Loop Shaping In Frequency Domain Research Articles

Design of Fractional-Order Lag Network and Fractional-Order PI Controller for a Robotic Manipulator

Abstract Motion control of robotic manipulators is frequently realized by independent control of the DC motors actuating robot joints. Namely, nonlinearities, coupling between actuators and other complex dynamics are neglected if high gear ratios between the actuators and robot joints are considered. This paper proposes a fractional-order lag network or a fractional-order PI controller to control the position of the actuators shafts. The introduced fractional compensators are designed by using the symmetrical optimum principle and by parameters optimization or by frequency-domain loop shaping, respectively. Simulation results and frequency response show effectiveness and robustness of the approach.

Spatio-Temporal Loop Shaping for Distributed Control of PDE Systems

Abstract The systems of interest in this paper are described by a possibly large number of interconnected subsystems, where the spatial discretization into subsystems is induced by applying an array of collocated actuator/sensor pairs. When considering these types of systems in a classical centralized fashion, they have a high number of input/output signals on one hand, and usually a sparse structure on the other. While the method of loop-shaping in classical control is well-established, the notion of spatially distributed systems makes it possible to extend frequency domain loop shaping to spatial frequencies and to include weighting filters with spatio-temporal dynamics. By using a Fourier transform, controller synthesis can be done for each spatial frequency at a time. This method is applied to the control of the temperature distribution of a thin metal rod.

Multi criteria H∞ optimal PID controllers from an undergraduate perspective

A simple design method for robust PID controllers is presented. It is based on a multi criteria H∞ optimal control formulation, which is shown to be easily solved by a few lines of MATLAB code. This optimal solution for PID controllers including low pass filtering, is complemented by a simple paper and pen solution that can be used to obtain nearly optimal solutions. The presented approach is shown to give significantly better results compared to ordinary text book solutions based on frequency domain loop shaping. The paper also includes a discussion on how to best formulate PID controllers for design, and how additional filtering may easily improve high frequency robustness.

Robust controller design based on generalized Bode envelopes

We propose simple tools for robust design of controllers for SISO linear systems with or without uncer- tainty. These tools are based on the generalization of frequency domain, where the uncertainty is defined by generalized Bode envelopes (GBE). The utilization of generalized Nyquist and Mikhailov theorems, which uses the number of GBE crossings with certain predefined horizontal lines, to deduce stability, allows to obtain stability as well as performance specifications simultaneously. The same design rules can be applied to continuous as well as discrete time systems. We provide examples to demonstrate our method of controller design for various control systems. The main problem of control theory is a design of an appropriate controller for a given plant with prescribed specifications. The controller should be robust enough to manage the errors in the model, noise and disturbances. Then, the designed controllers can be used in diverse applications ranging from automotive to process control. In the classical control design theory (e.g., Bode (1945)), the noise and uncertainties are not explicitly modeled, thus the phase and gain margins are used to make the system more robust. In the modern optimal control Kwakernaak & Sivan (1972), the specifications are converted to some performance criterion that should be minimized. In our approach, we avoid the need in gain and phase margins by exploring the poles and zeros clustering in the complex plane. If all the poles in the closed loop are clustered inside an arbitrary chosen bounded region G , we say that this system is G stable and all the specifications are met. To provide better stability margins we may choose the location of the region farther to the left from the imaginary axis (for continuous systems). By choosing the region inside the unit circle, we can use the same tools to design discrete controllers for discrete plants. Further development of the robust design went in a few directions described below. The parametric methods of robust control are described in Bhattacharyya et al. (1995), and Barmish (1993). In these methods, the structure of uncertainty is defined aforehand, and the design procedure is based on alge- braic and optimization methods. Another type which is based on H ¥ norm was proposed by Zames (1981). A loop shaping in frequency domain that is based on H ¥ theory was proposed by McFarlane et al. (1992). The methods of loop shaping try to consider the sensitivity at low and high frequencies in the design. A more recent approach is based on the linear matrix inequalities (LMI) (e.g., Iwasaki & Hara (2004)), but this approach uses state space representation and not a transfer function. Our aim is to fill the gap between the traditional classical control design theory, and more mathematically inclined sophisticated modern robust control theory. One of the earliest attempts to explicit plant uncertainty description was formulated in the quanti- tative feedback theory (QFT) by Horowitz (2001). In this theory, the fixed controller structure is not assumed, and the design is made by utilization of Nichols chart and conversion of the specifications to the frequency domain. Similarly to QFT, our method is very intuitive allowing a designer to achieve the desired performance and to see what trade-offs are necessary. In contrast to QFT, we use generalized

Robust controller synthesis with consideration of performance criteria

AbstractThis paper presents interactive controller synthesis methods based on an inward approach and offers some advantages over the traditional loop gain shaping methods. The indirect use of weighting functions for the robustness controller tuning is introduced. Besides that, the method allows transparent closed‐loop pole placement to achieve desirable transient performance. The obtained controllers are of lower order for comparable performance than those synthesized with rmH2, H∞ or µ‐synthesis. The method is particularly well suited for robust control problems where frequency domain constraints emerge from the analyses of non‐parametric uncertainties and also for control problems where the frequency domain loop shaping is used to achieve time domain performance specifications. Copyright © 2010 John Wiley & Sons, Ltd.

H∞ compensation of external vibration impact on servo performance of hard disk drives in mobile applications

AbstractH∞ compensation for external vibration impact on the positioning accuracy of hard disk drives is considered in this paper. A feedforward controller is designed to attenuate the impact with the aid of a sensor to detect external vibrations. Loop shaping in frequency domain and H∞ method in state space are used to design the feedforward controller. The linear matrix inequality approach is adopted for solving the H∞ feedforward control design problem. The application results in a 1.8‐in disk drive with an accelerometer to measure acceleration signal show that 97% reduction of the position error signal is achieved with the feedforward control designed by the H∞ method. The effectiveness of the two methods is also evaluated and compared when external vibration model is subjected to gain variations. Copyright © 2007 John Wiley & Sons, Ltd.

ROBUST CONTROL OF CHAOTIC VIBRATIONS FOR IMPACTING HEAT EXCHANGER TUBES IN CROSSFLOW

A robust feedback controller design to suppress flutter-type chaotic vibrations in baffled heat exchanger tubes is presented. The vibrations are the result of the fluid dynamic forces on the tube which behave as a negative damping element. A consequence of these vibrations is that the heat exchanger tubes impact with the baffle plates thereby reducing the service life of the heat exchanger. To eliminate the resulting tube impacts, a feedback control strategy is proposed. The heat exchanger tube and the fluid dynamic forces acting on the tube are modeled with linear delayed differential equations. Due to the presence of the delay, these equations do not have a rational realization. The feedback controller is realized using a frequency domain loop shaping approach which is well suited for systems with transcendental transfer functions. The control effector is a magnetic force transducer that acts on the heat exchanger tube. The design strategy is based upon the premise that stabilizing the linear instability about the undeformed tube position will preclude the formation of the nonlinear chaotic vibrations that arise from impacting. The feedback controller is shown to provide robust stability and performance over a large flow velocity regime

An interactive parameter space method for robust performance in mixed sensitivity problems

This paper presents an interactive graphical method to determine the set of fixed-order stabilizing controllers achieving robust performance, in the mixed sensitivity framework. The method is limited to single-input/single-output (SISO) systems but offers significant advantages over traditional loop gain shaping methods such as H/sup /spl infin// and /spl mu/-synthesis. It can handle pure time delays in an exact manner and the weighting functions need not be rational. The technique translates frequency-domain weighting functions and stability constraints into the parameter space and thus gives the user more insights into the design than conventional methods. By virtue of producing the required parameter space region for the frequency response criteria, subsequent optimization of secondary objectives is possible. The controllers obtained are of lower order for comparable performance than those produced by current H/sup /spl infin// and /spl mu/-synthesis techniques. The method is particularly well-suited to robust control problems where frequency-domain constraints emerge from the analysis of nonparametric uncertainties in the system and also to control problems where the frequency domain loop shaping is used to achieve time-domain specifications.

Interactive control system design by a mixed H/sup ∞/-parameter space method

This paper presents an interactive graphical method to determine sets of stabilizing controllers satisfying any combination of constraints on the sensitivity, complementary sensitivity, and input sensitivity transfer functions. The method is limited to single-input/single-output systems but offers significant advantages over current H/sup /spl infin// methods. It can handle pure time delays in an exact manner. The weighting functions need not be rational. By virtue of producing the required parameter space region for the frequency response criteria, subsequent direct time-domain optimization is possible. The controllers obtained are of lower order for comparable performance than those produced by current H/sup /spl infin// techniques. The method is particularly well suited to robust control problems, where frequency domain constraints emerge from the analysis of uncertainties in the system, and also to suboptimal problems, where the frequency-domain loop shaping is used to achieve time-domain specifications.