摘要:

There is given an n × n multiple-input multiple-output (MIMO) linear time-invariant plant of m cascaded sections P = PaPb... Pm, each an n × n matrix of transfer functions. The m vector outputs y, ya...,ym−1;y = Paya= PaPbyb=. = PaPbPmu =δ Pu) can be measured and the data used for feedback purposes. Each Piis known only to belong to a given set 𝒫idue to uncertainty in the plant parameters. P is embedded in a feedback structure with an n × 1 command input vector r = (r1,..., rn)’, and m free n × n loop compensation matrices to be chosen by the designer. There are assigned specifications on the n2system transfer functions fuv(s) = ŷ(s)/[rcirc]v(s), to be satisfied for all Pi; in ℬi,i = a,b,...,m. The basic problem is how to divide the feedback burden among the m available loop matrices. The technique presented in this paper is based upon two synthesis techniques previously devised for the following two problems: (1) the same as above but for single-input single-output (SISO) systems with each plant section a scalar, (2) the single-section (only one loop matrix) n × n system, with no internal plant variables available for feedback. The synthesis procedure has the following fealures: (a) conversion of the n × n MIMO cascaded m-section problem into n cascaded m-section SISO synthesis problems, the solutions of the latter being guaranteed to solve the former; (b) bandwidth propagation, wherein the loop matrices take turns dominating the design over specific frequency ranges; (c) design perspective wherein one can a priori make good estimates of the optimum division of the overall feedback burden between the loop matrices. It is shown how proper use of the internal MIMO plant variables may enormously reduce the effect of sensor noise at the plant input. Frequency response is the key tool in making quantitative synthesis possible.

ISSN:0020-7179    

DOI:10.1080/00207178508933365

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

There is given an n × n multiple-input multiple-output (MIMO) linear time-invariant plant of m cascaded sections P = PaPb... Pm, each an n × n matrix of transfer functions. The m vector outputs y, ya...,ym−1;y = Paya= PaPbyb=. = PaPbPmu =δ Pu) can be measured and the data used for feedback purposes. Each Piis known only to belong to a given set 𝒫idue to uncertainty in the plant parameters. P is embedded in a feedback structure with an n × 1 command input vector r = (r1,..., rn)’, and m free n × n loop compensation matrices to be chosen by the designer. There are assigned specifications on the n2system transfer functions fuv(s) = ŷ(s)/[rcirc]v(s), to be satisfied for all Pi; in ℬi,i = a,b,...,m. The basic problem is how to divide the feedback burden among the m available loop matrices. The paper presents a synthesis procedure, which is easier to implement, in some respects, and is much more economical in loop gains and bandwidths than the previous one. However, the relations and trade-offs between the mn individual loop transmissions are more subtle and complex. It has the following features: (a) conversion ofthe n × n MIMO cascaded m-section problem into n cascaded insertion SISO synthesis problems (the solutions ofthe latter are guaranteed to solve the former); (b) bandwidth propagation, wherein the loop matrices take turns in dominating the design over specific frequency ranges; (c) great transparency in relating the n × m available loop transmissions to the plant parameters and their uncertainties. This provides design perspective, wherein one can make good a priori estimates of the optimum division of the overall feedback burden between the loop matrices. In addition, there is good understanding ofthe trade-offs in transferring to some extent the feedback burden from one loop to another. It is shown how proper use ofthe internal MIMO plant variables may greatly reduce the effect of sensor noise at the plant input. Frequency response is the key tool in the quantitative synthesis.

ISSN:0020-7179    

DOI:10.1080/00207178508933366

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

The classical root locus and inverse Laplace transformation theories are generalised to homogeneous second-order non-linear systems and a connection with algebraic geometry is established.

ISSN:0020-7179    

DOI:10.1080/00207178508933367

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

An elementary non-linear control system with an adaptive mechanism that shows a strange attractor is analysed in this paper. The chaotic behaviour is due to a reinjection phenomenon associated with the folded characteristic of the non-linear element. Power spectra of the system confirm the existence of chaotic motion.

ISSN:0020-7179    

DOI:10.1080/00207178508933368

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

The geometry and application of K-functions is studied which provide a generalization of the Liapunov direct method in stability theory to allow the control of motion. A sufficiency theorem is proved that provides a means for quantitative design and investigation of dynamical systems.

ISSN:0020-7179    

DOI:10.1080/00207178508933369

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

For a given rational function G{z), analytic outside the closed unit disc and satisfying G(∞) = 0, a new method is proposed for the realization of G by a discrete linear system which is balanced (i.e. its controllability and observability gramians are equal and diagonal). The main numerical steps are the evaluation of a polynomial in a companion matrix, a Cholesky decomposition and a singular-value decomposition. The construction depends on properties of model operators—that is, compressions of the shift operator on the Hardy space H2.

ISSN:0020-7179    

DOI:10.1080/00207178508933370

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

Some relationships between the Lagrange multiplier method and a two-filter smoother are explored using orthogonal projection lemmas for linear discrele-time systems. The obtained expectation results are applied to algebraically derive a forward-pass fixed-interval smoothing algorithm that utilizes backward-pass information filter outputs. Furthermore, a convenient form for numerically efficient and stable algorithms is developed and the derived equation can also be used to quantitatively evaluate the effect of initial statistics on the smoothed estimate. Numerical results, pertaining to a linearized version for the in-track motion of a satellite travelling in a circular orbit, are included to illustrate the use of the given algorithms.

ISSN:0020-7179    

DOI:10.1080/00207178508933371

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

A comparative study is made of five methods for calculating the optimal control function for a linear parabolic tracking problem with boundary control. Questions of computational instability, numerical accuracy and economic computer usage are investigated. Open-loop methods based upon the variational equations are shown to have the advantages of efficiency, accuracy and ease of programming. Methods based on the method of lines and the Riccati equation are shown to be less straightforward in use. The fourth-order explicit Runge-Kutta algorithm has little scope for application because of its restricted stability range. The Kalman-Englar algorithm is much more robust but a Crank-Nicholson algorithm for the associated auxiliary equation is not very satisfactory in some cases. The auxiliary variable method may then confer some benefits.

ISSN:0020-7179    

DOI:10.1080/00207178508933372

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

New methods arc presented for evaluating the expected performance cost of partially observed closed-loop stochastic systems. When the variances of the process statistics are small, a linearized model of the closed-loop stochastic system is defined for which the expected cost can be evaluated by recursion on a set of purely deterministic difference equations. When the variances of the process statistics are large, the linearized model can be used in the control variate method of variance reduction for reducing the number of sample paths required for effective Monte Carlo estimation.

ISSN:0020-7179    

DOI:10.1080/00207178508933373

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

Consider the quadratic optimal control problems for scalar linear stochastic systems with two white coefficients. The influence of an incorrect covariance of the coefficients on the stability of the closed-loop systems is analysed by elementary methods. The set of the true covariance of the coefficients in the systems stabilized by the optimal control designed on a nominal covariance is obtained. It is shown that this set is classified into several patterns according to the parameters of the systems and the weighting coefficient in the performance index and that the particular control gains stabilize the systems with large uncertainty.

ISSN:0020-7179    

DOI:10.1080/00207178508933374

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor