Nonlinear Robust Control Algorithm Research Articles

Modeling and second-order sliding mode control for a full three-dimensional ridable ballbot

ABSTRACT The full 3D ridable ballbot (RB) system is a typical higher-order, multi-variable, underactuated, nonlinear, nonholonomic constraint, and strongly coupled control system. The dynamics of the RB also consists of uncertainties of the system parameters and unknown frictions. Such a complicated system requires a sophisticated control algorithm that can handle these difficulties to control the balancing and transferring of the RB. This study introduces a nonlinear robust control algorithm based on the sliding mode technique. The robust controller with sliding mode surfaces is designed to control the position of the ball on the floor and the angles of the body. The simulation and experimental results of the full 3D RB setup. The acquired results demonstrate the superior performance of the proposed controller. Meanwhile, the experimental performance of the proposed controller is validated on an actual RB.

An Improved Robust Predictive Control Approach Based on Generalized 3rd Order S-PARAFAC Volterra Model Applied to a 2-DoF Helicopter System

This paper proposes a generalized robust predictive control approach based on 3rd order S-PARAFAC Volterra Model. The main idea is to use the predictive control law based on the latter model with taking into account the parameter and operation uncertainties resulting from the measurement noise and the robust identification technique named Unknown But Bounded Error (UBBE). One of the advantages is the convexity of the objective function with respect to the parameter uncertainty set. The min-max optimization problem becomes thus simpler, by minimizing the objective function in the worst-case only over the set of uncertain models. This work proposes a new generalized nonlinear robust control algorithm dedicated for uncertain processes. In this algorithm we optimize a quadratic criterion and take into account the physical and geometrical constraints due to parameter uncertainties. The performances of this work are illustrated and validated on a benchmark as a continuous stirred-tank reactor system (CSTR) and on an experimental 2-DoF helicopter system.

Control of COVID-19 system using a novel nonlinear robust control algorithm

COVID-19 has been a worldwide concern since the outbreak. Many strategies have been involved such as suppression and mitigation strategies to deal with this epidemic. In this paper, a new mathematical-engineering strategy is introduced in order to control the COVID-19 epidemic. Thereby, control theory is involved in controlling the unstable epidemic alongside with the other suggested strategies until the vaccine will hopefully be invented as soon as possible. A new robust control algorithm is introduced to compensate the COVID-19 nonlinear system by propose a proper controller after using necessary assumptions and analysis are made. In addition, the Variable Transformation Technique (VTT) is used to simplify the COVID-19 system. Furthermore, the Most Valuable Player Algorithm (MVPA) is applied in order to optimize the parameters of the proposed controller. The simulation results are based on the daily reports of two cities Hubei (China) and Lazio (Italy) since the outbreak. It can be concluded that the proposed control algorithm can effectively compensate the COVID-19 system. In addition, it can be considered as an effective mathematical-engineering strategy to control this epidemic alongside with the other strategies.

Parameter Identification and Model-Based Nonlinear Robust Control of Fluidic Soft Bending Actuators

Soft actuators are of great interests in recent years due to inherent compliance and adaptability. However, most of current studies focus on the physical actuation phenomenon and their fabrication, few results can be found on the modeling and closed-loop control due to their complicated elastic deformation. This paper studies physical modeling, parameter identification, and model-based nonlinear robust control for fluidic soft bending actuators governed by high-speed on–off solenoid valves. With the dynamic complexity and characteristics of fluidic soft actuators, the system has been described by two parts: motion dynamics and air dynamics. A second-order transfer function is used for the motion dynamics which describes the behavior from driving pneumatic pressure to soft actuator bending angle, and the model parameters are identified by with different operating frequencies. The nonlinear physical modeling of air dynamics which describes the behavior from control voltage to driving pneumatic pressure is also built and its parameters are identified by using the least square method. Based on the identified high-order model, a nonlinear robust control algorithm is developed for soft actuator by backstepping design to deal with nonlinearities and uncertainties. Experimental results show that the closed-loop stability is guaranteed and the good tracking performance is achieved by the proposed method.

Optimum Design of CDM-Backstepping Control with Nonlinear Observer for Electrohydraulic Servo System Using Ant Swarm

Abstract This paper introduces an application of an Ant Colony Optimization algorithm to optimize the parameters in the design of a type of nonlinear robust control algorithm based on coefficient diagram method and backstepping strategy with nonlinear observer for the electrohydraulic servo system with supply pressure under the conditions of uncertainty and the action of external disturbance. Based on this model, a systematic analysis and design algorithm is developed to deal with stabilization and angular displacement tracking, one feature of this work is employing the nonlinear observer to achieve the asymptotic stability with state estimations. Finally, numerical simulations are given to demonstrate the usefulness and advantages of the proposed optimization method.

Robust predictive controller for nonlinear uncertain process based on S-PARAFAC Volterra models

This paper proposes a new approach for synthesizing a robust predictive controller for nonlinear uncertain process by exploiting a reduced complexity discrete-time Volterra model known as S-PARAFAC-Volterra model applied to the quadratic case. This proposed robust control copes with physical constraints and geometrical constraints due to parameter uncertainties and leads to the min-max optimization problem. The major advantage is that the objective function is convex with respect to the parameter uncertainty set which simplifies the min-max optimization problem and minimizes the worst-case value of the objective function taken over the set of uncertain models. A quadratic criterion is optimized and a new optimization algorithm, formulated as a quadratic programming (QP) under linear and nonlinear constraints, is proposed. The developed nonlinear robust control algorithm for uncertain process is illustrated on a benchmark as a continuous stirred-tank reactor system (SCTR).

A practical nonlinear robust control approach of electro-hydraulic load simulator

This paper studies a nonlinear robust control algorithm of the electro-hydraulic load simulator (EHLS). The tracking performance of the EHLS is mainly limited by the actuator’s motion disturbance, flow nonlinearity, and friction, etc. The developed controller is developed based on the nonlinear motion loading model. The problems of the actuator’s disturbance and flow nonlinearity are considered. To address the friction problem, the friction model of the loading motor is identified experimentally. The friction disturbance is compensated using the obtained friction model. Therefore, this paper considers the main three factors comprehensively. The developed algorithm is easy to apply since the controller can be obtained just with one step back-stepping design. The stability of the developed algorithm is proven via Lyapunov analysis. Both co-simulation and experiments are performed to verify the effectiveness of this method.

Decentralized Coordinated Excitation Control for Large Power System Based on Novel Delay-dependent Non-linear Robust Control Algorithm

Technological advances of the wide-area measurement system have enabled the use of a combination of measured information from remote locations for stability enhancement of large power systems. However, the time delays introduced by remote transmission in a wide-area measurement system have to be considered. In order to improve the stability of large power systems, this article focuses on a two-level decentralized coordinated excitation control scheme that decentralized a local power system stabilizer for each generator at the first level coordinated by wide-area measurement signals based on a supervisory power system stabilizer at the secondary level. Taking into account the multiple time delays and the non-linearities in system model, a novel delay-dependent non-linear robust control algorithm is proposed to design the decentralized coordinated controller. Finally, the effectiveness of the proposed design scheme is demonstrated through simulation examples.

A composite pulsating controller for achieving high-performance positioning

A non-linear robust control algorithm called a composite pulsating controller (CPC), which attains high-performance positioning specifications, is presented. The CPC is designed specifically for real product applications that have certain limitations such as friction, motor sizing, amplifier saturation, computational power and like. The CPC is composed of a bang-bang controller, a nominal proportional-integral-derivative (PID) controller, a high-gain PID controller and a pulsating controller in accomplishing the high-performance requirements. The mathematical structure of each component of the CPC is conceptualized, modelled and analysed in order to achieve superior positioning requirements for high performance. A bounded stability of the CPC is achieved and computer simulations are performed to demonstrate its practical applicability. Experimental digital implementation of the CPC with promising results is realized in the laboratory on a test bed equipped with a friction application apparatus.

Nonlinear Robust Control Algorithm for PM Linear Synchronous Motors Based on Model Quasi Linearization

A new nonlinear robust control scheme of permanent magnet linear synchronous motors (PMLSM) is proposed in this article. A quasi-linearized and decoupled model with uncertainties is derived by the mathematical model of PMLSM according to its characteristic. A fixed-boundary sliding mode controller using the msat function is designed to guarantee the robustness and remove the chattering that usually exists in normal sliding mode control. Design of a force observer is given to estimate the load force unknown in the new model. The validity of the proposed algorithm compared with the conventional PID control scheme is proved by MATLAB simulation results and DSP-based experimental results.