Mixed Sensitivity Design Research Articles

Robust Space Launcher Control with Time-Varying Objectives

This paper presents a novel approach to robust linear time-varying control design for space launchers. It allows the controller to explicitly account for the launcher’s time-varying dynamics and changing control objectives along the ascent trajectory. The latter are readily incorporated via time-varying weighting functions into a mixed sensitivity design. For a traceable and transparent control design, a physically motivated weighting scheme is applied, which requires little tuning effort. The controller is obtained via a novel observer-based finite horizon linear time-varying synthesis approach. It provides a transparent structure which is easy to implement. The approach is used to design a pitch controller for a flexible expendable launch vehicle in atmospheric ascent tracking the open-loop guidance reference signal.

Comparing Different Resonant Control Approaches for Torque Ripple Minimisation in Electric Machines

Electric machines are highly efficient and highly controllable actuators, but they do still suffer from a number of imperfections. One of them is torque ripple, which introduces high frequency harmonics into the motion. One (cost- and performance-neutral) countermeasure is to apply control that counters the torque ripple. This paper compares several single-input single-output (SISO) control approaches for feedback control of torque ripple of a Permanent Magnet Synchronous Machine (PMSM). The baseline is PI (proportional-integral) control, which does not suppress torque ripple, and the most popular control approach is proportional-integral resonant (PIR) control. Both are compared to an advanced PIR controller (PIRA), frequency modulation, a mixed sensitivity design, and an iterative learning controller (ILC). The analysis demonstrates that PIR control, mixed sensitivity state feedback, and the modulating controller achieve identical behaviour. The choice between these three options is therefore dependent on preferences for the design methodology, or on implementation factors. The PIRA and the ILC on the other hand show more sophisticated behaviour that may be advantageous for certain applications, at the expense of higher complexity.

Additive Mixed Sensitivity Design of PID Controllers for Continuous-Time System with Uncertain Time-Delay

This paper presents an algorithm for all achievable coefficients of Proportional Integral Derivative (PID) controllers in an integral-derivative plane that stabilizes and satisfies additive mixed sensitivity constraint with an uncertain time delay for a continuous-time system. This algorithm solves the singularity problem of designing PID controllers in the integral and derivative plane and estimates achievable ranges of proportional gain of the PID controllers. A numerical cascaded ball and beam with unity feedback control of an SRV-DC motor and uncertain communication time delays in the system process demonstrate the application of this methodology. In this application, the additive weight bounds the additive errors for the cascaded ball and beam and the closed-loop SRV-DC motor system transfer function with the internal communication time delays

Mixed-sensitivity design of a dynamic controller for systems pre-compensated by input shapers

We employ recent control design algorithms for delay systems to address the mixed sensitivity design of a dynamic controller for multiple degree of freedom systems interconnected with an inverse signal shaper. A delay based inverse shaper is included within a feedback loop in order to eliminate oscillatory modes due to an attached flexible substructure, which has been shown to be advantageous to inducing directly the filtering property by an appropriate controller design. Due to the presence of the inverse shaper, the closed loop dynamics become infinite dimensional. Furthermore we design fixed-order controllers, aiming at an easy implementation. As a consequence of these two features standard techniques from H-infinity control can no longer be used. We present a two-stage method, which firstly makes the closed-loop system asymptotically stable and, secondly, computes a low-order controller that minimizes the H-infinity norm of the weighted closed-loop transfer functions. The approach is grounded in recent methods for fixed-order H-infinity control of delay systems, and the delay-differential algebraic equations (DDAE) modelling and control framework.

Design of mixed sensitivity H<SUB align="right">∞ control for four-rotor hover vehicle

Design of mixed sensitivity H<SUB align="right">∞ control for four-rotor hover vehicle

Design of mixed sensitivity H∞ control for four-rotor hover vehicle

During the past one decade, multirotor unmanned aerial vehicles (MUAVs)'s control has become an active research area for flight control community. The reasons behind are the benefits offered by MUAV and its numerous commercial and consumer applications. In this paper, design of a robust attitude controller for four-rotor hover vehicle that is a kind of MUAV, based on H∞ mixed-sensitivity synthesis is presented. Firstly, a linear model of four-rotor hover vehicle is derived, which is formulated as a nominal plant perturbed by parameter and unstructured uncertainties. H∞ mixed-sensitivity controller is designed due to the uncertain nature of the system. The efficacy of the proposed controller is proved by simulations and experiment. Performance analysis, simulation, and experimental results show that the proposed controller guarantees stability, exhibits good performance, and robustness margins against the parameter and unstructured uncertainties.

Optimal feedback control of a twin rotor MIMO system

In this article, optimal feedback control of the twin rotor multiple input–multiple output (MIMO) system is investigated. The twin rotor MIMO system is a benchmark aero-dynamical laboratory model having strongly nonlinear characteristics and unstable coupling dynamics which make the control of such system for either posture stabilization or trajectory tracking a challenging task. This article first briefs the mathematical model of the twin rotor MIMO system and then illustrates the basic idea and technical formulation for controller design. The paper briefly explains the mixed sensitivity design method for feedback control of the twin rotor multiple input–multiple output system laboratory model. This approach has been considered in order to assure high control performance of the system. The simulation results show that the investigated controller has both static and dynamic performance, therefore the stability and the quick control effect can be obtained simultaneously for the twin rotor MIMO system.

The Design of the Simple Structure-Specified Controller of Magnetic Bearings for the High-Speed SRM

Magnetic bearing system controllers using H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> algorithms provide excellent interference rejection capability and robustness. However, in the conventional H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control design, the order of the controller is much higher than that of the plant, making implementation in practical engineering applications difficult. To solve the problem, based on the requirements of the theory of mixed sensitivity design method, this paper designs a simple structure-specified controller of magnetic bearings for the highspeed magnetic levitated switched reluctance motor (SRM) using backpropagation neural network function approximation characteristics. The proposed controller is of lower order than the traditional H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controller, and meets performance of H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controller, which is more suitable for practical implementation. By contrast with the traditional mixed sensitivity controller, results of simulations verify that the controller is reasonable. The controller is applied on the high-speed magnetic levitated SRM platform, and experimental results verify that the controller can achieve control of magnetic bearing systems with good disturbance rejection and robustness.

Disturbance rejection control for non-minimum phase systems with optimal disturbance observer

This paper investigates the disturbance rejection control for stable non-minimum phase (NMP) systems with time delay. A robust disturbance observer (DOB) based control structure is proposed. Specifically, the robust DOB is employed to compensate the uncertain plant into a nominal one, based on which a prefilter is adopted to acquire desired performance. Then, a novel DOB configuration strategy for stable NMP systems is proposed. This strategy synthesizes the internal and robust stability, relative order and mixed sensitivity design requirements together to establish the optimization function. The optimal solution is obtained by standard H∞ theory under the condition of guarantying the presented requirements. We also investigate how the DOB can compensate the uncertain plant into a nominal one. The specifical design procedure is presented for an uncertain plant with both unstable zeros and time delay.

Research of Air-Magnet Active Vibration Isolation System Based on H∞Control

Considering the uncertainty of air-magnet active vibration isolation system (AMAVIS), passive vibration isolation was combined with active vibration isolation, which adopted H∞ control strategies. System identification method was used to get the channel model. By adopting mixed sensitivity design strategy, weighting functions were chosen and H∞ controller was designed. Both simulation results and experimental results show AMAVIS based on H∞ control had satisfying effect of vibration reduction in assigned frequency band.

Robust Optimal Disturbance Observer Design for the Non‐Minimum Phase System

AbstractIn this paper, a design strategy of robust disturbance observer is proposed systematically for stable non‐minimum phase systems. This strategy synthesizes the internal and robust stability, relative order and mixed sensitivity design requirements together to establish the optimization function. The optimal solution is obtained by standard H∞ control theory under the condition of guarantying the presented requirements. Simulation results of a rotary mechanical system show the effectiveness of the proposed strategy.

A novel particle swarm optimization based robust H-infinity control for rotorcrafts

Purpose– The purpose of this paper is to present a novel optimization approach to design a robust H-infinity controller.Design/methodology/approach– To use a modified particle swarm optimization (PSO) algorithm and to search for the optimal parameters of the weighting functions under the circumstance of the given structures of three weighting matrices in the H-infinity mixed sensitivity design.Findings– This constrained multi-objective optimization is a non-convex, non-smooth problem which is solved by a modified PSO algorithm. An adaptive mutation-based PSO (AMBPSO) algorithm is proposed to improve the search accuracy and convergence of the standard PSO algorithm. In the AMBPSO algorithm, the inertia weights are modified as a function with the gradient descent and the velocities and positions of the particles.Originality/value– The AMBPSO algorithm can efficiently solve such an optimization problem that a satisfactory robust H-infinity control performance can be obtained.

Quasipolynomial Approach to Simultaneous Robust Control of Time-Delay Systems

A control law for retarded time-delay systems is considered, concerning infinite closed-loop spectrum assignment. An algebraic method for spectrum assignment is presented with a unique optimization algorithm for minimization of spectral abscissa and effective shaping of the chains of infinitely many closed-loop poles. Uncertainty of plant delays of a certain structure is considered in a sense of a robust simultaneous stabilization. Robust performance is achieved using mixed sensitivity design, which is incorporated into the addressed control law.

Identification and Control of an MR Damper With Stiction Effect and its Application in Structural Vibration Mitigation

This paper presents the parameter identification and control of a magnetorheological (MR) damper with stiction effect and its application to seismic protection of a model two-story structure. This semi-active device is utilized to reduce the vibration of the model structure in response to earthquake excitations. First, modified Bingham and LuGre models which consider the stiction effect and the velocity-dependent nature of the damper force are proposed. The parameters of the models are identified by solving a nonlinear optimization problem. The Bingham model is considered because of its simple structure to be used in linear parameter varying (LPV) design framework. The parameter identification is performed while the MR damper is attached to the structure. These models are verified experimentally for different operating conditions showing an acceptable level of accuracy. The subsequent part of the paper addresses the design of different types of controllers to command the MR damper to suppress the structural vibrations of a model building due to earthquake excitations. Two types of controllers are considered in this study: 1) an <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$H_{\infty }$</tex></formula> inverse control based on the mixed-sensitivity design and 2) a dynamic output-feedback LPV controller. In the former one, an <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$H_{\infty }$</tex></formula> controller is designed for the linear structure and the modified LuGre-based inverse model is used to determine the required voltage from the commanded force. The LPV controller is designed for the combined structure and MR damper based on the modified Bingham model considering the damper velocity as the scheduling parameter. Both controllers are combined with a classical anti-windup scheme to compensate the effect of the saturation on the control voltage. An optimal passive damping design is also obtained for comparison purposes. The performance of the controllers is compared with the passive damping case and clipped-optimal controller for the El Centro and Northridge earthquake inputs with different intensities. The experimental results show the improved performance of the LPV controller design in terms of the maximum acceleration and the RMS values of the structure response.

Design and Analysis of Robust Minimax LQG Controller for an Experimental Beam Considering Spill-Over Effect

In this brief the design and analysis of an optimal robust minimax linear quadratic Gaussian (LQG) control of vibration of a flexible beam is studied. The analysis is performed by transforming the minimax LQG control design problem to its equivalent mixed sensitivity design problem. The first six modes of the beam in the frequency range of 0-700 Hz are selected for control purpose. Among these modes, three modes in the frequency range of 100-400 Hz are used for control, while the other three modes are left as the uncertainty of modeling. Both the model and the uncertainty are measured based on experimental data. The nominal model is identified from frequency response data and the uncertainty is presented by frequency weighted multiplicative modeling method. For the augmented plant consisting of the nominal model and its accompanied uncertainty, a minimax LQG controller is designed. Analysis and tradeoff between robust stability and robust performance is shown by selecting two different choices of uncertainty modeling. Simulation results used to show how the uncertainty weights can be tuned so that the proposed robust controller increase the damping of the system in its resonance frequencies and maintain the robust stability of the feedback system at the same time.

On the prevention of pole-zero cancellation in H∞ power system controller design: A comparison

This paper compares two techniques that are commonly used to prevent the pole-zero cancellation phenomenon inherent to the Riccati-based H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> mixed sensitivity approach. The first technique uses a strategy based on the reformulation of the standard mixed-sensitivity design problem, where the closed loop transfer function from the plant input to the plant output is penalized. The second technique combines the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> optimal control with the bilinear transformation. The effectiveness of the techniques is illustrated by designing power system stabilizers for a simple power system. Computer simulations show that these techniques are effective in improving the damping of the system than the standard mixed sensitivity approach. However, the technique that combines the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> optimal control with the bilinear transformation provides a better damping to the system and is more robust than the technique based on the reformulation of the mixed sensitivity design problem.

Dynamic Compensation of a Synthetic Jetlike Actuator for Closed-Loop Cavity Flow Control

Actuation devices are crucial components of closed-loop flow control schemes. Synthetic jetlike actuators, which are commonly employed in cavity flow control, exhibit a dynamic response that, if ignored, may significantly affect the overall characteristics of the closed-loop system. This paper presents the development and implementation of a dynamic compensator for a synthetic jetlike compression driver actuator which has been successfully implemented for feedback control of subsonic cavity flows. A time-delay model of the actuator dynamics is obtained from experimental data using subspace-based identification methods. The model is designed to match the frequency response of the physical system in a frequency range of interest that covers the resonance frequencies of the cavity. The model is then used for the synthesis of a dynamic controller which employs a Smith predictor in conjunction with an H ∞ mixed-sensitivity design. Order reduction is applied to obtain a low-order digital controller amenable to real-time applications. The compensator is retrofitted to an existing cavity flow control architecture, and used to force the actuator output to closely follow the input commands, thereby compensating undesirable actuator dynamics. Experiments show that the integration of the actuator compensator within the cavity control system significantly improves closed-loop performance.

Design of simply structured robust controllers

A new method is presented for the design of simply structured multivariable controllers that can explicitly meet mixed sensitivity robust performance and robust stability criteria. Currently, most established robust controller design methods are synthesis-based and produce controllers that are often of much higher order than the plant. Based on the technique of diagonal dominance, this method proposes a novel means of directly ‘designing’ a robust controller, which among others, has the benefit that its order can be determined by the designer. By using elementary algebra, it is shown that the Gershgorin disks of a matrix may also be used to bind its singular values in addition to the eigenvalues. This fact is then exploited to create simple envelopes that bind the singular values of the sensitivity and complementary sensitivity functions, which are subsequently used in the design of the diagonal dominance-based controller such that the mixed criteria on the loop transfer function sensitivities may be met. As with other mixed sensitivity design techniques, this method does not guarantee that a controller is feasible for any set of arbitrary specifications. The method is applied to design a mixed-sensitivity controller for a mathematical model of the Rolls–Royce gas-turbine engine.

ROBUST DYNAMIC STIFFNESS DESIGN OF A LINEAR SERVO SYSTEM

As a popular controller used in the industrial servo drives, the pseudo derivative feedback with feedforward (PDFF) scheme has 3 parameters for tuning to achieve a good trade-off design between tracking and dynamic stiffness. However, the two parameters in the feedback path of the PDFF controller are restricted to constant for design simplicity that limits its dynamic stiffness. This paper presents a control design, namely “advanced PDFF controller,” in that the PDFF scheme is kept, but two feedback constant gains are extended to be dynamic. An H∞ mixed sensitivity design is presented to systemically obtain a robust controller for dynamic stiffness design in a linear servo system. Simulation and experimental results are given to show the effectiveness of the proposed design method.

FIXED-ORDER CONTROL OF ACTIVE SUSPENSION: A HYBRID APPROACH

This paper considers the design of a controller for an active suspension benchmark problem. For a plant model of 27th order, a 5th order controller that meets performance specifications in terms of sensitivity and control sensitivity is designed, using a novel Hybrid Evolutionary-Algebraic approach to low-order mixed-sensitivity design. This method combines evolutionary techniques with a Riccati approach by splitting the problem into a convex and a non-convex sub-problem. Simulation results demonstrate that a performance superior to that of previously published results can be achieved.