A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Design of Sliding Mode PID Controller with Improved reaching laws for Nonlinear Systems

In this thesis, advanced design technique in sliding mode control (SMC) is presented with focus on PID (Proportional-Integral-Derivative) type Sliding surfaces based Sliding mode control with improved power rate exponential reaching law for Non-linear systems using Modified Particle Swarm Optimization (MPSO). To handle large non-linearities directly, sliding mode controller based on PID-type sliding surface has been designed in this work, where Integral term ensures fast finite convergence time. The controller parameter for various modified structures can be estimated using Modified PSO, which is used as an offline optimization technique. Various reaching law were implemented leading to the proposed improved exponential power rate reaching law, which also improves the finite convergence time. To implement the proposed algorithm, nonlinear mathematical model has to be decrypted without linearizing, and used for the simulation purposes. Their performance is studied using simulations to prove the proposed behavior. The problem of chattering has been overcome by using boundary method and also second order sliding mode method. PI-type sliding surface based second order sliding mode controller with PD surface based SMC compensation is also proposed and implemented. The proposed algorithms have been analyzed using Lyapunov stability criteria. The robustness of the method is provided using simulation results including disturbance and 10% variation in system parameters. Finally process control based hardware is implemented (conical tank system)

Modified PSO based PID Sliding Mode Control using Improved Reaching Law for Nonlinear systems

In this paper, a new model based nonlinear control technique, called PID (Proportional-Integral-Derivative) type sliding surface based sliding mode control is designed using improved reaching law. To improve the performance of the second order nonlinear differential equations with unknown parameters modified particle swarm intelligent optimization (MPSO) is used for the optimized parameters. This paper throws light on the sliding surface design, on the proposed power rate exponential reaching law, parameters optimization using modified particle swarm optimization and highlights the important features of adding an integral term in the sliding mode such as robustness and higher convergence, through extensive mathematical modeling. Siding mode control law is derived using Lyapunov stability approach and its asymptotic stability is proved mathematically and simulations showing its validity. MPSO PID-type Sliding mode control will stabilize the highly nonlinear systems, will compensate disturbances and uncertainty and reduces tracking errors. Simulations and experimental application is done on the non-linear systems and are presented to make a quantitative comparison.Comment: arXiv admin note: substantial text overlap with arXiv:2207.1112

Robust Control Methods for Nonlinear Systems with Uncertain Dynamics and Unknown Control Direction

Robust nonlinear control design strategies using sliding mode control (SMC) and integral SMC (ISMC) are developed, which are capable of achieving reliable and accurate tracking control for systems containing dynamic uncertainty, unmodeled disturbances, and actuator anomalies that result in an unknown and time-varying control direction. In order to ease readability of this dissertation, detailed explanations of the relevant mathematical tools is provided, including stability denitions, Lyapunov-based stability analysis methods, SMC and ISMC fundamentals, and other basic nonlinear control tools. The contributions of the dissertation are three novel control algorithms for three different classes of nonlinear systems: single-input multipleoutput (SIMO) systems, systems with model uncertainty and bounded disturbances, and systems with unknown control direction. Control design for SIMO systems is challenging due to the fact that such systems have fewer actuators than degrees of freedom to control (i.e., they are underactuated systems). While traditional nonlinear control methods can be utilized to design controllers for certain classes of cascaded underactuated systems, more advanced methods are required to develop controllers for parallel systems, which are not in a cascade structure. A novel control technique is proposed in this dissertation, which is shown to achieve asymptotic tracking for dual parallel systems, where a single scalar control input directly affects two subsystems. The result is achieved through an innovative sequential control design algorithm, whereby one of the subsystems is indirectly stabilized via the desired state trajectory that is commanded to the other subsystem. The SIMO system under consideration does not contain uncertainty or disturbances. In dealing with systems containing uncertainty in the dynamic model, a particularly challenging situation occurs when uncertainty exists in the input-multiplicative gain matrix. Moreover, special consideration is required in control design for systems that also include unknown bounded disturbances. To cope with these challenges, a robust continuous controller is developed using an ISMC technique, which achieves asymptotic trajectory tracking for systems with unknown bounded disturbances, while simultaneously compensating for parametric uncertainty in the input gain matrix. The ISMC design is rigorously proven to achieve asymptotic trajectory tracking for a quadrotor system and a synthetic jet actuator (SJA)-based aircraft system. In the ISMC designs, it is assumed that the signs in the uncertain input-multiplicative gain matrix (i.e., the actuator control directions) are known. A much more challenging scenario is encountered in designing controllers for classes of systems, where the uncertainty in the input gain matrix is extreme enough to result in an a priori-unknown control direction. Such a scenario can result when dealing with highly inaccurate dynamic models, unmodeled parameter variations, actuator anomalies, unknown external or internal disturbances, and/or other adversarial operating conditions. To address this challenge, a SMCbased self-recongurable control algorithm is presented, which automatically adjusts for unknown control direction via periodic switching between sliding manifolds that ultimately forces the state to a converging manifold. Rigorous mathematical analyses are presented to prove the theoretical results, and simulation results are provided to demonstrate the effectiveness of the three proposed control algorithms

H∞ based control of a DC/DC buck converter feeding a constant power load in uncertain DC microgrid system

DC microgrids are gaining more and more popularity and are becoming a more viable alternative to AC microgrids (MGs) due to their advantages in terms of simpler power converter stages, flexible control algorithms and the absence of synchronization and reactive power. However, DC-MGs are prone to instability issues associated with the presence of nonlinear loads such as constant power loads (CPL) known by their incremental negative impedance (INI), which may lead to voltage collapse of the main DC Bus. In this paper, -based controller of a source side buck converter is designed to avoid the instability issues caused by the load-side converter acting as a CPL. Besides, the proposed controller allows a perfect rejection of all perturbations that may arise from parameter variations, input voltage and CPL current fluctuations. The design process of H-based controller is based on the Golver Doyle Optimization Algorithm (GDOA), which requires an augmented system extracted from the small-signal model of the DC/DC converter including the mathematical model of parameter variations and overall external perturbations. The​ based controller involves the use of weight functions in order to get the desired performances. The proposed controller is easy to implement and lead to reducing the implementation cost and avoid the use of current measurement that may have some disadvantages. The derived controller is validated by simulation performed in Psim software and experimental setup

Stabilization computation for a kind of uncertain switched systems using non-fragile sliding mode observer method

A non-fragile sliding mode control problem will be investigated in this article. The problem focuses on a kind of uncertain switched singular time-delay systems in which the state is not available. First, according to the designed non-fragile observer, we will construct an integral-type sliding surface, in which the estimated unmeasured state is used. Second, we synthesize a sliding mode controller. The reachability of the specified sliding surface could be proved by this sliding mode controller in a finite time. Moreover, linear matrix inequality conditions will be developed to check the exponential admissibility of the sliding mode dynamics. After that, the gain matrices designed will be given along with it. Finally, some numerical result will be provided, and the result can be used to prove the effectiveness of the method

State of the art of control schemes for smart systems featuring magneto-rheological materials

This review presents various control strategies for application systems utilizing smart magneto-rheological fluid (MRF) and magneto-rheological elastomers (MRE). It is well known that both MRF and MRE are actively studied and applied to many practical systems such as vehicle dampers. The mandatory requirements for successful applications of MRF and MRE include several factors: advanced material properties, optimal mechanisms, suitable modeling, and appropriate control schemes. Among these requirements, the use of an appropriate control scheme is a crucial factor since it is the final action stage of the application systems to achieve the desired output responses. There are numerous different control strategies which have been applied to many different application systems of MRF and MRE, summarized in this review. In the literature review, advantages and disadvantages of each control scheme are discussed so that potential researchers can develop more effective strategies to achieve higher control performance of many application systems utilizing magneto-rheological materials

Robust Impedance Control of a Four Degree of Freedom Exercise Robot

The CSU 4OptimX exercise robot provides a platform for future research into advanced exercise and rehabilitation. The robot and its control system will autonomously modify reference trajectories and impedances on the basis of an optimization criterion and physiological feedback. To achieve this goal, a robust impedance control system with trajectory tracking must be implemented as the foundational control scheme. Two control laws will be compared, sliding mode and H-infinity control. The above robust control laws are combined with underlying impedance control laws to overcome uncertain plant model parameters and disturbance anomalies affecting the input signal. The sliding mode control law is synthesized based on a nominal plant model due to its inherent nature of overcoming unspecified, un-modeled dynamics and disturbances. Implementation of the H-infinity control law uses weights as well as the nominal plant, a structured parametric uncertainty model of the plant, and a model with multiplicative uncertainty. The performance and practicality of each controller is discussed as well as the challenges associated with attempts to implement controllers successfully onto the robot. The findings of this thesis indicate that the closed loop controller with sliding mode is the superior control scheme due to its abilities to counter non-linearities. It is chosen as the platform control scheme. The 2 out of 3 H-infinity controllers performed well in simulation but only one was able to successfully control the robot. Challenges associated with H-infinity control implementation toward impedance control include determining proper weight shapes that balance performance and practicality. This challenge is a starting point for future research into general weight shape determination for H-infinity robust impedance control

H-infinity controller with graphical LMI region profile for liquid slosh suppression

This paper presents a H-infinity synthesis with pole clustering based on LMI region schemes for liquid slosh control. Using LMI approach, the regional pole placement known as LMI region combined with design objective in H-infinity controller guarantee a fast input tracking capability and very minimal liquid slosh. A graphical profile of the transient response of liquid slosh suppression system with respect to pole placement is very useful in giving more flexibility to the researcher in choosing a specific LMI region. With the purpose to confirm the design of control scheme, a liquid slosh model is considered to represent the lateral slosh movement. Supremacy of the proposed approach is shown by comparing the results with hybrid model-free fuzzy-PID controller with derivative filter. The performance of the control schemes is examined in terms of time response specifications of lateral tank tracking capability and level of liquid slosh reduction