A design of gain-scheduled control for a linear parameter varying system: an application to flight control

For multi-input–multi-output, multi-parameter, nonlinearly parameter-dependent linear parameter-varying systems, a gain-scheduled control design method using both minimum sensitivity eigenvalue assignment and quadratic stability check is proposed. The designed controller guarantees the stability of the closed-loop system and assigns the eigenvalues of the frozen parameter closed-loop LPV system in the prespecified disjointed regions. Fewer controllers than that of any other method are needed to cover the whole parameter space. The proposed design method is applied to the design of a flight vehicle's back-to-turn (BTT) controller and nonlinear six-degree-of-freedom (6-DOF) simulations are performed to show its usefulness as a gain-scheduled controller design method.     

Optimal regulators using time-weighted quadratic performance index with prespecified closed-loop eigenvalues

Optimization of linear time-invariant systems, using a given time-weighted quadratic performance index, is investigated for the prespecified closed-loop eigenvalues. The necessary conditions have simple forms and this algorithm gives a considerable amount of computational time savings compared to the previous algorithms [1]-[2].     

Linear quadratic regulators with eigenvalue placement in a vertical strip

A computational method is presented for finding the linear quadratic regulator such that the optimal closed-loop system has eigenvalues lying within a vertical strip in the complex plane. The proposed method is suitable for the two-stage optimal design of two-time scale systems.     

最优二次型渐近设计法及其应用

本文探讨了用闭环系统预期特征值及特征向量确定加权阵,及依靠最优调节器的渐近特 性确定Riccati代数方程迭代解起始阵的方法.据此提出了线性系统最优二次型渐近设计法, 编写了设计程序,实验结果表明方法是可行的.     

Sensitivity reduced optimal linear regulator with prescribed closed-loop eigenvalues

In this note, the design technique given by Sebakhy and Sorial [1], based on both pole placement and optimal control, is extended to obtain a sensitivity reduced optimal linear regulator with prescribed closed-loop eigenvalues. An efficient computational procedure based on direct cost optimization using a gradient type algorithm is also reported.     

Linear quadratic regulators with eigenvalue placement in a specified region

A linear optimal quadratic regulator is developed for optimally placing the closed-loop poles of multivariable continuous-time systems within the common region of an open sector, bounded by lines inclined at ±π/2k (k = 2 or 3) from the negative real axis with a sector angle ≤π/2, and the left-hand side of a line parallel to the imaginary axis in the complex s-plane. Also, a shifted sector method is presented to optimally place the closed-loop poles of a system in any general sector having a sector angle between π/2 and π. The optimal pole placement is achieved without explicitly utilizing the eigenvalues of the open-loop system. The design method is mainly based on the solution of a linear matrix Lyapunov equation and the resultant closed-loop system with its eigenvalues in the desired region is optimal with respect to a quadratic performance index.     

Parametric state feedback design of linear distributed-parameter systems

The parametric approach for the design of state feedback controllers has been formulated so far only for linear lumped-parameter systems. It yields an explicit parametric expression for the state feedback gain given the closed-loop eigenvalues and the set of corresponding parameter vectors. This contribution presents a parameterisation of state feedback controllers for linear distributed-parameter systems with scalar state and distributed control. By introducing the closed-loop eigenvalues and the parameter vectors as design parameters, an explicit expression for the state feedback is obtained. In contrast to the pure eigenvalue assignment, the parameterisation allows the assignment not only of the closed-loop eigenvalues but also of the closed-loop eigenfunctions. The usefulness of the proposed parametric approach is demonstrated by decoupling the transfer behaviour of a MIMO diffusion system with respect to its dominant modes.     

Approximate model matching with multivariable PI-controllers

A technique is proposed for the design of multivariable PI-controllers by approximately matching a prespecified model. The controller parameters are transparently tuned via a scalar model speed parameter. For slow models closed-loop stability can be guaranteed under mild conditions.     

A parametric approach to finite-dimensional control of linear distributed-parameter systems

This article considers the design of finite-dimensional compensators for distributed-parameter systems using eigenvalue assignment. The proposed compensator consists of an observer estimating additional outputs and a static feedback of the measurable and the estimated outputs. Since the additional outputs can be asymptotically reconstructed, the compensator can be designed using the separation principle, i.e. the closed-loop eigenvalues are given by the observer eigenvalues and the eigenvalues resulting from the static output feedback control. In order to solve the corresponding eigenvalue assignment problem, the parametric approach for the design of static output feedback controllers in finite-dimensions is extended to distributed-parameter systems. By using a parameter optimisation it is possible to assign all closed-loop eigenvalues within specified regions of the complex plane in order to stabilise the system and to assure a desired control performance. A heat conductor is used to demonstrate the proposed design procedure.     

线性定常系统的综合性最优控制问题

本文讨论了具有二次型性能指标的线性定常系统的降低性能指标灵敏度、降低轨迹灵敏 度和配置闭环极点的综合性最优控制问题,提出了新的综合性能指标,从而得到了易于计算 的结果;解决了多参数变化时降低轨迹灵敏度的综合性最优控制问题;推导了闭环特征值对 Q阵的梯度阵公式,提出了一种配置互异的全部闭环极点Q阵算法,并给出了算例.     

CACSD using the state-space L∞ theory-adesign example

The L^∞ optimal control theory is used to achieve singular value loop-shaping design objectives in a multivariable aircraft pitch-axis control design example involving an unstable nonminimum phase plant. Comparison to the frequency-weighted LQG (Linear quadratic Gaussian) design shows that the L^∞ theory easily produced a superior design having both higher bandwidth and greater stability margin, with no need for designer interaction for iterative adjustment of weights, than LQG. The design example provides a vivid illustration of how the all-pass property of the L^∞ theory enables precise shaping of closed-loop singular-value Bode plots to conform pointwise to prespecified weighting functions     

Minimum norm output feedback design under specified eigenvalue areas

Starting from a new parametric expression for the state feedback controller of a linear, time-invariant system a procedure is derived which reduces the design of output feedback controllers to an unconstrained optimization problem where all free parameters, both the closed-loop eigenvalues and the invariant parameter vectors, are used for its numerical solution by a gradient-based search technique. Thus minimal norm output feedback controllers can be designed that place the closed-loop eigenvalues within specified regions of the eigenvalue plane.     

Parametric state-feedback control with response insensitivity

A recent parametrization of the class of linear state-feedback controllers that assign a set of desired self-conjugate eigenvalues to the closed-loop system is used to formulate and solve a fundamental response insensitivity problem. It is established to what extent state-feedback control can be used to render the closed-loop system response insensitive to possibly many not necessarily small parameter variations in the open-loop state-space model. A non-conservative sequential design procedure is developed for making as many of the closed-loop system eigenmodes as possible totally insensitive while retaining arbitrary assignment of the maximum number of closed-loop eigenvalues. The main result is a class of desensitizing fixed-gain state-feedback controllers explicitly specified by a set of free parameters which may be chosen to satisfy additional design requirements.     

基于特征结构配置的二阶线性系统鲁棒容错控制设计

研究基于特征结构配置的二阶线性系统鲁棒容错控制设计问题,目的是重新设计状态反馈控制律,使得故障闭环系统和正常闭环系统具有相同的特征值.两闭环系统的特征向量依最小二乘法接近,而且能通过极小化灵敏度指标提高系统的鲁棒性.基于状态反馈特征结构配置的参数化结果,将系统灵敏度指标优化问题转化为含有约束条件的优化问题,并提出了鲁棒容错控制设计方法.数值算例及其仿真结果验证了所提出设计方法的有效性.     

Parametric output feedback control with response insensitivity

A recent parameterization of the class of linear output-feedback controllers that assign a set of desired self-conjugate eigenvalues to the closed-loop system is used to formulate and solve a fundamental response insensitivity problem. It is established to what extent output-feedback control can be used to render the closed-loop system response insensitive to possibly many not necessarily small parameter variations in the open-loop state space model. A non-conservative sequential design procedure is developed for making as many of the closed-loop system eigenmodes as possible totally insensitive while retaining arbitrary assignment of the maximum number of closed-loop eigenvalues. The main result is a class of desensitizing fixed-gain output-feedback controllers explicitly specified by a set of free parameters which may be chosen to satisfy additional design requirements. Conditions are given for total modal decoupling insensitivity to possibly many not necessarily small parameter variations in the open-loop state model. The mechanism of modal decoupling insensitivity for a given mode is interpreted in terms of the insensitivity of the corresponding left eigenmode. A parametric approach to output feedback design for modal decoupling insensitivity is discussed.     

Implicit and explicit LQG self-tuning controllers

The design of optimal controllers for use in self-tuning systems is considered. Linear Quadratic Gaussian (LQG) controllers are widely used elsewhere but have not until recently been applied in self-tuning systems, except in minimum output variance forms. The LQG controllers offer a guarantee of stability (when the plant parameters are known) which is particularly useful for nonminimum phase systems. The explicit LQG self-tuning controllers introduced in the following are relatively simple to implement. The first version of an implicit LQG self-tuning controller is also introduced. The magnitude of the transport delay terms need not be known a priori and integral action may be introduced easily. If required the desired closed-loop poles of the system can be prespecified.     

圆形区域极点及方差约束下线性离散系统的控制设计

本文考虑线性离散随机系统在圆形区域极点及方差约束睛的控制器设计问题，即设计状态反馈控制器，使闭环系统同时满足预先给定的圆形区域极点约束以及预先给定的各状态分量的方差约束。文中利用代数黎卡提方程方法解决了上述问题。     

Comments on “On the structure of digital controllers withfinite word length consideration”

In the above-mentioned paper by Li (ibid. vol.43 (1998)), a condition is presented as necessary and sufficient to give the optimal realization of state space controllers for minimal sensitivity of all closed-loop eigenvalues subject to finite word-length effects. The condition is shown here not to be sufficient. In addition, the condition for minimal sensitivity of a single closed-loop eigenvalue presented in the above-mentioned paper is not complete. The complete conditions are presented in this paper     

Model reduction of diagonally dominant systems

Model reduction methods based on open-loop considerations often fail to preserve the closed-loop interaction characteristics of the original system they represent and therefore lead to unreliable controller design. A method is presented that addresses the interaction aspects of multivariable-system model reduction and provides insight into the reasons for the failure of previous methods. The method results in models with satisfactory responses both in the open-loop configuration and in the closed-loop configuration with prespecified controller structure.