Robust Digital Control Research Articles

Robust digital controller design for processes with dead times: New results

The Dahlin controller is studied in the complex-frequency domain in terms of performance and robust stability. Several well known digital control algorithms are compared with the Dahlin controller and found to be equivalent to it. The possibility of extending the Dahlin controller to the control of plants with zeros outside the unit circle and unstable plants is discussed. The essential cause of ringing is investigated and some ambiguous formulation is clarified. A new procedure is developed for digital controller design. Compared with conventional methods, it provides a more effective method of eliminating ringing. Finally, numerical examples are given to illustrate the new approach.

Robust digital control using pole placement with sensitivity function shaping method

SUMMARY It is shown in this paper that based on identified discrete-time models a robust digital linear controller can be designed using the pole placement method combined with sensitivity function shaping in the frequency domain. Two di⁄erent design techniques are presented. The first one is based on the shaping of the sensitivity functions using the fixed parts in the controller and the auxiliary poles of the closed loop while keeping the dominant poles in the desired places. The main idea of the second one is to determine a weighting filter for the output sensitivity function in an H = optimization approach which assures partial pole placement and desired performances. In this technique the weighting filter is interpreted as the inverse of the desired output sensitivity function and is computed using a constrained optimization program. The application of this technique on a flexible transmission system is presented. ( 1998 John Wiley & Sons, Ltd. The controller design methodology considered in this paper is based on pole placement combined with the shaping of the sensitivity function. The computation of the controller in the pole placement technique requires the specification of the desired closed-loop poles (the nominal stability problem) and of some fixed parts of the controller for the rejection of disturbances at various frequencies (the nominal performance problem). However, this is not enough to guarantee the robustness of the design with respect to the plant model uncertainties (the robust stability and robust performance problem). A robust controller design requires also the shaping of the sensitivity functions. The sensitivity functions, particularly the output sensitivity function, are key indicators for the nominal and robust performance as well as for the robust stability of the closed-loop system. The inverse of the maximum value of the output sensitivity function, i.e., the inverse of its H = norm, gives the minimum distance between the Nyquist plot of the open-loop system and the critical point [!1, j0]. This quantity, called the modulus margin, is a much more significant robustness indicator than the phase and gain margins. On the other hand, conditions for assuring a certain delay margin which is also a very important robustness indicator, particularly in the high frequency region, can also be expressed in terms of the shape of the output sensitivity function. It seems therefore reasonable to combine the pole placement with the shaping of the output

A Digital Robust Controller for Cutting Force Control in the End Milling Process

In this work, a digital robust controller is designed via Quantitative Feedback Theory (QFT) to maintain a constant cutting force in the presence of parametric uncertainty for a time varying end milling process. The QFT controller is designed using the delta transform method for discrete systems. The controller is designed to limit the overshoot and settling time of the cutting force levels over a range of cutting parameters. Models are presented for the cutting process and machine dynamics including parametric uncertainty, and these models are used to develop a controller which meets given tracking and regulation specifications for all plant values. Experimental results are obtained by implementing the controller on a milling machine.

Robust digital motion controllers for mechanical systems

This paper describes several methodologies for the design of robust digital motion controllers. While key ideas are given either in the continuous time domain (Laplace domain) or in the discrete time domain, all the methodologies are suited for digital implementation. Application examples will be mentioned.

Improvement of robust digital control by identification in the closed loop. Application to a 360° flexible arm

This paper presents a procedure for the improvement of identification results from open-loop experiments by identification in a closed loop without modification of the identification protocol. Several available identification algorithms are considered, and two methods for the validation of the model identified in a closed loop are introduced. As a consequence, an improved robust controller is obtained. Results are presented from experiments on a very flexible 360° arm.

Closed Loop Identification as a Design Tool for the Robust Digital Control of a 360° Flexible Arm

In this paper it is shown how a robust controller designed for a model identified in open loop can be improved by an identification in closed loop. A suitable structure for closed loop identification is given and the treatment of the data is discussed. Several methods for the validation of the model are introduced. Results are presented from experiments on a very flexible arm.

H2 robust digital vector control for the induction machine

Using a discrete time-variant state-space model for the induction machine, the authors consider the plant variations as being uncertainties represented by polytopes. In addition, an alternative scheme of vector control is proposed for digital control of the induction machine. This scheme involves treatment of the machine equations in state space and the acquisition of a robust state-feedback gain by an H2 convex optimisation method.

Robust digital tracking controller design for high-speed positioning systems

In this paper, a robust digital tracking controller for high-speed positioning is proposed.For high-speed tracking problems, the combination of a feedforward controller and a robust feedback controller is desirable, because the feedforward controller anticipates and compensates for closed-loop dynamics and the feedback controller compensates mechanical nonlinearities, parameter variations, and disturbances. A disturbance observer and PD compensation was used as a robust feedback controller and a zero-phase error-tracking controller was used as the feedforward controller.This method was applied to an X-Y table, and experimental results demonstrate that this method yields excellent tracking performance and robustness to plant parameter variations.

Digital interval modeling and hybrid control of uncertain systems

This paper addresses two issues: (1) converting a continuous-time uncertain system to an equivalent discrete-time interval model; and (2) constructing a robust digital control law from a robust analogue control law for hybrid control of sampled-data uncertain systems. The system matrices characterizing the state-space representation of the original continuous-time uncertain systems are assumed to be interval matrices. The Pade approximation method together with a geometric-series approximation method is employed to obtain the generalized enclosing discrete-time interval models. The generalized enclosing interval models are able to tightly enclose the exact discrete-time uncertain model, and can be utilized for digital simulation and digital design of continuous-time uncertain systems. A new family of digitally redesigned interval controllers is constructed from a continuous-time robust controller for robust digital control of continuous-time uncertain systems. Using the newly digitally redesigned interval controllers, the dynamic states of the digitally controlled sampled-data uncertain systems are able to closely match those of the original analogously controlled continuous-time uncertain systems for a relatively longer sampling period.

Optimal and robust digital current controller synthesis for vector-controlled induction motor drive systems

The vector-controlled induction-motor drive is a multi-input multi-output system. By using modern control techniques, all feedback loops can be closed simultaneously, in addition to obtaining optimal gains for the controllers. A systematic approach to the design of the digital current controllers is proposed. A vector-controlled induction-motor-drive system is usually viewed as a full-state feedback problem, where the non-measurable states are estimated using suitable reduced-order observers. Here, the induction-motor-drive system is viewed as a linear quadratic (LQ) tracker problem with output feedback, as this approach uses only the measurable states of the system and provides flexibility in choosing the control structure. The current controllers are designed for the torque dynamics of the induction motor. The controller should also be so designed that the whole drive system is stable for a class of induction motors, i.e. the whole drive system should be stable in the face of uncertainties in the parameters of the induction motor. Therefore, it becomes essential to build stability robustness into the controller design. Here, the proposed systematic approach determines the optimal controller gains for a given performance specification under the constraint that the whole system has stability robustness for uncertainties in the specified parameters of the induction motor. The concepts are illustrated by simulation.

Digital modelling and digital redesign of sampled-data uncertain systems

A new method for digital model conversion of a continuous-time uncertain system and a new digital redesign method for robust control of a sampled-data uncertain system are presented. The concept of the principle of equivalent areas together with interval arithmetic is utilised for finding the discrete-time uncertain model and the digital robust control law from the continuous-time uncertain state equation and the analogue robust control law, respectively. Using the newly digitally redesigned controllers, the resulting dynamic states of the digitally controlled sampled-data uncertain systems are able to closely match those of the original analogously controlled continuous-time uncertain systems for a relatively longer sampling period.

Robust digital control of systems with time delay (the Smith predictor revisited)

The design of robust digital controllers for systems with time delay is investigated. A particular class of digital controller is considered, namely those for which the closed-loop poles include the poles of the system to be controlled. Robust design with respect to time delay variations requires the introduction of additional closed-loop poles and/or reduction of the gain of the feedback path at high frequencies (near 0-5 fs , where fs is sampling frequency). Relationships with other robustification procedures are examined.

Microprocessor based robust digital control for UPS with three-phase PWM inverter

This paper describes a novel method of robust (insensitive to system parameter variations and load current changes) and fast digital control for an uninterruptible power supply (UPS) with a three-phase PWM inverter. The purpose of this paper is to propose a method by which characteristics better than those by conventional methods are obtained using an algorithm simpler than that of conventional methods. The experiments show that the purpose is achieved and the proposed method offers a total harmonic distortion of 0.6% of the output voltage waveform at a full nonlinear load. The analysis shows that the stability of the method is sufficient. Three features of the method are: (a) a capacitor current observer for stabilization and a disturbance observer for robustness are used to compensate the time lag by the computation and the disturbances, in a minor loop of the capacitor current through an inductor-capacitor filter of the inverter; (b) new models of the inverter and the disturbances are established to simplify these observers; and (c) the output voltage control loop can be designed easily and exactly because the minor loop realizes a rapid and robust control of the current.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Robust Digital Control of Flexible Transmissions Using the Combined Pole Placement/Sensitivity Function Shaping Method

The control of very flexible transmissions in the presence of load variations is a challenging control problem. In this paper it is shown that based on identified discrete time models a robust digital linear controller can be designed using the combined pole placement method with sensitivity function shaping in the frequency domain. This controller provides satisfactory performance for a large range of load variations.

Design of a Robust Digital Controller for a Nonlinear Heat-Transfer Process.

In this paper, we propose a systematic controller design which treats problems of system identification and robust controller design, for a nonlinear heat-transfer process. First, we construct a convenient parametric model of the object possessing the nonlinear characteristic. Then, by using the modelling error between the real system and the model as the dominant design parameter, we construct a robust control system based on a mixed-sensitivity approach. This method avoids the need to linearize of a nonlinear system and provides robustness against nonlinear input. The effectiveness of the control method is verified by both numerical simulation and direct experiment for producing a constantly rising temperature of a microheater.

Robust Control of Uncertain Resonant Systems

This work deals with the control synthesis of resonant systems. In this work we present a new resonance approximation which enables efficient calculation of closed loop properties at resonant frequencies. The approximation is used to accommodate low damping resonances in a QFT design procedure. The extended design procedure is applied to the solution of the benchmark problem: ‘robust digital control of a flexible transmission’. The results offer insight to the fundamental tradeoffs of single input single output resonant system design.

A Flexible Transmission System as a Benchmark for Robust Digital Control*

A benchmark problem for digital robust control design is described. The robustness in stability and in performance of eight solutions to this benchmark which have been presented at the 1995 European Control Conference in Rome (Italy) are evaluated. The eight controllers have been designed using several different methods, including discrete time H∞ optimisation, quantitative feedback theory, non-integer order control, generalised predictive control, combined pole placement/sensitivity function shaping and model free optimisation. Simulations and-experimental results are given.

VSS Approach to the Design of Robust Digital Controller Using Transfer Equation

In this paper, a variable structure controller based on a sliding sector for discrete-time systems is proposed. The sliding sector is designed to be stable by minimum variance control algorithm. The proposed discrete-time VSS control law moves the system state from the outside to the inside of the sliding sector. The robustness to bounded parameter uncertainty is discussed. A simulation on the flexible transmission system of the benchmark illustrates this approach. The result shows the robustness of the proposed VSS controller.

Robust Adaptive and Repetitive Digital Tracking Control and Application to a Hydraulic Servo for Noncircular Machining

This paper presents the development of robust digital tracking control algorithms and their real-time implementation on an electrohydraulic servo-actuator for tool positioning in noncircular machining. Robust adaptive feedforward controller for tracking arbitrary signals and robust repetitive controller for tracking periodic signals against disturbances and unmodeled dynamics have been developed. Experimental results are presented to illustrate the control system synthesis procedures and tracking performance.

A delta transform approach to loop gain‐phase shaping design of robust digital control systems

AbstractThis paper addresses the existence of loop gain‐phase shaping (LGPS) solutions for the design of robust digital control systems for SISO, minimum‐phase, continuous‐time processes with parametric uncertainty. We develop the frequency response properties of LGPS for discrete‐time systems using the Δ‐transform, a transform method that applies to both continuous‐time and discrete‐time systems. A theorem is presented which demonstrates that for reasonable specifications there always exists a sampling period such that the robust digital control problem has a solution. Finally, we offer a procedure for estimating the maximum feasible sampling period for LGPS solutions to robust digital control problems.