Analysis and simple design using the Nichols chart

An extensive small-signal analysis of a single-loop current-mode control strategy for a pulse-width-modulated (PWM) boost DC-to-DC power converter operating in continuous conduction mode (CCM) is proposed using a new non-symmetric phase controller. To model the boost power stage, a linear circuit model is used which includes all parasitic components such as the equivalent series resistance (ESR) of the filter capacitor, the ESR of the inductor, the transistor ON-resistance, and the diode forward resistance and offset voltage. A boost power stage design example gives component design equations and will serve to illustrate the closed-loop converter design. A design procedure for the new non-symmetric phase controller is presented. Open-loop and closed-loop circuit models and transfer functions are derived for the boost PWM converter and illustrated by Bode plots. An approach is presented for simplifying closed-loop transfer functions, using Euler's identity, into a format which is conducive to modeling in any high level programming language on a personal computer. Bode plots are obtained using a data analysis software package Axum 3.0 which combines a programming language, spread-sheet, and publication quality technical graphics. The proposed control scheme directly controls the inductor current and indirectly controls the load current and output voltage. The closed-loop transfer functions of the proposed control scheme do not contain a righthalf plane (RHP) zero, in contrast to the closed-loop transfer functions of a single-loop voltage-mode control scheme. The absence of the RHP zero provides better stability by making it easier to obtain large or specified gain and phase margins.

The authors apply H/sub /spl infin//-designed controllers to a wheeled inverted pendulum using transfer function shaping techniques. This design study motivates the use of H/sub /spl infin//-techniques and shows the control procedure applied to multi-output and unstable plants. Two disturbances are considered to shape transfer functions: one corresponds to the influence of the gravity force, and the other is disturbance on the control input. Two H/sub /spl infin// designs are made and compared with a design of the conventional pole allocation method to examine the relations between robust stability and closed loop transfer functions. Experimental data prove the superiority of H/sub /spl infin// designs with the shaping of transfer functions.

Controller Synthesis for Maximizing Disturbance Bounds in Linear Uncertain Systems

Chapter 9 - Frequency-Domain Approach

This chapter discusses an evaluation method for rotor vibration characteristics by utilizing the open-loop frequency response of the system, instead of conventional eigenvalue analysis. The vibration characteristics of a rotor system are represented by the (damped) natural frequency and damping ratio. They have been estimated in the previous chapters from the viewpoint of the eigenvalue solution, the impulse response waveform, and the resonance curve (FRA) under harmonic excitation. The open-loop characteristics are from a concept in control engineering. A rotor-bearing system can be conceived as a control system as shown in Fig. 8.1, of which the open-loop characteristics are related to the vibration characteristics: the gain cross-over frequency is an estimate of the natural frequency, and the phase margin is an indicator for the damping ratio. Details of estimation are described below.

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.

Tapered transmission line resonators can be used to achieve specific frequency responses and enhance the performance of microwave devices and impedance transformers. To develop a mathematical model (transfer function) of such a wideband resonator will facilitate the construction of an equivalent circuit and the synthesis of resonators of this type. This study discusses the system modeling of tapered transmission line (TTL) resonators using the singularity expansion method (SEM). The transfer function is analytically established for two types of wideband TTL resonators: exponential tapered transmission lines (ETTL) and linear tapered transmission lines (LTTL). The analytical transfer function is derived for the general tapered ratio (k/β). The physical poles of the structures are identified using the pole-energy matrix pencil (MP) approach. The transfer function expression is then utilized to develop an accurate equivalent lumped-element circuit for the TTL resonator. This study’s simplified approach for estimating the transfer function and associated poles and zeros from the S-parameters is the main contribution, whereas it is known that the transfer function becomes complicated for wideband frequency response. A direct synthesis approach is presented to develop two-stage and four-stage ultra-wideband (UWB) bandpass filters. The agreement between the frequency response data and the derived transfer function of the system model of the synthesized TTL filters demonstrates the reliability of the presented method. The proposed system modeling and synthesis methodology can be applied to more sophisticated filter TTL architectures.

In this study, a two‐dimensional (2D) H ∞ ‐based method is presented for the iterative learning control (ILC) design problem of a class of linear discrete‐time systems with iteratively periodic factors, including initial states, parametric uncertainties, disturbances, measurement noises, and reference trajectories. First, the ILC design problem of the linear systems is described as a controller design problem of 2D uncertain Roesser models. Second, the H ∞ performance of 2D Roesser models is studied under a general boundary condition. Third, an ILC design criterion is presented to achieve the perfect tracking and specified H ∞ performance by using linear matrix inequality approaches. Finally, a numerical example is given to illustrate the efficiency of the proposed ILC design method.

A problem of globally asymptotically stable control design is investigated for a class of high-order uncertain nonlinear systems. These systems, unlike the existing results, have double control input channels; that is, the control input directly affects two one-dimensional subsystems. This makes the existing methods of control design inapplicable or the control design problem difficult to solve, and therefore, it is of interest to explore a new control design method to solve the control design of high-order nonlinear systems with multiple control input channels. First, an effective feedback transformation is introduced. Hence, this control design problem under appropriate assumptions can be transformed into one with a single control input channel. Then, using existing results, particularly, the method of adding a power integrator, a methodology is proposed to design the globally asymptotically stable controller for the nonlinear systems under investigation. Although the systems studied in the paper are a special case of high-order nonlinear systems with multiple control input channels, the results obtained in the paper, while unavoidably having certain limitations, will provide a reference and guidance in tackling the general case. Finally, a simulation is provided to verify the effectiveness of the theoretical results obtained.

This article, based on the main circuit structure of full-bridge DC/DC converter in the transmitter of the borehole-ground electrical potential measurement system, presents the structure of single-closed-loop current feedback control system with voltage mode control for output current stabilization. According to the average state space method, the state space equation of the main circuit with steady output current of transmitter was established, the AC small-signal model of the main circuit was acquired and the open-loop transfer function was then deduced as a result. The method of design and specific parameters of the PI compensation network were provided and the open-loop transfer function of the system was deduced. The incremental PI control algorithm was adopted and the digital control was realised by TMS320F2812 DSP system programming. MATLAB was used to analyze the system for its open-loop frequency characteristics and its closed-loop dynamic characteristics, the result of which shows the correctness of the modelling approach.

We present a trajectory tracking control law for a quadrotor unmanned aerial vehicle (UAV) for handling the complete failure of a single rotor. The control design problem considers the reduced state space, which excludes the angular velocity and orientation about the vertical body axis. The proposed controller enables the quadrotor to track the orientation of this axis and consequently any prescribed position trajectory using only three rotors. The control design is carried out in two stages. First, to track the reduced attitude dynamics, a geometric controller with two input torques is designed on the Lie group SO(3). This controller is then extended to SE(3) by designing a saturation-based feedback law to track the center of mass position with bounded thrust. The control law for the complete dynamics achieves an almost global exponential tracking. The novelty of geometric control design lies in its ability to effectively execute aggressive global maneuvers despite the complete loss of a rotor. Numerical simulations on a conventional quadrotor model, carried out for complete trajectory tracking, together with preliminary experimental tests on a real platform under a hover scenario with sudden motor failure, are presented to demonstrate the practical applicability of the proposed control design.

Actuator placement has a significant impact on the dynamic response of actively controlled structures. Misplaced actuators and sensors often lead to controllability and observability problems, and the desired system performance may not be achieved with any choice of control law. This paper addresses the design of actively controlled structures wherein both the actuator placement and controller design aspects are addressed simultaneously. It is assumed that a hierarchical structure exists between the actuator placement and controller design objective functions with the actuator placement problem considered as being more important. The resulting multiobjective design problem is solved as a bi-level Stackelberg game. A computational procedure based on variable updating using response surface methods is developed for exchanging information between the two levels (leader and follower). The optimization problem has mixed discrete-continuous variables with discrete variables corresponding to actuator placement and continuous variables associated with the controller design problem. The solution approach includes a blend of genetic algorithms and sequential quadratic programming techniques and is applied to the design of a flexible truss structure. The proposed approach successfully designed an optimum controller while minimizing the weight of the structure and simultaneously maximizing the energy dissipated by the controller to bring the structure to its equilibrium position when subjected to an external disturbance.

Gradient search methods that fit the parameters of a user-defined transfer function to experimental logarithmic frequency response data are presented. The methods match a model based on physically significant parameters, including natural frequencies of poles and zeros and damping ratios of complex poles and zeros. The algorithms construct and utilize their own analytical gradient descent functions, based on the desired model. One method attempts to fit both log magnitude and phase, while another identifies a minimum phase transfer function model from only log magnitude frequency response data. The log magnitude algorithm is shown to be superior to traditional methods using nonlogarithmic frequency response data, including those used in commercially available frequency response analyzers. The algorithms are shown to perform well, especially for systems with lightly-damped dynamics.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Stability analysis and control design of LTI discrete-time systems by the direct use of time series data

The paper considers the iterative learning control (ILC) design problem of a network system under changing operating mode of subsystems (agents) and configuration of information network. The network system consists of identical agents, which are discrete linear dynamic plants operating in a repetitive mode. The operating modes of agents depend on their parameters and the reference trajectory, which must be tracked with required accuracy at output of system. The configurations of information network define the group of functioning agents and the type of information exchange between them. The mode and the configuration change takes place in accordance with certain external rules. The control design is based on the divergent method of the vector Lyapunov function. For reducing the transient error caused by the mode change and the connection of new agents, a special rule for switching the ILC law is proposed. The results of modeling the obtained control law for a group of manipulators with flexible link are presented.