxing the stability conditions derived in previous papers, LMI-based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions. Other LMI's with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures. Design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the LMI-based design procedures     

Synthesis of optimal control systems with near sensitivity feedback

Design of optimal control systems with reduced sensitivity to parameter variations is attempted by employing trajectory sensitivity feedback and minimizing a cost term that includes the trajectory sensitivity. Since the trajectory, sensitivity, cannot be assessed directly, a successive approximation method that results in "near" sensitivity feedback is given for the case of linear regulators. The method may be extended to more general optimal control problems.