Early control textbooks in Sweden

The computer program LCAP2 (Linear Controls Analysis Program) provides the analyst with the capability to numerically perform classical linear control analysis techniques such as transfer function manipulation, transfer function evaluation, frequency response, root locus, time response and sampled-data transforms. It is able to deal with continuous and sampled-data systems, including multiloop multirate digital systems, using <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s, z</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">w</tex> transforms. This program has been used extensively for years at the Aerospace Corporation in the analysis and design of satellite and launch vehicle control systems.

This paper describes a package of digital computer subprograms which provides control systems engineers at Autonetics with an easy-to-use, comprehensive, and flexible design-aid tool The subprograms are written in FORTRAN IV for the IBM 7094. Most of the subprograms are similar to ones found in almost every company's program files. They provide such standard capabilities as the generation of Bode plots, Root Locus plots, Nyquist plots, Nichols charts, and time and frequency response. The package contains three subprograms, however, which are not standard. These employ dichotomous techniques to generate transfer functions for active networks and continuous control systems. Since these techniques are currently attracting widespread interest, the three subprograms which implement them will be discussed in some detail.

The increasing complexity associated with many modern engineering applications, including autonomous robot guidance and navigation, process control in sensor-rich environments, and control of biological systems, has far-reaching implications for control system design. As an example, reactive, embedded software systems, interacting among themselves and remote users over communication networks, introduce a whole new set of system-level challenges, and classic control design objectives such as stability, performance, and robustness are being complemented with a number of new questions. These include the cost of hardware implementation, measured for example not only by computational requirements such as speed and memory, but also by communication requirements such as available communication bandwidth. Moreover, the complexity associated with specifying the control procedures and with verifying the behavior of the closed-loop system increasingly plays a fundamental role, especially in safety-critical control systems arising in energy and transportation networks, and in medical applications.

By now it is known that several problems in control and matrix theory are NP-hard. These include matrix problems that arise in control theory, as well as other problems in the robustness analysis and synthesis of control systems. These negative results force us to modify our notion of “solving” a given problem. If we cannot solve a problem exactly because it is NP-hard, then we must settle for solving it approximately. If we cannot solve all instances of a problem, we must settle for solving “almost all” instances of a problem. An approach that is recently gaining popularity is that of using randomized algorithms. The notion of a randomized algorithm as defined here is somewhat different from that in the computer science literature, and enlarges the class of problems that can be efficiently solved. We begin with the premise that many problems in robustness analysis and synthesis can be formulated as the minimization of an objective function with respect to the controller parameters. It is argued that, in order to assess the performance of a controller as the plant varies over a prespecified family, it is better to use the average performance of the controller as the objective function to be minimized, rather than its worstcase performance, as the worst-case objective function usually leads to rather conservative designs. Then it is shown that a property from statistical learning theory known as uniform convergence of empirical means (UCEM) plays an important role in allowing us to construct efficient randomized algorithms for a wide variety of controller synthesis problems. In particular, whenever the UCEM property holds, there exists an efficient (i.e., polynomial-time) randomized algorithm. Using very recent results in VC-dimension theory, it is shown that the UCEM property holds in several problems such as robust stabilization and weighted H∞-norm minimization. Hence it is possible to solve such problems efficiently using randomized algorithms. The paper is concluded by showing that the statistical learning methodology is also applicable to some NP-hard matrix problems.

Chapter 1 - Introduction to Controls

Design and analysis of high-order control systems requires a great deal of laborious calculations. Stability analyses are usually conducted with standard techniques such as root locus or frequency response. The calculations involved in these analyses are generally too complex to do by hand. Graphical techniques and approximations may be used, but often introduce unacceptably large errors.

In this paper, an optimal controller is investigate d based on the Linear Quadratic Control method. The controller simulation is execut ed based on a small-scale autonomous model helicopter, Yamaha R-50. Genetic algorithms are employed to generate weighting matrices by optimizing the performance index of the control system. As a result, this method produces optimal weighting matrices which further improve the Linear Quadratic Controller. A full state feedback approach is used in the control design process. A Kalman observer is integrated into the controller to predi ct full state variables, since only a limited number of state variables are measured. Finally, th e performance of the controller is evaluated in the time domain with and without disturbances when the model helicopter is in hovering flight and forward flight. I. Introduction utonomous helicopters offer special advantages for major operations in both civilian and military sect ors, particularly in cases that are considered either in accessible or dangerous for human beings, due to th eir vertical take-off and landing (VTOL) capabilities. The contr ol system of autonomous helicopters plays a key rol e in its ability to carry out the assigned task effectively. This has lead to a growing interest in the design and analysis of the control system of autonomous helicopters. In 1990s, classic control theory was widely used for autonom ous helicopter control systems, which is mainly a succe ssive loop closure approach. The control gains are selected separately using tools such as Root locus, Bode and Nyquist plots. The controller parameters are usual ly tuned based on the controller performance measured either in ti me domain or in frequency domain. This design procedure becomes increasingly difficult as more and more loo ps are added, specifically, when the dynamics invol ve multiple inputs, multiple outputs, or multiple feedback loop s with complex performance criteria. To control an autonomous helicopter modeled as a complex Multiple Input Multiple Output (MIMO) system, the performance criteria can not be easily met by the approach based on classis cont rol theory. Several researchers have developed a number of diff erent ways for the control system design of autonom ous helicopters in the literature. Shim et al 1 presented three different control methods using li near robust, fuzzy logic, and nonlinear tracking controls, for an autonomous helicopter in hover and low speed flight. Johnson a nd Kannan 2

Early control textbooks in Norway

Control theoretical concepts for synthetic and systems biology

A novel approach is provided for the analysis of multi-loop control systems by a digital computer introducing operational arrays, in which all the instructions are given through the data input. Changing parameters for optimisation purposes or the introducing of additional networks becomes a matter of changing the operational array in the data, leaving the main programme untouched. Although the method is general, only the frequency response of a control system is considered, but at the same time the way has been left open to expand the method as experience reveals the need for further facilities, i.e. root locus, time response, etc. The programme has been written in Algol, but the basic flow diagram can be easily converted into any other language. Whatever the language is, the programme provides the necessary software design facilities translated into control engineering terms in a readily usable computational form.

Stability is one of the most important concepts of analysis and design of control systems. Stability analysis of fuzzy control systems has been difficult since fuzzy systems are essentially nonlinear systems. Recently, stability analysis techniques [l]-[6] [13]-[16] based on nonlinear stability theory have been reported. Langari and Tomizuka [2, 6] analyzed stability of fuzzy linguistic control systems. Kitamura [3] realized stability analysis of fuzzy control systems by using extended circle criterion. Farinwata [5] and Kato [14] utilized phase plane analysis type of techniques, tanaka and co-authors [1,3,4] applied Lyapunov approach to fuzzy control systems and recently developed LMI-based designs [10, 17, 28-37], where LMI stands for nonlinear matrix inequality.

Significant advances in the theory of linear robust control in recent years have led to powerful new tools for the design and analysis of control systems. A popular paradigm for such theory is depicted in Figure 3.1, which shows the interconnection of three system blocks G, K, and Δ. The plant G relates a control input u and a disturbance input v to a measurement output y and a penalized output z. The control input u is generated from the measured output y by the controller K. All uncertainty is located in the block Δ which generates the disturbance input v from the penalized output z. The plant G, which is assumed to be linear and precisely known, may incorporate some nominal plant as well as frequency-dependent weights on the uncertainty Δ (for this reason G is sometimes called a generalized plant). Once G is determined, the robust stabilization problem is to construct a controller K which guarantees closed-loop stability for all systems Δ belonging to a given family of admissible (possibly nonlinear) uncertain systems.

Root locus method is the common analysis method in the classical control theory, it can judge the types of system transient response intuitively to analyze if the system can achieve the stationary state without solving differential equation. Qualitative analysis of the impact the change simulation parameters main vehicle steering characteristics of the vehicle, according to the vehicle structure parameter changes cause the system to change the type of the transient response, reaction to the nature of the various branches of the root locus on the same trend of root locus vehicle structural parameters obtained The reasonable range. In this paper, based on the three degrees of freedom vehicle model, we derived characteristic equation model to analyze the impact on vehicle handling stability by changes of speed, yaw moment of inertia as well as front and rear cornering stiffness, and obtain the reasonable range of yaw moment of inertia and front and rear cornering stiffness based on vehicle simulation.

: Several block canonical forms for describing a class of multivariable control systems have been developed in this project. Based on these canonical structures, some algebraic and geometric theories have been developed for analysis and design of multivariable control systems. Several matrix-valued functions have been defined and computational algorithms have been established for computing these matrix-valued functions. These matrix-valued functions and associated computational algorithms have been utilized for analysis and design of general large-scale continuous-time and discrete-time systems. Based on these research results, twenty-two papers have been published in the referred journals. Keywords: Control theory; Linear systems; Matrix algebra; Abstracts.

Accurate modeling of many dynamic systems leads to a set of Fractional Differential Equations (FDEs). This paper presents a general formulation and a solution scheme for a class of Fractional Optimal Control Problems (FOCPs) for those systems. The fractional derivative is described in the Riemann–Liouville sense. The performance index of a FOCP is considered as a function of both the state and the control variables, and the dynamic constraints are expressed by a set of FDEs. The Calculus of Variations, the Lagrange multiplier, and the formula for fractional integration by parts are used to obtain Euler–Lagrange equations for the FOCP. The formulation presented and the resulting equations are very similar to those that appear in the classical optimal control theory. Thus, the present formulation essentially extends the classical control theory to fractional dynamic system. The formulation is used to derive the control equations for a quadratic linear fractional control problem. An approach similar to a variational virtual work coupled with the Lagrange multiplier technique is presented to find the approximate numerical solution of the resulting equations. Numerical solutions for two fractional systems, a time-invariant and a time-varying, are presented to demonstrate the feasibility of the method. It is shown that (1) the solutions converge as the number of approximating terms increase, and (2) the solutions approach to classical solutions as the order of the fractional derivatives approach to 1. The formulation presented is simple and can be extended to other FOCPs. It is hoped that the simplicity of this formulation will initiate a new interest in the area of optimal control of fractional systems.