Digital flight control design for a tandem-rotor helicopter

Methods and results in the continuing development of a digital flight control system (DFCS) for a CH-47B helicopter are presented. The helicopter is the research vehicle for the NASA VTOL Approach and Landing Technology (VALT) Program, and it equipped with comprehensive equipment for the investigation of navigation, guidance, and control requirements for future VTOL aircraft. Two control modes (attitude-command and velocity-command) are implemented, and each mode provides ‘Type 1’ response to guidance commands. DFCS design is based upon optimal estimation and control methods, which are found to provide flexible and efficient means for defining practical digital control systems.     

Discrete-time optimal control of systems with unilateral time-delays

Industrial plants which contain unilateral flow of material are considered. First, it is shown that such plants can be represented by finite-dimensional difference equations after sampling. Then, the design of discrete-time optimal control systems is studied based on the difference equations. The main difficulty in this design problem is the high dimensionality resulting from the discretization of long delays. In this paper, a new algorithm to solve the discrete Riccati equation for this class of systems is proposed. An example is given to illustrate how the computational difficulties are effectively reduced.     

Multistage linear programming for discrete optimal control with distributed-lags

A multistage decomposition scheme is developed for optimizing discrete-time dynamic systems, which include distributed and/or multiple pure delays. The discrete optimal control problem in this paper consists of a system dynamics described by a multidimensional linear difference equation of high-order which is called the distributed-lag model, a linear objective function, and linear state and control constraints. This problem may be solved as a linear program by, for example, a revised simplex method. However, this leads to excessive storage requirement for large problems. Instead, by taking advantage of the staircase-structure of equality constraints (system equation), Dantzig-Wolfe decomposition principle is applied repeatedly in each stage, and an effective multistage decomposition algorithm for distributed-lag models is obtained. Significant advantage of the optimization technique in this paper is that it can handle any number of delay terms in the system without reducing the multidimensional high-order system equation to a conventional larger dimensional first-order system equation (state equation of normal form). Therefore, a substantial reduction of computational burden, the so called curse of dimensionality, in the existing discrete optimal control algorithms, is obtained. A numerical example of a congested urban road traffic control problem with many delays is included.     

Insensitive observers for discrete time linear systems

This paper considers the problem of designing an observer insensitive to system parameter variations in discrete time linear multivariable systems. A K-insensitive observer is defined as an observer that can reconstruct a linear function of the state vector in spite of the variations of system parameters, provided the initial state of the observer is suitably chosen. A deadbeat observer is defined to be an observer that reconstructs the linear function for an arbitrary initial condition of the observer. Then, the existence of the K-insensitive observer is examined, and the class of K-insensitive observers is characterized. A necessary and sufficient condition is derived under which the K-insensitive deadbeat observer can be designed, and a simple algorithm is proposed to design the observer. The resulting observer is shown to be stable. The order of the observer is evaluated. The condition for generic solvability of the problem is also given.     

Continuous-discrete gain transformation methods for linear feedback control

The problem of transforming between continuoustime state variable feedback gains and equivalent discrete gains suitable for digital implementation is considered. The concepts of state and control equivalence yield two simple transformation rules, a pseudo-inverse method and an average gain method, respectively. As the sampling interval δ→0, these methods are contrasted with existing Taylor series based approaches. The new transformation rules are also studied numerically using a ship course-keeping example. Transformed optimal continuous gains are compared with optimal discrete gains over a wide range of sampling intervals.     

A subspace algorithm for the identification of discrete time frequency domain power spectra

In this paper we present a new subspace algorithm for the identification of multi-input multi-output linear discrete time systems from measured power spectrum data. We show how the state space system matrices can be determined by taking the inverse discrete Fourier transform of the given data and applying the result to a new realization algorithm. Special attention is paid to ensure the positive realness of the identified power spectrum. The computational speed is improved by applying a Lanczos algorithm. The algorithm is illustrated with two practical examples.     

Time/fuel optimal control of constrained linear discrete systems

A unified approach to solving three common optimal control problems is presented, for linear systems under general constraints. The problems are: (1) the time optimal control problem; (2) the fuel optimal control problem in fixed time; (3) the time optimal control problem with a fuel constraint. A special purpose linear programming algorithm is used. State variable constraints are efficiently handled by a cutting plane algorithm. An example of a sixth order system with two inputs and two state variable constraints illustrates the method as implemented on a personal computer.     

Integrated fault detection system design for linear discrete time‐varying systems with bounded power disturbances

This paper investigates the problem of an integrated fault detection system design for linear discrete time‐varying systems with bounded power disturbances. In the integrated design of residual generator and evaluator, an approximated energy constraint is first imposed on the bounded power disturbances, and then selected by solving a min–max problem to achieve minimal‐size set of undetectable faults under the condition of zero false alarms. To tackle the problem that the computational burden involved in solving the min–max optimization grows with time, the moving horizon method is proposed. The proposed approach in this paper has two advantages: (i) the approximated energy constraint on bounded power disturbances is explicitly selected as a min–max solution in the integrated design to improve fault detection rate; by contrast, when directly applying any existing fault detection method to the case of bounded power disturbances, a predefined approximated energy constraint is implicitly introduced without considering fault detection performance; (ii) the design objective of the proposed approach can choose to consider faults only in the recent time horizon rather than faults in the complete time horizon; this strategy enhances detection performance of recent faults and benefits early fault detection, but has not been considered by existing fault detection methods. Copyright © 2012 John Wiley & Sons, Ltd.     

Study of the discrete singularly perturbed linear-quadratic control problem by a bilinear transformation

This paper presents a new approach in the study of the linear quadratic control problem of singularly perturbed discrete systems. By applying a bilinear transformation, the algebraic discrete Riccati equation is converted into a continuous one, which can be solved by using the reduced-order recursive method already documented in the control literature. This method produces the reduced-order near-optimal solution up to an arbitrary order of accuracy and reduces the size of required computations. The method is very suitable for parallel programming. A real world example, an F-8 aircraft, demonstrates the efficiency of the proposed method.     

Recursive estimation of the parameters of linear multivariable systems

A recursive algorithm is proposed for the identification of linear multivariable systems. Utilization of a canonical state space model minimizes the number of parameters to be estimated. The problem of identification in the presence of noise is solved by using a recursive generalized least-squares method.     

受扰线性离散系统的前馈2反馈最优控制

研究具有已知动态特性但未知初始条件的持续外界扰动的线性离散系统最优控制问题。给出了前馈一反馈最优控制律的存在唯一性条件，并提出了最优控制律的设计算法．通过降维扰动观测器解决了前馈一反馈最优控制律的物理不可实现问题．对近海结构物振动控制的实例仿真表明，该设计算法易于实现，在抑制外部持续扰动和鲁棒性方面优于经典的状态反馈最优控制。     

A self-tuning regulator based on optimal output feedback theory

Self-tuning control of stochastic systems is considered. The underlying control problem is a parametric linear quadratic problem for fixed structure controllers. An explicit self-tuning regulator is described based on optimal output feedback theory. The proposed self-tuner is a generalization of state-space LQG self-tuners to parametric LQ problems. Two interesting application areas of parametric LQ self-tuners are autotuning of parameters of low-order regulators, such as PID-regulators, and adaptive decentralized control.     

Frequency domain analysis and robust control design for an ideal flexible beam

We study the problem of designing a feedback controller for a highly flexible Euler-Bernoulli beam using a distributed-parameter H^∞-method. Employing skew Toeplitz theory, we derive the H^∞-optimal controller for a weighted mixed sensitivity design for the beam. Based on the structure of the optimal controller we obtain suboptimal, finite-dimensional, linear, time-invariant controllers. With this approach we are able to include the added difficulties of a pure time delay and a noncollocated actuator/sensor pair directly into the design process.     

Quadraticity and neutrality in discrete time stochastic linear quadratic control

A general discrete-time stochastic linear model with a quadratic objective function is analyzed with regard to its neutrality and a rarely-discussed property called quadraticity. Such a problem having quadraticity is relatively easily solved, and most variations of the linear quadratic control problem for which exact solutions are known possess this property. A generally less tractable set of problems is that consisting of nonneutral models, those in which it is possible to learn about system unknowns through experimentation. It is shown that quadraticity and neutrality apparently neither imply nor preclude one another within the class of linear quadratic models.     

Mixed Constrained Infinite Horizon Linear Quadratic Optimal Control

For a given initial state, a constrained infinite horizon linear quadratic optimal control problem can be reduced to a finite dimensional problem [12]. To find a conservative estimate of the size of the reduced problem, the existing algorithms require the on‐line solutions of quadratic programs [10] or a linear program [2]. In this paper, we first show based on the Lyapunov theorem that the closed‐loop system with a mixed constrained infinite horizon linear quadratic optimal control is exponentially stable on proper sets. Then the exponentially converging envelop of the closed‐loop trajectory that can be computed off‐line is employed to obtain a finite dimensional quadratic program equivalent to the mixed constrained infinite horizon linear quadratic optimal control problem without any on‐line optimization. The example considered in [2] showed that the proposed algorithm identifies less conservative size estimate of the reduced problem with much less computation.     

Optimal discrete higher‐order sliding mode control of uncertain LTI systems with partial state information

The concept of discrete higher‐order sliding mode has received increased attention in the recent literature. This paper presents an optimal discrete higher‐order sliding mode control for an uncertain discrete LTI system using partial state information, which has been missing in literature. A new technique is proposed to design an optimal time‐varying higher‐order sliding surface and control input through the minimization of a quadratic performance index. Moreover, disturbance estimation technique is utilized to modify the control algorithm to reduce the width of the discrete higher‐order sliding mode band. The proposed algorithm is experimentally validated on a rectilinear plant. Copyright © 2017 John Wiley & Sons, Ltd.     

Zeros of sampled systems

The zeros of the discrete-time system obtained when sampling a continuous time system are explored. Theorems for the limiting zeros for large and small sampling periods are given. Conditions which guarantee that the sampled system has stable zeros are also presented.     

On the discrete and continuous time infinite-dimensional algebraic Riccati equations

The standard state space solution of the finite-dimensional continuous time quadratic cost minimization problem has a straightforward extension to infinite-dimensional problems with bounded or moderately unbounded control and observation operators. However, if these operators are allowed to be sufficiently unbounded, then a strange change takes place in one of the coefficients of the algebraic Riccati equation, and the continuous time Riccati equation begins to resemble the discrete time Riccati equation. To explain why this phenomenon must occur we discuss a particular hyperbolic PDE in one space dimension with boundary control and observation (a transmission line) that can be formulated both as a discrete time system and as a continuous time system, and show that in this example the continuous time Riccati equation can be recovered from the discrete time Riccati equation. A particular feature of this example is that the Riccati operator does not map the domain of the generator into the domain of the adjoint generator, as it does in the standard case.     

组合计算模型实现系统设计与仿真*

在模块化的系统设计中,适合各个模块的最佳计算模型往往不尽相同,这些计算模型包括有穷状态自动机、Petri网、离散事件和事件关系图等.为了方便设计者和提高工作效率,有必要允许对模块采用不同的计算模型,再运用组合计算模型的理论将这些模块组合成完整的模型以用于仿真和系统的自动生成.作为应用实例,通过分层组合离散事件和事件关系图,可以设计易于扩展、修改和维护的动态系统;同样的原理也可以应用于其他计算模型,从而使它们在模块化设计中发挥各自的优点.     

反馈控制系统Delta算子理论的研究与发展

反馈控制系统的Ｄｅｌｔａ算子理论在高速信号处理与数字采控制领域具有重要作用，本文对Ｄｅｌｔａ算子方法的研究现状存在问题进行综述，内溶涉及Ｄｅｌｔａ算子模型描述与转换、系统辨识与状态估计，自适应控制与预测控制等方面，并探讨了将来的发展方向。