Robust Multi-loop PI/PID Controller Design for Multivariable Processes

트롱 영남대학교 대학원 2009 국내박사

다중루프 비례-적분/비례-적분-미분(PI/PID) 제어기는 그것이 가진 다양한 장점들 - 산업적 전망, 효율, 생산성 및 품질 향상 – 로 인하여 현재 산업용 제어기로 가장 널리 사용되고 있는 제어기 중의 하나이다. 다중루프 제어시스템은 보다 효율적인 운전전략을 위한 요구사항을 충족하면서 이의 구현을 위한 진보된 도구의 사용을 가능하게 한다. 또한 명확한 이론적 근거를 가지고 있어 이해가 쉬우며 다변수 제어시스템보다 조율을 위한 변수가 적어 경제적 이익을 극대화하고 실제적 응용에 필수적인 요건인 루프 고장에의 강건성 등을 갖추고 있다. 이러한 이유로 다중루프 PI/PID 제어기의 설계를 위한 수많은 방법들이 수년에 걸쳐 공정제어 관련 문헌에 제시되어 왔다. 그 중에서도, 잘 알려져 있는 IMC-PID 접근방법은 설계와 구현 상의 효율성과 강력한 구도로 빈번히 사용되고 있는 방법이다. 이 방법은 강건성과 성능 간의 절충을 한 개의 설계변수, 즉, IMC 필터 상수 또는 닫힌루프 시상수를 조정하여 달성할 수 있기 때문에 제어 엔지니어와 연구자들에게 매우 매력적이다. 이것은 IMC-PID 접근방법이 가지는 매우 유용한 특성으로서 다중루프 제어시스템이 강건 안정성 조건을 만족하도록 조율될 수 있도록 해준다. IMC-PID의 접근법과 비슷한 특징을 가지는 다중루프 PI/PID 제어 시스템을 위한 직접 합성법 또한 많은 저자에 의해 연구되고 있다. 이 논문에서는 다중루프 PI/PID 제어기의 강건한 설계를 위한 새로운 해석적 방법이 일반화된 다중루프 IMC-PIC 접근법과 직접 합성법을 근간으로 제안되었다. 제안된 방법들은 다중시간지연을 가지는 다중변수 공정에서 원하는 닫힌루프 응답을 달성하고자 하는데 목적이 있다. 입력/출력 변수들 간의 상호작용은 다중루프 되먹임 제어 루프에서 공통적으로 접하는 현상으로서 다중루프 시스템에서의 만족스러운 성능 구현에 심각한 장애로 작용할 수 있는 것으로 알려져 있다. 이 장애사항을 극복하기 위한 방안으로서, 가중 합 Mp 기준과 다중루프 Ms 기준 등과 같은 몇 가지 방법들이 상호작용 효과를 완전하게 반영하기 위하여 제안되었다. 강건 안정성과 성능도 본 연구에서 고려된 두 가지 중요한 요소이다. 기본적으로, 실제 시스템과 그 모델 간의 차이점은 닫힌루프의 불안정성을 야기할 수 있다. 제어시스템이 다양한 불확실성 하에서도 만족스럽게 제어될 때 강건하다고 한다. 제안된 다중루프 제어 시스템은 강건 안정성과 성능을 고려하여 설계되었다. 제안된 방법의 우수성을 증명하기 위해 여러가지 시뮬레이션을 수행하였으며 그 결과 제안된 방법에 의하여 설계된 다중루프 PI/PID 제어시스템은 빠르고 균형 잡힌, 그리고 최소의 Integral Absolute Error (IAE) 값을 가지는 강건한 응답을 가져옴을 확인하였다. In recent years, multi-loop proportional-integral/proportional-integral-derivative (PI/PID) controllers have become one of the most widely used industrial controllers. The reason for this popularity is due to the industrial perspective, efficiency, improved productivity, and product quality goals since multi-loop control systems satisfy all demands for more effective operational strategies to be integrated in the production line and allows more advanced tools to be implemented. In addition, they are also self-explanatory and easily understood by their sound theoretical foundation, and require fewer parameters to tune than multivariable controllers, which help to maximize economic benefits. Moreover, loop failure tolerance can be easily obtained with the multi-loop control system, which is very important for practical applications. Therefore, various design methods of multi-loop PI/PID controllers have been suggested in the literature over the years. Among them, the well-known IMC-PID approach is often utilized because of its powerful framework and effectiveness for the designing and implementation. It is attracted to control engineers and academics because the tradeoffs between robustness and performance are directly related to one design parameter as the time constant of IMC filter or the closed-loop time constant, equivalently. This is very useful characteristic of the IMC-PID approach, which guarantees multi-loop control systems to be tuned satisfying the robust stability condition. Furthermore, the direct synthesis for the design of multi-loop PI/PID controllers that has the similar features as the IMC-PID approach is also considered by many authors. In this thesis, the novel analytical methods based on the generalized IMC-PID approach and direct synthesis are proposed for the different states of the robust design of multi-loop PI/PID controllers. The proposed methods are aimed at achieving the desired closed-loop responses for multivariable processes with multiple time delays. It is known that the interactions between input/output variables are a very common phenomenon encountered in control loops, which can be a serious obstacle for achieving a good performance of the multi-loop control system. To overcome this impediment, several techniques are suggested for taking interaction effects fully into account such as weighted sum Mp criterion, multi-loop Ms criterion, etc. Stability and performance robustness are also two important issues that should be considered in this work. Basically, the gap between the actual system and its model may be major cause of the closed-loop instability. The control system is robust if it performs satisfactorily under parameter variations and various possible uncertainties. Therefore, the proposed multi-loop control system is essentially designed by considering robust stability and performance analysis. Several simulation studies are carried out to demonstrate the superiority of proposed methods. The simulation results show that multi-loop PI/PID control systems designed by proposed methods achieve fast, well-balanced, and robust responses with minimum integral absolute error (IAE) values.

A Study on Transient and Robust Control Performance Enhancement via Boundary Condition and Reinforcement Learning-based Hybrid Strategy

아마레 네비옐룰 다니엘 명지대학교 대학원 2025 국내박사

This dissertation presents a comprehensive study of robust control strategies aimed at improving both robustness and transient-state performance in systems subject to uncertainty. The research focuses on two primary control methods in particular: disturbance observer (DOB)-based control and internal model principle (IMP)-based control, offering novel solutions to overcome key implementation challenges. The study begins by proposing a dual proportional-integral observer (PIO)-based robust scheme to address key implementation challenges with the cascade control method. To showcase the performance of the proposed robust cascade controller, a magnetic levitation system is considered. In addition to enhancing the widely used cascade control method, the proposed controller is designed to maintain nominal performance under both parameter uncertainties and external disturbances while avoiding the computational burden of advanced control schemes. Performance validation, grounded in singular perturbation theory, confirmed the controller's ability to achieve nominal performance, as demonstrated through extensive simulations. The dissertation then investigates the stability issues associated with high-gain disturbance observer-based control (DOBC) under relative degree uncertainty. By establishing stability boundary conditions using the Routh-Hurwitz criterion, the research provides crucial design guidelines for maintaining system stability while balancing the trade-off between transient-state performance and robustness. This analysis enables the safe integration of high-gain DOBs in reduced-order model-based control (ROMBC) systems without compromising stability. While the established design criteria help prevent closed-loop instability in DOBC under relative degree uncertainty, challenges associated with high-gain remain significant. A commonly adopted alternative for achieving robustness without high-gain issues is IMP; however, IMP often suffers from overshoot and oscillations following transient events. To overcome these limitations, this study proposes a hybrid control structure that combines IMP-based controllers with cascade subcontrollers optimized for transient response. A deep Q-network (DQN)-based state update and switching logic is used to ensure seamless transitions between the control modes. Validation through simulations and experimental tests on a DC motor position control system confirmed the effectiveness of the hybrid controller in enhancing transient performance and robustness. The controller successfully addressed performance trade-offs, delivering faster transient response and nominal performance recovery. The dissertation concludes by summarizing the overall contributions of the studies presented and highlighting potential future research directions. 본 논문은 불확실성이 존재하는 시스템에서 강인성과 과도 상태 성능을 향상시키기 위한 강인 제어 전략에 대한 포괄적인 연구를 제시한다. 두 가지 주요 제어 방법인 외란 관측기 기반 제어(DOB)와 내부 모델 원리(IMP) 기반 제어에 중점을 두고, 두 방식의 구현 과정에서 발생하는 문제를 해결하기 위한 새로운 제어기 설계 방법을 제안하였다. 본 연구는 제어 시스템의 강인성을 개선하기 위한 듀얼 비례-적분 관측기(PIO) 기반 강인 캐스케이드 제어기를 제안하는 것에서 시작한다. 제안된 제어기는 고급 제어 기법의 높은 계산 비용을 피하면서 파라미터 불확실성과 외란이 존재하는 상황에서도 공칭 성능을 유지하도록 설계한다. 특이 섭동 이론을 기반으로 한 성능 해석을 통해 제어기가 공칭 성능을 달성할 수 있음을 자기부상 시스템에 대한 시뮬레이션을 통해 확인하였다. 이어서 고이득 DOB를 사용한 저차 모델 기반 제어기(ROMBC)에서의 안정성 문제를 조사한다. Routh-Hurwitz 판별법을 이용한 안정성 경계 조건을 설정하여 과도 상태 성능과 강인성 간의 균형을 유지하면서 시스템 안정성을 유지하기 위한 중요한 설계 지침을 제시하였다. 이러한 분석은 고이득 DOB를 ROMBC 시스템에 안전하게 통합하여 안정성을 손상시키지 않도록 할 수 있다. 마지막으로 고이득 DOB의 한계를 극복하기 위해 본 연구는 과도 응답에 최적화된 캐스케이드 제어기와 IMP 기반 제어기를 통합하는 하이브리드 제어 구조를 제안한다. 다양한 시스템 조건에서 성능을 향상시키고 매끄러운 전환을 보장하기 위해 제어 전략을 동적으로 전환하는 심층 Q-네트워크(DQN)를 사용한다. 오프라인에서 학습된 DQN 모델은 두 가지 제어 접근법의 장점을 결합하여 하이브리드 구조를 최적화할 수 있음을 확인하였다. 시뮬레이션 및 DC 모터 시스템에 대한 실험 검증을 통해 하이브리드 제어기의 강인성 및 성능 회복 능력을 테스트하였다. 제안하는 방식은 성능 트레이드오프를 성공적으로 해결하고 더 빠른 과도 응답 및 공칭 성능 회복을 달성함을 확인하였다.

Wasserstein Distributionally Robust Control and Optimization for Autonomous Systems

아스트힉 서울대학교 대학원 2023 국내박사

Distributionally robust control (DRC) and optimization (DRO) have recently become popular approaches for handling uncertain distributional information in stochastic systems with accuracy. In this work, we develop novel control methods for autonomous systems in situations where only limited information is available about the uncertainties in system or environment models. To achieve this, we estimate the uncertainty distribution using disturbance samples or state-of-the-art learning techniques and construct an ambiguity set around the nominal distribution. Our ambiguity set contains all distributions whose Wasserstein distance from the nominal one is less than the given radius. We then solve the optimal control problem with respect to the worst-case distribution within the ambiguity set. However, the resulting problem is infinite-dimensional and intractable. Therefore, we apply modern tools from DRO to develop several methods for solving the Wasserstein DRC (WDRC) problem in various settings with different theoretical properties and applications. Our first method proposes a novel safety specification tool, the distributionally robust risk map (DR-risk map), for motion planning and control of a mobile robot in a learning-enabled environment. The DR-risk map reliably assesses the conditional value-at-risk of collision with obstacles whose movements are inferred by Gaussian process regression. Our tool measures the risk under the worst-case distribution within the ambiguity set to account for errors in the inferred distribution. To resolve the intractability, we develop a semidefinite programming (SDP) formulation that provides an upper bound of the risk. We apply the DR-risk map to perform motion planning and control of autonomous systems in learning-enabled environments. Our second method introduces a novel learning-based motion control tool that uses an uncertainty propagation scheme based on an unscented transform to achieve better prediction accuracy and computational efficiency. In addition, this approach replaces the DR-risk constraint for any arbitrary safety loss function with a novel simpler upper bound. The WDRC framework can be applied not only to fully observable systems but also to partially observable systems, which are more realistic. In our next stage, we focus on the WDRC problem for partially observable linear stochastic systems and present a new approximation scheme. This method leverages the Gelbrich bound of the Wasserstein distance to penalize deviations from the nominal distribution. We derive a closed-form expression for the optimal control policy and a tractable SDP problem for the worst-case distribution policy in both finite-horizon and infinite-horizon average-cost settings. Our proposed method features several salient theoretical properties, such as a guaranteed cost property and a probabilistic out-of-sample performance guarantee, demonstrating the distributional robustness of our controller. Furthermore, the resulting controller ensures the closed-loop stability of the mean-state system. Finally, we present a novel distributionally robust differential dynamic programming algorithm for approximately solving the general nonlinear WDRC problem in a tractable and scalable way. It provides a closed-form control policy for nonlinear stochastic systems and therefore is applicable to learning-enabled environments. Our approach features a novel decomposition of the value function and its iterative local-quadratic approximations, making our method tractable and scalable without the need for numerically solving any minimax optimization problems. We analyze and demonstrate the effectiveness of our methods through simulation studies on various systems, ranging from oscillator synchronization to autonomous driving problems. Our contributions enable controllers that can handle distributional uncertainties in both system and environment dynamics, as well as learning outcomes. 분포 강건 제어(Distributionally robust control, DRC)와 분포 강건 최적화(Distributionally robust optimization, DRO)는 최근에 스토캐스틱 시스템에서 부정확한 분포 정보를 처리하는 효과적인 방법으로 등장하였다. 본 연구에서는 시스템 또는 환경 모델의 불확실성에 대한 제한된 정보만이 주어진 자율 시스템에 대한 새로운 제어 방법을 개발한다. 이를 위해, 주어진 데이터를 이용하여 불확실성 분포를 추정하고, 해당 분포를 중심으로 ambiguity set을 구성한다. Ambiguity set은 추정된 분포로부터 Wasserstein 거리가 주어진 반지름보다 작은 모든 분포를 포함한다. 추정 결과의 불확실성을 고려하기 위해 ambiguity set 내에서 최악의 경우 분포에 대한 최적 제어 문제를 푼다. 그러나 이 문제는 무한 차원 최적화 문제이기 때문에, DRO 분야의 최신 도구를 적용하여 Wasserstein DRC(WDRC) 문제를 계산 가능한 형태로 바꾸는 범용적인 여러 방법을 개발한다. 이 방법들은 다양한 이론적 특성을 가지며, 여러 응용 분야에서 탁월한 성능을 보인다. 본 연구에서 제안하는 첫 번째 방법은 학습 가능한 환경에서 이동 로봇의 동작 계획과 제어를 위한 분포적으로 강건한 위험 함수(DR-risk map)이라는 새로운 안전 평가 방법을 제안한다. DR-risk map은 Gaussian process regression(GPR)에 의해 움직임이 추론되는 장애물과의 충돌 위험성을 안정적으로 계산한다. 이 방법은 추론된 분포의 오류를 고려하기 위해 ambiguity set 내 최악의 분포에 대한 위험을 측정한다. 무한차원 특성으로 인한 문제를 해결하기 위해, DR-risk map의 상한을 해로 갖는 semidefinite programming(SDP) 문제를 유도한다. 더 나아가 DR-risk map을 학습 가능 환경에서 자율 시스템의 동작 계획 및 제어를 수행하기 위해 적용한다. 본 논문에서 제안하는 두번 째 방법은 unscented transform을 사용하는 새로운 학습 기반의 동작 제어 도구이다, 이 방법은 GPR에서 이루어지는 불확실성 전파에 unscented transform을 적용함으로써 분포 추정 정확성과 계산 효율성을 향상시킨다. 또한, 임의의 안전 손실 함수에 대한 DR-risk 제약 조건을 대체하는 새로운 상한을 제시한다. 분포 겅건 제어의 아이디어는 완전 관찰 가능 시스템보다 현실적인 부분적 관찰 가능한 스토캐스틱 시스템에도 적용 가능하다. 특히 본 논문에서는 부분적 관찰 가능한 선형 스토캐스틱 시스템을 위한 WDRC 문제를 고려하고, Wasserstein 거리의 Gelbrich 상한을 이용한 새로운 근사 문제를 제안하고, 최적 제어 정책의 closed-form 표현과, 최악의 분포 정책을 찾는 SDP 문제를 finite-horizon 및 infinite-horizon 설정에서 모두 유도한다. 제안한 방법은 out-of-sample performance에 대한 보장과 안정성 등 여러 가지 중요한 이론적 특성을 가지며, 제어 정책의 분포 강건성을 보장한다. 마지막으로, 일반적인 비선형 WDRC 문제를 해결하기 위한 새로운 분포 강건한 differential dynamic programming 방법을 제시한다. 이 방법은 비선형 스토캐스틱 시스템에 대한 closed-loop 제어 정책을 제공하며, 학습 가능한 환경에도 적용 가능하다는 측면에서 열거한 방법론들을 포괄한다. 이 접근법은 value function의 분해와 국소적 이차 근사를 특징으로 하여, 최소-최대 최적화 문제를 수치적으로 풀 필요 없이 효율적이고 고차원 시스템에도 쉽게 적용 가능하다. 다양한 시스템에서 실증적 연구를 통해 본 논문에서 소개된 방법론들의 성능과 효율성을 분석하고 입증한다. 결론적으로, 본 연구에서 제안한 방법들을 통하여 시스템 및 환경, 그리고 추론 결과의 분포적 불확실성을 체계적으로 다룰 수 있는 제어 정책을 제공한다.

Model reduction and robust controller design scheme for structural acoustics

장우석 Pennsylvania State University 2001 해외박사

As science and technology progress, people seek a better quality of environment. Sound and vibration have become one of the important factors for determining such quality. Many engineers in acoustics, structures, electronics, materials and mathematics have explored control and structural acoustics to reduce the level of sound and vibration that surround our living and working environments. Structural acoustics explains the interaction between acoustic wave and structural vibration. This interaction involves either sound transmission or reflection from the structure. Proper control of structural vibration can control the reflection and/or transmission of the sound wave. There have been many research efforts to develop simple, reliable, high performance and wide operation frequency band control algorithms and control devices. Much progress and many achievements in this technology have been reported in related literature. Still, these reports show the need for further development in practical and commercially feasible application. This thesis research was devoted to developing a feasible control system for structural acoustics. Simplicity and robustness of the system are the key issues in the controller design concept. This study was also devoted to building a bridge between state space based control theories with structural acoustics. Simplicity of structure models and controllers was realized by developing the concept of the Modal Hankel Singular Value (MHSV) based model reduction method and fabrication of analog controllers. The MHSV is a modified version of the Hankel Singular Value (HSV) that is popularly used for model reduction in many state space-based control applications. However, MHSV is developed for a modal coordinates system that is more useful in describing vibrating structures than state space. Analog controllers are designed from the transfer functions of controllers, which has great advantage over digital controllers in simplicity and cost. Secondly, robust control theory is exploited for the design of controllers. In contrast to optimal control, which is designed to minimize the square norm of performance index variables, this control theory aims at reduction of the infinity norm of the variables. It delivers not only sufficient reduction of the variables in a specified frequency band, but also strong robustness in the control performance. In addition, the uncertainty of the vibrating structure model is included in the controller design in terms of modal parameters. This results in a control system that is robust to the uncertainty of modal parameters. Hence, the control system will be more reliable in a real application. Uncertainty analysis of the control systems was added to quantitatively describe the robustness of the control system. It identifies which parameter of the model is critical to the control performance. It is expected that this analysis can provide a guideline for further development of a more robust control system. This simple and robust controller design for structural acoustics is applied for controls of sound transmission and sound reflection, numerically and experimentally. MHSV shows good model reduction of finite element based structure models. Numerical and experimental results of both transmission control and reflection control show good agreement, which supports the validity of the proposed control methods. The analog control circuit is easier and cheaper to be miniaturized in a microchip than digital one. The proposed controller design method for structural acoustics application would be more practical if such a miniaturized chip were used as a controller.

Robust Vehicle State Estimation and Lateral Control Strategy for Autonomous Driving

성준영 한양대학교 대학원 2025 국내석사

Robust Vehicle State Estimation and Lateral Control Strategy for Autonomous Driving Jun Yeong Seong Department of Future Mobility The Graduate School Hanyang University The capabilities of modern vehicles are increasingly reliant on the performance of integrated software. Advanced driver assistance systems (ADAS) have long been employed to improve driver safety and vehicle control. With advancements in both software and ADAS technologies, fully autonomous driving is now within reach, offering significant potential to improve safety and comfort further. The push for autonomous driving has stimulated significant research into vision, path planning, and control technologies. Vehicle motion control can be divided into two primary categories: longitudinal and lateral control. Lateral control is critical to vehicle safety, as failures in managing slip or roll can have catastrophic consequences. Like all control systems, effective lateral control requires accurate knowledge of both the vehicle’s state and the environment, along with an appropriate control algorithm. State and parameter estimation in lateral control is particularly important, as lateral vehicle signals are usually small and easily affected by noise. Moreover, the lateral dynamics between the road and tire is highly nonlinear and constantly changing. This challenge is often encapsulated in the estimation of tire cornering stiffness, a parameter that has been extensively studied. The difficulties in accurately obtaining lateral parameters and states introduce a high potential for errors, necessitating robust control algorithms for lateral control. This paper tackles the lateral control problem by introducing a robust lateral vehicle control system with two core components for control robustness and accuracy: a tire cornering stiffness and vehicle sideslip angle estimator, and a robust model predictive lane-keeping controller paired with a cornering stiffness uncertainty estimator. The estimator is designed to obtain real-time cornering stiffness and sideslip angle simultaneously, using signals accessible from production vehicles. Estimation is made based on the interacting multiple models (IMM) filter, which is modified to enhance estimation accuracy. Additionally, a novel tire-model based estimation error filter is introduced to detect and compensate for significant signal errors. The estimations update the vehicle model in the controller, which is based on the robust model predictive control (RMPC) strategy. In addition to the widely recognized smooth and stable control characteristics of model prediction and optimization, the RMPC controller is designed to be robust against cornering stiffness errors. Utilizing the probability matrix from the IMM, cornering stiffness estimation uncertainty is derived and implemented in the RMPC as model uncertainty. The performance of the control system is tested by simulations. Carsim is used for the estimator, while CARMAKER is used for the validation of the full control system.

Disturbance Observer-based Robust Controller for MIMO Nonlinear Systems

하원석 광운대학교 대학원 2020 국내박사

This thesis deals with robust controllers design based on a disturbance observer for uncertain multi-input multi-output nonlinear systems. The controllers are designed for two perspectives; system states are available for feedback, and system output is only available for feedback. The systems considered by each controller are as follows • State feedback disturbance observer – general uncertain multi-input multi-output nonlinear systems – n-DOF (degree of freedom) robot manipulators • Output feedback disturbance observer – general uncertain multi-input multi-output nonlinear systems – 2-DOF magnetic levitation system For general uncertain multi-input multi-output nonlinear systems subject to external disturbances, we consider a stabilization problem. We assume that the system has a well-defined vector relative degree and the zero dynamics is input-to-state stable. Based on the assumption that there exists a state feedback controller that makes the origin of the nominal closed-loop system asymptotically stable, we present a stabilizer that recovers the stability of the nominal closed-loop system in the practical sense. We allow that the nominal system can have a nonlinear input gain matrix that is a function of system state. To validate the proposed controllers, simulation results on a 2-DOF robot manipulator and a 2-DOF magnetic levitation system are included, for state feedback and output feedback, respectively. For uncertain robot manipulators subject to external disturbance torques, we consider the trajectory tracking problem. We propose three versions of state feedback disturbance observers for robot manipulators: • State feedback disturbance observer • Internal model embedded state feedback disturbance observer • Momentum-based state feedback disturbance observer In the case of basic state feedback disturbance observer, we consider uncertain robot manipulators subject to external disturbance torques. The external disturbance torques are assumed to be unknown and time-varying. We present a disturbance observer-based controller which estimates the lumped disturbance (the external disturbance torque combined with the effect of system uncertainties), and compensates it so that the overall closed-loop system behaves like the nominal closed-loop system that is composed of the nominal model of robot manipulator and the feedback linearization-based tracking controller. A simplified implementation of the proposed controller is also introduced. Next, for internal model embedded state feedback disturbance observer, we consider disturbances which are composed of sinusoids. The controller employs the disturbance observer-based controller which can effectively estimate and compensate the effect of system uncertainties and the disturbances. Assuming that the frequencies of sinusoids are known, we embed the internal model of disturbances into the controller so that the design parameters of the controller can be chosen without using the magnitude of disturbance or its time derivative. A rigorous stability analysis shows that the closedloop system under the proposed controller behaves like the nominal closed-loop system free of disturbances. Finally, momentum-based state feedback disturbance observer is designed using robot manipulator properties. The passivity-based controller chosen as an outer-loop controller is one of the most widely-used controllers for robot manipulators. Since it strongly exploits the system properties, it does not produce unnecessarily large control effort and has inherent robustness against system uncertainty and disturbance. We present an inner-loop controller which can enhance the robustness of the passivity-based tracking controllers. The inner-loop controller developed robustly estimates the lumped disturbance, which is defined by the effect of system uncertainty and external disturbance, and generates a compensating signal so that the closed-loop system consisting of the uncertain robot, disturbance observer, and passivity-based controller behaves like the nominal closed-loop system composed of the nominal model of the robot and the passivity-based controller. It is seen that the tracking error can be made arbitrarily small by choosing the controller parameters appropriately. Simulation results on a 2-DOF robot manipulator and experiment results on a 3-DOF robot manipulator are given to validate the performances of the three versions of the state feedback controller.

Design of Robust and Adaptive Fuzzy Controllers for Uncertain Robot Manipulators

박창우 연세대학교 2002 국내박사

점차 그 구조가 복잡·다양해지는 로봇 매니퓰레이터의 효율적인 제어를 위해 대상 플랜트의 정확한 모델링이 필요하나 실제적으로 플랜트 내부의 다양한 불확실성으로 인하여 로봇 매니퓰레이터의 유효한 모델을 얻기가 매우 힘들거나 불완전한 형태의 모델을 얻을 수 밖에 없는 경우가 많다. 따라서 본 연구에서는 퍼지 시스템을 이용하여 불확실한 로봇 매니퓰레이터의 모델을 구하고, 이를 기반으로 전체 제어 시스템의 안정도를 보장하는 강인 퍼지 피드백 선형화 제어기와 적응 퍼지 슬라이딩 모드 제어기의 설계 방법을 제시한다. 강인 퍼지 피드백 선형화 제어기를 사용한 시스템의 안정도 분석을 위해 먼저 제어 대상 플랜트에 대해 Takagi-Suegeno 퍼지 모델을 구성하고, 폐루프 시스템을 Diagonal Norm bounded Linear Differential Inclusion과 Generalized Eigen Value Problem의 형태로 변환하여 선형 행렬 부등식의 해를 구함으로써 L_2 강인 안정도의 판별이 가능해진다. 또한 선형 행렬 부등식 기반의 최적화 방법을 사용하여 제어 대상 플랜트의 고유 상수에 대한 불완전한 이해, 시스템 파라메터의 변화, 외부 외란, 퍼지 모델링 에러 등에 의해 생기는 불확실성에 대해 강인한 안정성을 보장하는 퍼지 피드백 제어 이득의 최대 허용 범위를 구함으로써 기존의 도해적인 방법으로 제어 이득을 구하는 방법과는 달리 체계적이고 수치적인 퍼지 제어기의 설계가 가능하다. 시스템 내부의 여러 가지 변화 요소가 너무 커서 플랜트의 퍼지 모델을 얻기가 힘들 경우, Mamdani 퍼지 시스템의 근사화 이론을 이용하여 시스템 모델을 온라인으로 추정하고, 슬라이딩모드 제어기의 강인성과 적응 규칙을 이용하여 외란과 퍼지 모델링 에러를 보상하는 퍼지 간접 적응 슬라이딩 모드 제어기의 설계 방법을 제안한다. 또한 플랜트 모델이 아닌 슬라이딩 모드 제어기의 등가 제어 입력을 추정하여 적응 제어를 수행하는 직접 적응 퍼지 슬라이딩 모드 제어기의 설계 방법과 적응 규칙을 제안하며, 리아푸노프 안정도 이론에 따라 제안한 적응 퍼지 제어 시스템의 점근적 안정성과 제어 신호의 유계성을 입증한다. 기존의 적응 퍼지 슬라이딩 모드 제어기와는 달리 제안된 제어기는 시스템 모델을 구성하는 함수의 범위와 같은 어떠한 플랜트의 정보 또는 가정을 사용하지 않고 시스템의 안정도를 보장하는 제어기의 설계가 가능하다. 파라메터 불확실성과 외부 외란을 포함하는 단일 링크 유연 로봇 매니퓰레이터의 안정화 제어에 제안된 강인 피드백 선형화 제어기를 적용하여 제어기의 유용성과 효율성을 확인하며, 불확실한 2 자유도 로봇 매니퓰레이터의 추적 제어를 위해 적응 퍼지 슬라이딩 모드 제어기를 설계하고, 시뮬레이션을 통해 제안된 제어기의 적응 성능을 검토한다. There are two major topics developed in this research. One is a robust fuzzy feedback control and the other is an adaptive fuzzy feedback control. These controllers are designed to guarantee the overall stability for a class of uncertain nonlinear system using fuzzy models. The robust stability analysis and design methodology of fuzzy feedback control systems based on Takagi-Sugeno fuzzy models are presented. Uncertainty and disturbance with known bounds are assumed to be included in the Takagi-Sugeno fuzzy models representing the nonlinear plants. L_(2) robust stability of the closed system is analyzed by casting the systems into the diagonal norm bounded linear differential inclusion formulation. Based on the linear matrix inequality optimization programming, a numerical method for finding the maximum stable ranges of the fuzzy feedback linearization control gains is also proposed. In addition, a new adaptive fuzzy feedback control design is presented for the plants whose dynamic structure is too complicated to obtain the reliable fuzzy models describing them via off-line tuning. By using the sliding mode scheme and Lyapunov stability theory, both direct and indirect adaptive fuzzy sliding mode controllers are developed for the completely unknown robot manipulator. The proposed adaptive tuning algorithm can on-line tune the parameters of fuzzy rules describing the plant models in the indirect approach and equivalent control law in the direct approach. It is proved that the proposed adaptive method can achieve an asymptotically stable tracking of a reference input with a guarantee of the bounded system signals without any prior information of the target plant and assumption in both the adaptive fuzzy control systems. A flexible joint robot and a two-degree-of-freedom robot manipulator are simulated to demonstrate the validity of the proposed analysis and design methods. Various simulations are performed comparing conventional PD and sliding mode controllers with the proposed controller.

Robust control and fully-actuated flight mechanism for multirotor-based versatile aerial robotics platform

이승제 서울대학교 대학원 2020 국내박사

오늘날 멀티로터 무인항공기는 단순한 비행 및 공중 영상 촬영용 장비의 개념을 넘어 비행 매니퓰레이션, 공중 화물 운송 및 공중 센싱 등의 다양한 임무에 활용되고 있다. 이러한 추세에 맞추어 로보틱스 분야에서 멀티로터 무인항공기는 부과된 임무에 맞추어 원하는 장비 및 센서를 자유로이 탑재하고 비행할 수 있는 다목적 공중 로봇 플랫폼으로 인식되고 있다. 그러나 현재의 멀티로터 플랫폼은 돌풍 등의 외란에 다소 강건하지 못한 제어성능을 보인다. 또한, 병진운동의 제어를 위해 비행 중 지속적으로 동체의 자세를 변경해야 해 센서 등 동체에 부착된 탑재물의 자세 또한 지속적으로 변화한다는 단점을 가지고 있다. 위의 두 가지 문제들을 해결하고자 본 연구에서는 외란에 강건한 멀티로터 제어기법과, 병진운동과 자세운동을 독립적으로 제어할 수 있는 새로운 형태의 완전구동 멀티로터 비행 매커니즘을 소개한다. 강건 제어기법의 경우, 먼저 정확한 병진운동 제어를 위한 병진 힘 생성 기법을 소개하고 뒤이어 병진 힘 외란에 강건한 제어를 위한 외란관측기 기반 강건 제어 알고리즘의 설계 방안을 논의한다. 제어기의 피드백 루프 안정성은 mu 안정성 분석 기법을 통해 검증되며, mu 안정성 분석이 가지는 엄밀한 안정성 분석의 결과를 검증하기 위해 스몰게인 이론 (Small Gain Theorem) 기반의 안정성 분석 결과가 동시에 제시 및 비교된다. 최종적으로, 개발된 제어기를 도입한 멀티로터의 3차원 병진 가속도 제어 성능 및 힘 벡터의 형태로 인가되는 병진 운동 외란에 대한 극복 성능을 실험을 통해 검증하여, 제안된 제어기법의 효과적인 비행 지점 및 궤적 추종 능력을 확인한다. 완전 구동 멀티로터의 경우, 기존의 완전구동 멀티로터가 가진 과도한 중량 증가 및 저조한 에너지 효율을 극복하기 위한 새로운 매커니즘을 소개한다. 새로운 매커니즘은 기존 멀티로터와 최대한 유사한 형태를 가지되 완전구동을 위해 오직 두 개의 서보모터만을 포함하며, 이로 인해 기존 멀티로터와 비교해 최소한의 형태의 변형만을 가지도록 설계된다. 새로운 플랫폼의 동적 특성에 대한 분석과 함께 유도된 운동방정식을 기반으로 한 6자유도 비행 제어기법이 소개되며, 최종적으로 다양한 실험과 그 결과들을 통해 플랫폼의 완전구동 비행 능력을 검증한다. 추가적으로 본 논문에서는 완전구동 멀티로터가 가지는 여분의 제어입력(redundancy)를 활용한 쿼드콥터의 단일모터 고장 대비 비상 비행 기법을 소개한다. 비상 비행 전략에 대한 자세한 소개 및 실현 방법, 비상 비행 시의 동역학적 특성에 대한 분석 결과가 소개되며, 실험결과를 통해 제안된 기법의 타당성을 검증한다. Recently, multi-rotor unmanned aerial vehicles (UAVs) are used for a variety of missions beyond its basic flight, including aerial manipulation, aerial payload transportation, and aerial sensor platform. Following this trend, the multirotor UAV is recognized as a versatile aerial robotics platform that can freely mount and fly the necessary mission equipment and sensors to perform missions. However, the current multi-rotor platform has a relatively poor ability to maintain nominal flight performance against external disturbances such as wind or gust compared to other robotics platforms. Also, the multirotor suffers from maintaining a stable payload attitude, due to the fact that the attitude of the fuselage should continuously be changed for translational motion control. Particularly, unstabilized fuselage attitude can be a drawback for multirotor's mission performance in such cases as like visual odometry-based flight, since the fuselage-attached sensor should also be tilted during the flight and therefore causes poor sensor information acquisition. To overcome the above two problems, in this dissertation, we introduce a robust multirotor control method and a novel full-actuation mechanism which widens the usability of the multirotor. The goal of the proposed control method is to bring robustness to the translational motion control against various weather conditions. And the goal of the full actuation mechanism is to allow the multi-rotor to take arbitrary payload/fuselage attitude independently of the translational motion. For robust multirotor control, we first introduce a translational force generation technique for accurate translational motion control and then discuss the design method of disturbance observer (DOB)-based robust control algorithm. The stability of the proposed feedback controller is validated by the mu-stability analysis technique, and the results are compared to the small-gain theorem (SGT)-based stability analysis to validate the rigorousness of the analysis. Through the experiments, we validate the translational acceleration control performance of the developed controller and confirm the robustness against external disturbance forces. For a fully-actuated multirotor platform, we propose a new mechanism called a T3-Multirotor that can overcome the excessive weight increase and poor energy efficiency of the existing fully-actuated multirotor. The structure of the new platform is designed to be as close as possible to the existing multi-rotor and includes only two servo motors for full actuation. The dynamic characteristics of the new platform are analyzed and a six-degree-of-freedom (DOF) flight controller is designed based on the derived equations of motion. The full actuation of the proposed platform is then validated through various experiments. As a derivative study, this paper also introduces an emergency flight technique to prepare for a single motor failure scenario of a multi-rotor using the redundancy of the T3-Multirotor platform. The detailed introduction and implementation method of the emergency flight strategy with the analysis of the dynamic characteristics during the emergency flight is introduced, and the experimental results are provided to verify the validity of the proposed technique.

Optimal Trajectory Generation and Robust Control of a Launch Vehicle during Ascent Phase

김승현 서울대학교 대학원 2018 국내박사

This research focused on trajectory generation and control of a flexible launch vehicle during ascent flight. An important issue of a launch vehicle design is generating optimal trajectory during its atmospheric ascent flight while satisfying constraints such as aerodynamic load. These constraints become more significant due to wind disturbance, especially in the maximum dynamic pressure region. On the other hand, modern launch vehicles are becoming long and slender for the reduction in structure mass to increase payload. As a result, they possess highly flexible bending modes in addition to aerodynamically unstable rigid body characteristics. This dissertation proposes a rapid and reliable optimization approach for trajectory generation via sequential virtual motion camouflage (VMC) and non-conservative robust control for an unstable and flexible launch vehicle. First, an optimal trajectory is generated in a rapid and reliable manner through the introduction of the virtual motion camouflage. VMC uses an observed biological phenomenon called motion camouflage to construct a subspace in which the solution trajectory is generated. By the virtue of this subspace search, the overall dimension of the optimization problem is reduced, which decreases the computational time significantly compared to a traditional direct input programming. Second, an interactive optimization algorithm is proposed to find a feasible solution easier. For this, the constraint correction step is added after VMC optimization. Since VMC is a subspace problem, a feasible solution may not exist when subspace is not properly constructed. In order to address this concern, a quadratic programming (QP) problem is formulated to find a direction along which the parameters defining the subspace can be improved. Via a computationally fast QP, specific parameters (such as prey and reference point) used in VMC can be refined quickly and sequentially. As a result, the proposed interactive optimization algorithm is less sensitive to the initial guess of the optimization parameters. Third, a non-conservative 2-DOF H infty controller for an unstable and flexible launch vehicle is proposed. The objectives of the control system are to provide sufficient margins for the launch vehicle dynamics and to enhance the speed of the closed-loop response. For this, a robust control approach is used. The key of the control design is to overcome conservativeness of the robust control. The baseline controllers using the optimal control such as LQG and LQI are designed prior to a robust controller. These optimal controllers are used to find a desirable shape of the sensitivity transfer function in order to reduce conservativeness of the robust control. After implementation and analysis of the baseline controllers, an improved sensitivity weighting function is defined as a non-conventional form with different slopes in the low frequency and around crossover frequency, which results in performance enhancement without loss of robustness. A two-degree-of-freedom H infty controller is designed which uses feedback and feedforward control together to improve tracking performance with the proposed sensitivity weighting function as a target closed-loop shape. The resulting H infty controller stabilizes the unstable rigid body dynamics with sufficient margins in the low frequency, and also uses gain stabilization in addition to phase stabilization to handle the lightly damped bending modes in the high-frequency region.

Control of Multiple Degree of Freedom Fast Tool Stages for Noncircular Turning Process : 비원형 회전가공을 위한 다중자유도 기구 제어

김병섭 Univ. of Illinois at Urbana-Champaign 2001 해외박사

"There are a lot of cases in the industrial control area where the reference and/or disturbance signals are periodic. To utilize this specific characteristic of the periodic signal in control system design, a variety of repetitive controllers has been developed and applied to several applications. One of the manufacturing applications is the noncircular turning process. The goal of the proposed research is to extend the capability of the noncircular turning process. The major work of this research can be divided into three sections: (1) A prototype variable rake angle mechanism has been developed and controlled. The objective of the variable rake angle mechanism is to provide another degree of freedom to the conventional noncircular turning process in parallel fashion, so that the rotational tool mechanism can compensate for the rake angle change caused by the noncircular cam profile itself. Kinematics, dynamics, and design of the variable rake angle mechanism are discussed. The equations of motion of the variable rake, angle mechanism are derived and numerical analysis of the equations of motion is presented. Experimental results on the variable rake angle mechanism support the design concept and control approach. (2) A robust repetitive controller is designed for a dual stage actuator system and it demonstrates the tracking performance improvement through a dual stage actuator system. The dual stage actuator system has a piezoelectric actuator inside of the hollow piston of an electrohydraulic actuator system, so it has another degree of freedom in serial fashion in addition to the main tool motion. Cascading two SISO control loops results in the squaring effect on the overall sensitivity function and improves the tracking performance. Experimental and simulation results show the effectiveness of the dual stage actuator system for the noncircular turning process. (3) A new discrete-time robust repetitive controller design with improved performance is proposed. The basic idea to improve the tracking performance at fundamental frequencies is to achieve the squaring effect on the sensitivity function. The fundamental frequencies are defined as integer multiples of the frequency of the periodic signal. Conceptually, the goal is the same as that of the dual stage actuator system, even though it is proposed to use the modified q(z, z-1) filter structure instead of adding another actuator stage in series. It is shown that this design method improves not only tracking performance but also robustness for small variations in the period of the periodic signal. A systematic controller design methodology is presented to guarantee the robust stability. Experimental and simulation results from an electrohydraulic actuator system validate this approach.