Brogan, W.L., Lee, G.K. F, Sage, A.P., Kuo, B.C., Phillips, C L, Harbor, R D, Jacquot, R.G., McInroy, J.E., Atherton, D P, Bay, J.S., Baumann, W.T., Chow, M-Y."Control Systems The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton CRC Press llc. 2000
Brogan, W.L., Lee, G.K.F., Sage, A.P., Kuo, B.C., Phillips, C.L., Harbor, R.D., Jacquot, R.G., McInroy, J.E., Atherton, D.P., Bay, J.S., Baumann, W.T., Chow, M-Y. “Control Systems” The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000
100 Control Systems 100.1 Models University of Nevada, Las vegas Classes of Systems to Be Modeled. Two Major Approaches to Gordon K e lee Modeling. Forms of the Model. Nonuniqueness Approximation of Continuous Systems by Discrete Models 100.2 Dynamic Response Andrew P. Sage Computing the Dynamic System Response. Measures of the George Mason University Dynamic System Response 100.3 Frequency Response Methods: Bode Diagram Approach enjamin C. Kuo Frequency Response Analysis Using the Bode Diagram. Bode iversity of Illinois (Urbana Diagram Design-Series Equalizers. Composite Equalizers Charles L. Phillips 100.4 Root locus Auburn University Root Locus Properties. Root Loci of Digital Control Systems Design with Root Locus Royce D. Harbor nsation University of West Florida Control System Specifications. Design. Modern Control Raymond G. Jacquot Design. Other Modern Design Procedures 100.6 Digital Control Systems A Simple Example . Single-Loop Linear Control Laws John E. McInroy Proportional Control. PID Control Algorithm. The Closed Loop System. A Linear Control Example 100.7 Nonlinear Control System Derek P Atherton The Describing Function Method. The Sinusoidal Describing Function. Evaluation of the Describing FI Limit Cycles and Stability. Stability and Accuracy. Compensator John S Bay Design.Closed-Loop Frequency Response. The Phase Pla Virginia Polytechnic Institute and Method. Piecewise Linear Characteristics Discussion State University 100.8 Optimal Control and Estimation William. Baumann Linear Quadratic Optimal Estimation: The Kalman Virginia Polytechnic Institute and Filter. Linear-Quadratic-Gaussian(LQG)Control. H- Control· Example· Other Approaches 100.9 Neural Control Mo- Yuen Chow Brief Introduction to Artificial Neural Networks. Neural North Carolina State University Observer· Neural control· HVAC Ilustration· Conclusion 100.1 Models William L. Brogan A naive trial-and-error approach to the design of a control system might consist of constructing a controller, installing it into the system to be controlled, performing tests, and then modifying the controller until satisfactory performance is achieved. This approach could be dangerous and uneconomical, if not impossible. A more rational approach to control system design uses mathematical models. A model is a mathematical description of system havior, as influenced by input variables or initial conditions. The model is a stand-in for the actual system during the control system design stage. It is used to predict performance; to carry out stability, sensitivity, and trade-off c 2000 by CRC Press LLC
© 2000 by CRC Press LLC 100 Control Systems 100.1 Models Classes of Systems to Be Modeled • Two Major Approaches to Modeling • Forms of the Model • Nonuniqueness • Approximation of Continuous Systems by Discrete Models 100.2 Dynamic Response Computing the Dynamic System Response • Measures of the Dynamic System Response 100.3 Frequency Response Methods: Bode Diagram Approach Frequency Response Analysis Using the Bode Diagram • Bode Diagram Design-Series Equalizers • Composite Equalizers • Minor-Loop Design 100.4 Root Locus Root Locus Properties • Root Loci of Digital Control Systems • Design with Root Locus 100.5 Compensation Control System Specifications • Design • Modern Control Design • Other Modern Design Procedures 100.6 Digital Control Systems A Simple Example • Single-Loop Linear Control Laws • Proportional Control • PID Control Algorithm • The ClosedLoop System • A Linear Control Example 100.7 Nonlinear Control Systems The Describing Function Method • The Sinusoidal Describing Function • Evaluation of the Describing Function • Limit Cycles and Stability • Stability and Accuracy • Compensator Design • Closed-Loop Frequency Response • The Phase Plane Method • Piecewise Linear Characteristics • Discussion 100.8 Optimal Control and Estimation Linear Quadratic Regulators • Optimal Estimation: The Kalman Filter • Linear-Quadratic-Gaussian (LQG) Control • H∞ Control • Example • Other Approaches 100.9 Neural Control Brief Introduction to Artificial Neural Networks • Neural Observer • Neural Control • HVAC Illustration • Conclusion 100.1 Models William L. Brogan A naive trial-and-error approach to the design of a control system might consist of constructing a controller, installing it into the system to be controlled, performing tests, and then modifying the controller until satisfactory performance is achieved. This approach could be dangerous and uneconomical, if not impossible. A more rational approach to control system design uses mathematical models. A model is a mathematical description of system behavior, as influenced by input variables or initial conditions. The model is a stand-in for the actual system during the control system design stage. It is used to predict performance; to carry out stability, sensitivity, and trade-off William L. Brogan University of Nevada, Las Vegas Gordon K. F. Lee North Carolina State University Andrew P. Sage George Mason University Benjamin C. Kuo University of Illinois (UrbanaChampaign) Charles L. Phillips Auburn University Royce D. Harbor University of West Florida Raymond G. Jacquot University of Wyoming John E. McInroy University of Wyoming Derek P. Atherton University of Sussex John S. Bay Virginia Polytechnic Institute and State University William T. Baumann Virginia Polytechnic Institute and State University Mo-Yuen Chow North Carolina State University
CONTROL MECHANISM FOR ROCKET APPARATUS Robert h. goddard Patented April 2, 1946 #2,397,657 A excerpt from Robert Goddard's patent application: This invention relates to rockets and rocket craft which are propelled by combustion apparatus using liquid fuel and a liquid to support combustion, such as liquid oxygen. Such combustion apparatus is disclosed in my prior application Serial No 327, 257 filed April 1, 1940 It is the general object of my present invention to provide control mechanism by which the necessary operative steps and adjustments for such mechanism will be affected automatically and in predetermined and orderly To the attainment of this object, I provide control mechanism which will automatically discontinue flight in a safe and orderly manner. Dr. Goddard was instrumental in developing rocket propulsion in this country, both solid-fuel rocket engines and later liquid-fuel rocket motors used in missile and spaceflight applications. Goddard died in 1945, before this pivotal patent(filed June 23, 1941)on automatic control of liquid-fuel rockets was granted. He assigned half the rights to the Guggenheim Foundation in New York.( Copyright o 1995, Dewray Products, Inc. Used with permission. c 2000 by CRC Press LLC
© 2000 by CRC Press LLC CONTROL MECHANISM FOR ROCKET APPARATUS Robert H. Goddard Patented April 2, 1946 #2,397,657 An excerpt from Robert Goddard’s patent application: This invention relates to rockets and rocket craft which are propelled by combustion apparatus using liquid fuel and a liquid to support combustion, such as liquid oxygen. Such combustion apparatus is disclosed in my prior application Serial No. 327,257 filed April 1, 1940. It is the general object of my present invention to provide control mechanism by which the necessary operative steps and adjustments for such mechanism will be affected automatically and in predetermined and orderly sequence. To the attainment of this object, I provide control mechanism which will automatically discontinue flight in a safe and orderly manner. Dr. Goddard was instrumental in developing rocket propulsion in this country, both solid-fuel rocket engines and later liquid-fuel rocket motors used in missile and spaceflight applications. Goddard died in 1945, before this pivotal patent (filed June 23, 1941) on automatic control of liquid-fuel rockets was granted. He assigned half the rights to the Guggenheim Foundation in New York. (Copyright © 1995, Dewray Products, Inc. Used with permission.)
arameter Stochastic Deterministic Discrete Nonlinear Linear arying coefficient FIGURE 100.1 Major classes of system equations. Source: W.L. Brogan, Modern Control Theory 3rd ed, Englewood Cliffs, N J. Prentice-Hall, 1991, P. 13. With permission.) studies; and answer various"what-if" questions in a safe and efficient manner. Of course, the validation of the model, and all conclusions derived from it, must ultimately be based upon test results with the physical hardwar The final form of the mathematical model depends upon the type of physical system, the method used to develop the model, and mathematical manipulations applied to it. These issues are discussed next Classes of Systems to Be Modeled Most control problems are multidisciplinary. The system may consist of electrical, mechanical, thermal, optical, fluidic, or other physical components, as well as economic, biological, or ecological systems. Analogies exist between these various disciplines, based upon the similarity of the equations that describe the phenomena. The discussion of models in this section will be given in mathematical terms and therefore will apply to several disciplines. Figure 100.1 [Brogan, 1991] shows the classes of systems that might be encountered in control systems modeling. Several branches of this tree diagram are terminated with a dashed line indicating that additional branches have been omitted, similar to those at the same level on other paths. Distributed parameter systems have variables that are functions of both space and time(such as the voltage along a transmission line or the deflection of a point on an elastic structure). They are described by partial differential equations. These are often approximately modeled as a set of lumped parameter systems(described by ordinary differential or difference equations) by using modal expansions, finite element methods, or other appro mations [Brogan, 1968]. The lumped parameter continuous-time and discrete-time families are stressed here. Two Major Approaches to Modeling In principle, models of a given physical system can be developed by two distinct approaches. Figure 100.2 shows the steps involved in analytical modeling. The real-world system is represented by an interconnection of idealized elements. Table 100.1[Dorf, 1989] shows model elements from several disciplines and their elemental equations. An electrical circuit diagram is a typical result of this physical modeling step(box 3 of Fig. 100.2). Application of the appropriate physical laws(Kirchhoff, Newton, etc. )to the idealized physical model (consisting of point masses,ideal springs, lumped resistors, etc. leads to a set of mathematical equations. For a circuit these will c 2000 by CRC Press LLC
© 2000 by CRC Press LLC studies; and answer various “what-if” questions in a safe and efficient manner. Of course, the validation of the model, and all conclusions derived from it, must ultimately be based upon test results with the physical hardware. The final form of the mathematical model depends upon the type of physical system, the method used to develop the model, and mathematical manipulations applied to it. These issues are discussed next. Classes of Systems to Be Modeled Most control problems are multidisciplinary. The system may consist of electrical, mechanical, thermal, optical, fluidic, or other physical components, as well as economic, biological, or ecological systems. Analogies exist between these various disciplines, based upon the similarity of the equations that describe the phenomena. The discussion of models in this section will be given in mathematical terms and therefore will apply to several disciplines. Figure 100.1 [Brogan, 1991] shows the classes of systems that might be encountered in control systems modeling. Several branches of this tree diagram are terminated with a dashed line indicating that additional branches have been omitted, similar to those at the same level on other paths. Distributed parameter systems have variables that are functions of both space and time (such as the voltage along a transmission line or the deflection of a point on an elastic structure). They are described by partial differential equations. These are often approximately modeled as a set of lumped parameter systems (described by ordinary differential or difference equations) by using modal expansions, finite element methods, or other approximations [Brogan, 1968]. The lumped parameter continuous-time and discrete-time families are stressed here. Two Major Approaches to Modeling In principle, models of a given physical system can be developed by two distinct approaches. Figure 100.2 shows the steps involved in analytical modeling. The real-world system is represented by an interconnection of idealized elements. Table 100.1 [Dorf, 1989] shows model elements from several disciplines and their elemental equations. An electrical circuit diagram is a typical result of this physical modeling step (box 3 of Fig. 100.2). Application of the appropriate physical laws (Kirchhoff, Newton, etc.) to the idealized physical model (consisting of point masses, ideal springs, lumped resistors, etc.) leads to a set of mathematical equations. For a circuit these will FIGURE 100.1 Major classes of system equations. (Source: W.L. Brogan, Modern Control Theory, 3rd ed., Englewood Cliffs, N.J.: Prentice-Hall, 1991, p. 13. With permission.)
model Define boundaries 如 of interest model element tinuity and quations Modify model Final form of if necessary mathematical model Analy with real world Steps in modeling URE 100.2 Modeling considerations. Source: W.L. Brogan, Modern Control Theory, 3rd ed, Englewood Cliffs, NJ Prentice-Hall, 1991, P. 5. With permission. be mesh or node equations in terms of elemental currents and voltages. Box 6 of Fig. 100.2 suggests a generalization to other disciplines, in terms of continuity and compatibility laws, using through variables (generalization of current that flows through an element)and across variables(generalization of voltage, which has a differential value across an element)[Shearer et al., 1967; Dorf, 1989] Experimental or empirical modeling typically assumes an a priori form for the model equations and then uses available measurements to estimate the coefficient values that cause the assumed form to best fit the data The assumed form could be based upon physical knowledge or it could be just a credible assumption. Time- (MA)models, and the combination, called ARMA models. All are difference equations relating the input variables to the output variables at the discrete measurement times. of the form y(k+1)=aoy(k)+a1y(k-1)+a2y(k-2) +b(k+1)+b(k)+…+b(k+1-p)+v(k) where wk)is a random noise term. The z-transform transfer function relating u to y is c 2000 by CRC Press LLC
© 2000 by CRC Press LLC be mesh or node equations in terms of elemental currents and voltages. Box 6 of Fig. 100.2 suggests a generalization to other disciplines, in terms of continuity and compatibility laws, using through variables (generalization of current that flows through an element) and across variables (generalization of voltage, which has a differential value across an element) [Shearer et al., 1967; Dorf, 1989]. Experimental or empirical modeling typically assumes an a priori form for the model equations and then uses available measurements to estimate the coefficient values that cause the assumed form to best fit the data. The assumed form could be based upon physical knowledge or it could be just a credible assumption. Timeseries models include autoregressive (AR) models, moving average (MA) models, and the combination, called ARMA models. All are difference equations relating the input variables to the output variables at the discrete measurement times, of the form y(k + 1) = a0y(k) + a1y(k – 1) + a2y(k – 2) + … + any(k – n) + b0u(k + 1) + b1u(k) + … + bpu(k + 1 – p) + v(k) (100.1) where v(k) is a random noise term. The z-transform transfer function relating u to y is (100.2) FIGURE 100.2 Modeling considerations. (Source: W.L. Brogan, Modern Control Theory, 3rd ed., Englewood Cliffs, N.J.: Prentice-Hall, 1991, p. 5. With permission.) y z u z b bz b z az a z H z p p n n ( ) ( ) ( ) ( ) – – – – = + ++ − ++ = − 0 1 1 0 1 1 1 L L