... Notions ofSystemsand Signals Signals andsystems are basic notions ofsystemsandcontrol theory Therefore, we briefly summarize the most important concepts of the mathematical description of signals ... Concepts and Designs K.F Man, K.S Tang and S Kwong Neural Networks for Modelling andControlof Dynamic Systems M Nørgaard, O Ravn, N.K Poulsen and L.K Hansen Modelling andControlof Robot Manipulators ... and Director Professor Michael A Johnson, Professor ofControlSystemsand Deputy Director Industrial Control Centre, Department of Electronic and Electrical Engineering, University of Strathclyde,...
... Cataloging-in-Publication Data [Analyse des systèmes linéaires/Commande des systèmes linéaires eng] Analysisandcontrolof linear systemsanalysisandcontrolof linear systems/ edited by Philippe de Larminat p cm ... Observability of linear and invariant systems 2.5.3 Case of partially observable systems 2.5.4 Case of partially controllable and partially observable systems 2.6 ... 370 370 xii AnalysisandControlof Linear Systems Chapter 12 Predictive Control Patrick BOUCHER and Didier DUMUR 12.1 General principles of predictive control ...
... at 5%) and ω t m according to the damping ξ Figure 1.21 ω0 tr and ω0 tm according to the damping ξ 30 AnalysisandControlof Linear Systems The alternation of slow and fast variations of product ... final value of the response at the end of time T, which is called time constant of the system The response reaches 0.63 K in T and 0.95 K in T 24 AnalysisandControlof Linear Systems Figure ... 2π jf0 20 AnalysisandControlof Linear Systems Table 1.1 sums up the features of a system’s transfer function, the existence conditions of its frequency response and the possibility of performing...
... 84 AnalysisandControlof Linear Systems 3.2.2 Delay and lead operators The concept of an operator is interesting because it enables a compact formulation of the description of signals andsystems ... parts The analysisand manipulation of signals and discrete-time systems are presented in sections 3.2 and 3.3 The discretization of continuous-time systemsand certain concepts of the sampling ... development of X (z) by polynomial division according to 86 AnalysisandControlof Linear Systems the decreasing powers of z −1 or apply the method of deviations, starting from the definition of the...
... 110 AnalysisandControlof Linear Systems The object of this chapter is to describe certain structural properties of linear systems that condition the resolution of numerous control problems ... illustrates the invariance properties of the various structures of these canonical forms (indices of controllability, of observability, finite and infinite zeros) andof the associated transformation ... BF )T, B ' = T−1BG 122 AnalysisandControlof Linear Systems ⎡ T 0⎤ (To be sure, it is sufficient to note that P=T-1 and Q = ⎢ ⎥ ) ⎣FT G ⎦ Kronecker’s canonical form of a controllability beam...
... [5.9] 144 AnalysisandControlof Linear Systems On the other hand, the Fourier transform preserves the energy (Parseval theorem) Indeed, the energyof a continuous-time signal y(t) or of a discrete-time ... proximity of ν0 152 AnalysisandControlof Linear Systems Figure 5.1 Typical power spectrum of an MA (left) or AR (right) model In the case of a single denominator (nc = 0), we talk of an AR ... 142 AnalysisandControlof Linear Systems A discrete-time deterministic signal y[k], k ∈ Z is, by definition, a sequence of complex numbers: y = y[k] k∈Z In short, we often speak of a discrete...
... case of multi -control systems at the expense of additional developments (see [DOR 95, FRI 86]) 188 AnalysisandControlof Linear Systems Figure 6.10 Control by the observer, compared to control ... stronger control, whereas the increase of ξ leads to better dynamics 164 AnalysisandControlof Linear Systems Figure 6.2 Stabilization by pole placement 6.3 Reconstruction of state and observers ... system is controllable In this part, we will assume that the system has only one control; however, the result cannot be extended to the 162 AnalysisandControlof Linear Systems case of multi-control...
... 196 AnalysisandControlof Linear Systems in performing the roles of the procedure, in connection with a structure and behavior of components They are used for the design of procedure ... determining the value of x = τ2 /τ1 Calculating the numeric values of τ1 and τ2 with: τ1 = τsum 1+x τ2 = x τsum 1+x 1+x Inferring [7.46] 210 AnalysisandControlof Linear Systems Similar method ... 214 AnalysisandControlof Linear Systems recording of a specific response We need to be aware of the fact that it is essential to have a little, even very little, noise on the responses and, ...
... the relation: Φ Γ A B h [8.7] = exp I 0 230 AnalysisandControlof Linear Systems The sizes of blocks and I are such that the partitioned matrices are of size (m + n) × ◦ (m + n) This result is ... recurrence and n thus evolve as zi , where zi is a root of the polynomial: r p(z) = i=0 αi z r−i + µ r i=0 βi z r−i [8.42] 242 AnalysisandControlof Linear Systems Consequently, the field of absolute ... unknown factor does not enable us to 232 AnalysisandControlof Linear Systems directly apply the results of the previous section From a theoretical point of view, we can, however, return by transforming...
... in CL and (b) frequency response in CL 258 AnalysisandControlof Linear Systems When the system has good damping, let ξ be the value of the damping coefficient delimited between 0.4 and 0.7, ... equation of n order The roots of this equation are of strictly negative real part if and only if the terms of this first column of the table have the same sign and are not zero Statement of Routh’s ... time constants of physical Analysis by Classic Scalar Approach 271 systems, on the one hand and to the interferences acting on the system on the other hand The quality of the feedback control is...
... 296 AnalysisandControlof Linear Systems Figure 10.12 Bode graph with insufficient phase margin Figure 10.13 Bode graph in OL of the corrected system Synthesis of Closed Loop ControlSystems ... Points A and B are thus the separations of cases and Synthesis of Closed Loop ControlSystems Between A and B: µ1 µ µ β > and B: µ1 µ µ β < µ1 µ β C µ1 µ β C 317 , i.e µ C > (1st case) and outside ... 284 AnalysisandControlof Linear Systems 10.1.1 Analysisofsystems behavior 10.1.1.1 Static errors For a zero static error: –...
... and R and thus5: number of unknown factors = ∂S + ∂R + A polynomial of degree n has n + coefficients [11.36a] 338 AnalysisandControlof Linear Systems The number of equations is the number of ... neglected in the model 366 AnalysisandControlof Linear Systems Figure 11.17 Evolution of sA Ao (⎯ο⎯) .of sAS ' Ao Am ⎛ ⎞ ⎟ Ao = ⎜ s + ⎜ To ⎟ ⎝ ⎠ andof B Am (⎯⎯) in the case of From these answers ... corrector as a system having two inputs c(t) and y(t) and one output u(t) and thus it 346 AnalysisandControlof Linear Systems is enough to write an equation of state verified by this system The following...
... the number of estimated values of the sequence 376 AnalysisandControlof Linear Systems 12.2 Generalized predictive control (GPC) 12.2.1 Formulation of the control law The objective of this section ... ideas of the method, starting with the form of the model, the quadratic criterion and up to the examination of adjustment parameters The formalism and the 390 AnalysisandControlof Linear Systems ... 378 AnalysisandControlof Linear Systems 12.2.1.4 Synthesis of the equivalent polynomial RST regulator The minimization of the criterion is based on writing the prediction equation [12.5] and...
... response g(⋅) = TL−1 (⋅) u G(s) y Standard whose physical importance in terms ofenergy is obvious 404 AnalysisandControlof Linear Systems The “H2 standard” of the input-output operator associated ... closed loop control can be formulated in the standard form of Figure 13.1 408 AnalysisandControlof Linear Systems Figure 13.1 Standard feedback diagram The quadripole G , also called a standard ... by y is solution of Let us give the idea of the equivalence proof of properties and 2., the equivalence of properties and resulting by duality Methodology of the State Approach Control 421 We...
... 14.5 Area of the complex plane corresponding to the desired performances and to the constraints on the bandwidth 460 AnalysisandControlof Linear Systems 14.4.2 Choice of eigenvectors of the closed ... mode ξi (t) does not have any effect on z k 452 AnalysisandControlof Linear Systems 14.2.2.7 Summarization The analysisof the time behavior of a controlled system was done in the modal basis ... Shift of a set of poles with minimum dispersion 464 AnalysisandControlof Linear Systems EXAMPLE 14.4 To illustrate these points, let us take a set of models pertaining to the lateral side of...
... 512 AnalysisandControlof Linear Systems where N R and N S form a base of cores of ( Bu T Deu T ) and (C y Dyw ) respectively Inequalities [15.70], calculated on inequalities [15.20.a, b, c] of ... [15.48] 500 AnalysisandControlof Linear Systems a) Robustness of stability b) Robustness of performance Figure 15.10 Upper bounds of the structured single value 15.2.4 Evaluation of structured ... diagram of the closed loop control system in the form given in Figure 15.9 (always with 498 AnalysisandControlof Linear Systems K ( s ) = ) We easily identify the matrices ∆ (s ) and H (s ) of...
... λ + t and H (λ ) = λ−1 so ∑ y(t ) = u(t ) 1 530 AnalysisandControlof linear Systems 16.4.2 Parallel systems Let ∑1 and ∑ be two systemsof transfer functions H1 (λ) = Q1 (λ )−1 P (λ) and H ... Time-Variant Systems 531 16.5 Applications In this section, two types of usage of this algebra are presented in the field of modeling andcontrol 16.5.1 Modeling One of the methods of signal andcontrol ... 522 AnalysisandControlof linear Systems both the controland identification fields indispensable Firstly, it is important to have the basic mathematical tools indispensable to their analysis...
... number of degrees of freedom of a system Three possibilities arise in the analysisof the motion -of- mass systems First, the system may consist of a small number of masses and hence its number of ... kinetic energyof a system is equal to the kinetic energyof the center of mass plus the kinetic energyof the motion relative to the center of mass 1.3.3 Angular Momentum of a System (Moment of Momentum) ... LAWS OF DYNAMICS 1.3 1.3 THE DYNAMICS OF A SYSTEM OF MASSES 1.5 1.3.1 The Motion of the Center of Mass 1.6 1.3.2 The Kinetic Energyof a System 1.7 1.3.3 Angular Momentum of a System (Moment of...
... 4.2 Conservation ofEnergyand the First Law of Thermodynamics 4.3 Nonconservation of Entropy and the Second Law of Thermodynamics 4.4 Semistability and Large-Scale Systems 4.5 Energy Equipartition ... behaviors of the individual subsystems and their interconnections The need for decentralized analysisandcontrol design of large-scale systems is a direct consequence of the physical size and complexity ... aerospace systems, power systems, communications systems, network systems, transportation systems, large-scale manufacturing systems, integrative biological systems, economic systems, ecological systems, ...
... spectral analysisof climate dynamics 325 D Maraun, J Kurths and M , Holschneider 13 Synchronization of complex systems: Analysisandcontrol 347 M.Rosenblum and A Pikovsky 14 Critical states of seismicity ... - the understanding of chaos synchronization andof stochastic synchro- nizat ion, - the manifold role and the many applications of delayed feedback in chaos control, the evidence of synchronization ... structures in dynamical systems far from equilibrium Their analysisand possible control are intriguing and challenging aspects of the current research The duality of fundamental and applied research...