Root-Locus Methods for Robust Control Systems Quality and Stability Investigations

This work is proposed to continue the discussion of the problems, theoretical foundations and practical features of the construction and synthesis of robust control systems with high gain, allowing us to control multidimensional nonlinear dynamic objects of high dimensional with functional uncertainties. If problems could not be solved at the level where they appeared, it is necessary to rise the level of understanding of the laws of nature, or in the words of master Lui-Shi Chun Qiu (China, 3rd century BC): "The boy of five chi growth leads the bull by the bridle and the bull obeys him in everything. This is because the person in this case follows naturalness" (the laws of nature). The judo philosophy ("soft way") is based on the principles of using the power and energy of the opponent to achieve victory. The purpose of this work is to demonstrate the theoretical aspects and practical features of the methods of synthesis of optimal control systems by the criterion of maximum reproduction accuracy using the example of robust systems, which allow to control dynamic objects with functional uncertainties, including unstable objects, no minimal-phase objects, neutral objects and objects with differentiation properties. The simplicity (at the level of the engineer) and universality, mathematical rigor and physical validity of this approach is based on the judo philosophy: suppressing the dynamics of a functionally uncertain object and external disturbances by the infinitely large gain with the finite control signal and at the same time maintaining sustainability. Theoretically exhaustive solution of the problem of robust control is given by the idea of constructing systems that are stable with an unlimited increase of the gain coefficient. The sustainability properties are valid for optimal systems that were synthesized using quadratic quality functionals that do not explicitly depend on the control signal, and using a restriction on the control signal. It is significant that in contrast to continuous systems with un-measurable disturbances and not well known control object (in which the conditions of invariance imply the use of infinitely large gain), in relay (discontinuous) systems the equivalent effect is achieved with the help of finite control signal. A nice bonus is the highest accuracy which leads to mathematically zero error of regulation, thus all error coefficients (of position, speed, acceleration, acceleration derivative, etc.) is also equal to zero in the presence of external and internal interferences. In fact, the optimal accuracy control system is equivalent to a system with astatism of the n-th order: the regulator contains n serial connected integrators.

One of the actual problems for the theory and practice of control of dynamic objects is the development of methods for research and synthesis of control systems of multidimensional objects. The paper proposes a universal approach to construct Lyapunov vector functions directly from the equation of state of control system and a new gradient-speed method of Lyapunov vector functions to study aperiodic robust stability of linear control system with m inputs and n outputs. The study of aperiodic robust stability of automatic control systems is based on the construction of Lyapunov vector functions and gradient-speed dynamic control systems. The basic statements of Lyapunov's theorem about asymptotic stability and notions of stability of dynamic systems are used. The representation of control systems as gradient systems and Lyapunov functions as potential functions of gradient systems from the catastrophe theory allow to construct the full-time derivative of Lyapunov vector functions always as a sign-negative function equal to the scalar product of the velocity vector on the gradient vector. The conditions of aperiodic robust stability are obtained as a system of inequalities on the uncertain parameters of the automatic control system, which are a condition for the existence of the Lyapunov vector-function. A numerical example of synthesis of aperiodic robustness of a multidimensional control object is given. The example shows the main stages of the developed synthesis method, the study of the system stability at different values of the coefficients k, confirming the consistency of the proposed method. Transients in the system satisfy all requirements

We propose a robust control system which has robustness for disturbance and can deal with a nonlinear system with partially unknown structure by fusing reinforcement learning and robust control theory. First, we solved an optimal control problem without using unknown part of functions of the system, using neural network and the repetition learning of reinforcement learning algorithm. Second, we built the robust reinforcement learning control system which permits uncertainty and has robustness for disturbance by fusing the idea of H infinity control theory with above system.

This paper discusses an application of Robust Model Matching (RMM) to the spill position control of a fuel injection pump. Since the fuel injection servo mechanism is soaked in fuel oil, the parameters of the plant vary due to differences in the viscosity coefficient caused by wide changes in temperature. The invariable fuel injection characteristic is required to meet the demands of the drivability, exhaust emissions and fuel consumption, even though the parameters change. The RMM is an idea which makes up a robust control system against parameter uncertainties.In this paper, we design a robust discrete-time control system based on the RMM: (1) For the low sensitivity, to make small pulse transfer functions from equivalent disturbances to controlled variables. (2) For the robust stability, to increase the margin of pulse transfer functions from conceptual inputs to control variables. The experimental results show that this robust compensator makes up a robust control system against the parameter variations due to the change in temperature. And it is confirmed that the idea of the RMM is effective for the fuel injection pump which includes the variations, identification errors, friction, hysteresis and delay time of the calculation.

The antilock braking systems are designed to maximize wheel traction by preventing the wheels from locking during braking, while also maintaining adequate vehicle steerability; however, the performance is often degraded under harsh road conditions. In this study, a robust hybrid control system is developed for the antilock braking systems. In this design method, the robust hybrid control system is comprised of a hybrid controller and a robust controller to achieve a desired H/sup /spl infin// control performance. The hybrid controller containing a fuzzy uncertainty observer is the principal controller, and the robust controller is designed to achieve the desired H/sup /spl infin// tracking performance. Finally, simulations are performed to demonstrate the effectiveness of the proposed robust hybrid control system for antilock braking control under various road conditions.

The problem of structural-parametric synthesis of automatic control systems (ACS) of technological objects is deter-mined by the multi-dimensionality, multi-connectedness and nonlinearity of their mathematical models. Despite the indicated properties of such objects, traditional linear systems based on PID-algorithms are still used for process control. Since the synthesis of linear systems using input-output models does not take into account the multi-dimensionality and mutual influence of state coordinates, such systems increase the influence of parametric and signal perturbations on the quality of control processes. The increasing requirements for the quality and efficiency of technological processes control made it expedient to apply the control principle by the state vector based on the use of uninertial state regulators or combined state regulators including flexible feedback on the derivative state coordinates or state coordinate integrals. The research uses methods of system analysis of technological processes as control objects, methods of automatic control theory, methods of control systems synthesis on the state regulators basis, meth-ods of computer simulation. The linearized mathematical model of liquid-phase chemical reactor in the state space has been obtained. It has been established that the investigated object has the property of free movement stability and it is fully controlled in the state space. The problem of synthesis of a single-channel concentration vector control system in a chemical reactor using state regulator has been solved. The parameters of state regulator settings have been determined using the method of modal control. The efficiency of the automatic control system on the basis of the state regulator with an integral component has been shown using the method of computer simulation of the ‘nonlinear object – linear control subsystem’ complex. It has been demonstrated that the absence of an integral component in the control algorithm structure leads to a great static error of regulation. To eliminate the static error of control and ensure the robustness of the control system, it is recommended to introduce an integral component into the structure of state controller. This ensures the efficiency of the control system both for the case of complete measurement of the state vector and for the case of measurement of the output controlled variable only.

Rotorcraft flight control systems present design challenges which often exceed those associated with fixed-wing aircraft. First, large variations in the response characteristics of rotorcraft result from the wide range of airspeeds of typical operation (hover to over 100 kts). Second, the assumption of vehicle rigidity often employed in the design of fixed-wing flight control systems is rarely justified in rotorcraft where rotor degrees of freedom can have a significant impact on the system performance and stability. Proposed herein is a methodology for the design of robust rotorcraft flight control systems utilizing Quantitative Feedback Theory (QFI'), a technique which accounts for variability in the dynamic response of the controlled element in the design of robust control systems. It was developed to address a Multiple-Input-Single-Output (MISO) design problem, but was extended to the address the Multiple-Input-Multiple-Output (MIMO) flight control system (FCS) design problem of a UH-60 Black Hawk Helicopter. Inherent conservatism in this design technique leads to limitations in its utility. A modified QFI' approach proved a viable method for designing robust MIMO flight control systems. An analysis of the two flight control system design methodologies is presented.

This paper proposes a new robust feedforward tracking servo system for optical disk recording systems in the case of a sudden disturbance for the optical disk recording system. In optical recording systems, the tracking servo system must suppress tracking error below its tolerance. This paper designs the robust feedback control system by using the coprime factorization and disturbance observer. The proposed robust feedback control system suppresses the sudden disturbance caused by walking and running. The detecting signal of optical disk recording systems is only a tracking error. Hence, the feedforward controller of the proposed tracking control system is constructed based on both Zero Phase Error Tracking (ZPET) control theory and prediction of tracking error. The experimental results point out that the proposed tracking servo system has a quick and precise tracking response and keeps the residual tracking error below its tolerance. © 2006 Wiley Periodicals, Inc. Electr Eng Jpn, 156(4): 60– 68, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20257

Since the computed torque or inverse dynamics control techniques are based on a good understanding of the controlled system dynamics and even its environment; the objection for the real-time application is unrealizable for the unknown systems. To tackle this problem, this study developed a robust adaptive fuzzy sliding-mode control system based on the H/sup /spl infin// tracking design technique. The developed control system is comprised of a fuzzy controller and a robust controller. The fuzzy controller is utilized to approximate an ideal controller by the tuning algorithms based on the Lyapunov sense, and the robust controller is designed to achieve H/sup /spl infin// robust tracking performance. To investigate the effectiveness of the developed control system, it is applied to a wing rock motion control system. Simulation results demonstrate that the proposed control system can achieve favorable tracking performances with unknown system dynamics.

The controlled atmospheric re-entry associated with the precision soft-landing of Reusable Launch Vehicles (RLVs) on Earth is very challenging as it depends on multiple parameters [1]. Over the last decade, the cost-effectiveness of such a technology has been finally demonstrated with the successful recoveries of SpaceX’s Falcon 9 first-stage rocket first [2], then followed by other companies such as the Rocket Lab’s Electron micro-launcher [3]. This breakthrough has been made possible by the development of advanced and robust computational methods able to generate in real time the flight conditions and to command the optimal vehicle's deflections accordingly to achieve a safe pinpoint landing. Indeed, during an Earth atmospheric re-entry, the vehicle is subjected to fast system dynamics changes partly induced by external loads associated with the terrestrial environment (e.g., lift, drag, wind and gusts), but also by the actuation commands to answer the landing constraints satisfaction and the vehicle integrity preservation. All those involve uncertainties and nonlinearities, which lead to vehicle’s instability and therefore give reason why for a highly performant Guidance, Navigation and Control system implementation [4]. More particularly, one of the critical aspects is the design of a robust control strategy capable of counteracting the previously defined disturbances and uncertainties while satisfying the strict accuracy requirements associated with the pinpoint landing [5]. As demonstrated by the current state-of-the-art on control design for launchers [6-7], the classical linear control theory represents a rich heritage with a lot of applications. This choice was motivated by its relative easiness of implementation and the possibility to use gain-scheduling techniques to adapt to nonlinear systems. Nevertheless, these techniques are well-adapted to the control system design of single-input single-output systems, such as for example a reusable rocket using a Thrust Vector Control (TVC) system as the unique actuator. The implementation of multiple-input multiple-output control systems becomes then complex since every channel is addressed in a single-loop fashion. This capability is however required for the future generation of reusable rocket, using also aerodynamic steering based on fins in addition to the TVC system for enhancing control authorities. Moreover, model uncertainties are not accurately considered in the design process, developed only with nominal conditions and stability margin requirements. For all these reasons, it results in an extensive (both in terms of time and cost) Verification and Validation campaign with many iterations and Monte-Carlo analyses to assess the performance and robustness of the control system. To overcome these drawbacks, the H-infinity family of methods, introduced a few years ago [8], provides with a powerful solution for robust control design. It relies on defining the control requirements in the frequency domain in terms of weighting functions and minimising the maximum gain of the resulting weighted system from the exogenous inputs to the outputs to be controlled. Moreover, the control-plant interaction is modelled through a Linear Fractional Transformation (LFT) representing the feedback action. Finally, the structured H-infinity method [9] allows to directly impose a specific control structure – like a Proportional-Integral-Derivative (PID), enabling the re-use of gain-scheduling techniques – and to consider parametric uncertainties for enhanced robustness. This paper studies the synthesis of a robust control system via structured H-infinity for the RLV atmospheric re-entry problem. First, the nonlinear 6-Degree-of-Freedom (6-DoF) RLV re-entry dynamics are simplified into a linear model and then linearised along a reference trajectory to get the nominal LFT of the system, then augmented with parametric uncertainties. The model covers the atmospheric re-entry and vertical landing of a first-stage rocket equipped with a TVC system and steerable planar fins. The controllers are built at different points of the re-entry trajectory, using the structured H-infinity framework through PID-like structures. Weighting functions considering the control objectives and requirements of a realistic RLV re-entry scenario are implemented. A robust stability analysis of the obtained system is performed via classical stability margins and structured singular value. Finally, the controllers are gain-scheduled and validated via Monte-Carlo analyses, using a nonlinear 6-DoF RLV re-entry dynamics simulator equipped with successive convex optimisation guidance. The performance of the resulting guidance and control architecture is compared with the baseline developed in previous works [10], using a TVC system only and classical linear feedback control through gain-scheduled PID controllers. This study lies within the ASCenSIon (Advancing Space Access Capabilities - Reusability and Multiple Satellite Injection) project, an innovative training network funded within H2020.

For field tasks, it is quite challenged to operate in a complex environment for the underwater robots, especially for those with multiple control surfaces due to different response and gain characteristics. To this end, this paper develops a highly integrated robotic dolphin followed by a robust motion control system. For better maneuverability and fault-tolerant capabilities, a newly-designed robotic dolphin is presented, owning a wide array of sensors and multiple control surfaces, in which passive flukes are particularly applied. On this basis, a robust motion control system is proposed, including a depth controller based on velocity-related allocation strategies and a heading controller based on clearance compensation. In detail, considering the degradation of motion performance caused by passive flukes, a sliding mode controller for gain uncertainty and an allocation-related parameter tuning strategy for inputs response characteristics are designed. Extensive simulations and aquatic experiments are conducted, and the obtained results demonstrate the satisfied maneuverability of the designed prototype and the effectiveness of the proposed methods. This study can lay a foundation for further development of robotic dolphins with a robust motion system to execute complex tasks in the field. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is inspired by the issue of robust motion control system for a newly-designed practical robotic dolphin that possesses a passive tail and redundant control surfaces. The traditional methods are usually susceptible to uncertainties in the passive tail gain, exhibiting degraded control performance. Moreover, control oscillations and slow convergence speed often occur caused by neglecting the characteristics of different control surfaces, including response patterns and clearance. This paper suggests a robust depth controller based on velocity-related allocation strategies and a robust heading controller based on clearance compensation. Specifically, an allocation-related parameter tuning strategy is given by considering inputs response characteristics, including response speed, saturations, and hydrodynamic force variation patterns. To guarantee fine regulations of heading control, a nonlinear disturbance observer (NDOB)-based clearance compensation is proposed. Extensive aquatic experiments on the newly-designed robotic dolphin verified the effectiveness of the proposed methods. It is envisioned that all these presented results can provide valuable engineering practice insights for industry practitioners.

In the paper, the impact of atmospheric turbulence on the Unmanned Aerial Vehicles (UAV) motion is studied. The models of Dryden turbulence are discussed, and the airplane models of lateral directional under the atmospheric turbulence are deducted, the application of linear matrix inequality (LMI) is used to design a kind of robust flight control system based on H∞ control theory. The effect of the roll angle control of Robust flight controller is compared to that of PID controller and several characteristics of the state points in full-flight envelope are selected to validate the robust flight control system. The analysis shows that the designed controller is better than PID controller to attenuate the disturbance, and the flight control system has good dynamic performance and satisfactory robustness.

This paper discusses designing and implementing an adaptive thrust distribution algorithm on the already robust control system for serial split-hull underwater vehicles to maximise operational efficiency. Split-hull underwater vehicles are gaining popularity in subsea operations due to their flexible hyper-redundant design and enhanced manoeuvrability. These features facilitate them to replace conventional solutions, including torpedo-shaped Autonomous Underwater Vehicles (AUVs) and Remotely Operated Vehicles (ROVs). The field of research is currently undergoing a considerable transition toward operations on subsea activities that are more economical and efficient. Thus, implementing a robust and energy-efficient control system is of utmost importance. The robust Super Twisting Algorithm (STA) based control system is used on the vehicle, and an adaptive thrust distribution algorithm is proposed and implemented to optimise the energy efficiency further. The work involves modelling the vehicle, fluid forces, torque effects, and thruster configuration matrix and implementing the adaptive weight distribution on the STA-based control system. With the help of simulations, the improvements in the control system are proved.

In this paper, we overview the design and development of robust multivariable control design to highlight some of the pragmatic automotive engineering control issues with an emphasis on a non-trivial application of Hybrid Electric Vehicle (HEV) Torque Management. We shall outline that most existing torque management approaches are not model-based dynamical systems, or do not address key concepts of robust stability and performance. We shall also discuss some advantages that robust control systems could offer to a wider automotive control applications. In part II, we show representative simulation results verifying that robust control systems design could be a breakthrough to the production of hybrid electric vehicles by yielding significant improvements on the emission, fuel consumption, calibration time and cost. Our contribution is aimed at the fact that cutting-edge robust controllers could be broadly adopted to tackle increasingly challenging problems of the automotive industry.

Undesirable environmental effects of industrial development can be significantly reduced by advanced process control strategies. Although criteria of particular process control problems are often mutually contradictive, a reasonable compromise solution reflecting manufacturing and environmental considerations can be found. This problem presents a challenging task due to the high complexity of typical manufacturing processes. Development of the theoretical fundamentals for the solution of relevant mathematical modeling, control, information, software development and implementation problems is proposed. The study utilizes the principle of binarity formulated for variable-structure systems, Rasumihin's principle (1988) and vector Lyapunov's functions applied to robust multipurpose automatic control systems.