From PID to Nonlinear State Error Feedback Controller

Abstract

Abstract-In this paper an improved nonlinear state error feedback controller (INLSEF) has been proposed for perfect reference tracking and minimum control energy. It consists of a nonlinear tracking differentiator together with nonlinear combinations of the error signal. The tracking differentiator generates a set of reference profile for the input signal, which is the signal itself in addition to its derivatives. On the other hand, the 12-parameters nonlinear combinations of the error signal make the INLSEF controller can handles with time-varying and system's nonlinearity. Digital simulation studies have been conducted for the proposed controller and compared with several works from literature survey on two case studies, mass-springdamper which is a very nonlinear system and nonlinear ball and beam systems. The parameters of the nonlinear combination of the error signal are tuned to satisfy the optimality condition by minimizing the OPI performance index defined in this work. From the simulations results one can conclude that the proposed INLSEF controller performance is better than that of its counterpart in terms of speed and control energy and minimum error. Also, the results showed that the proposed controller is effectively enhancing the stability and performance of the closed loop system.

Genetic Optimization-Based Consensus Control of Multi-Agent 6-DoF UAV System

“…The aim of the tracking formation is to keep the agents in a formation on the 3D space ( ) and the angle of rotation around -axis ( ) while tracking the leader. Therefore, the leader control is different from the followers, which can be represented by normal quadrotor control using a combination of NLPID for the outer loop control (OLC) and IADRC for the inner loop control (ILC) of the quadrotor system, which was designed in our previous works [ 26 , 27 , 28 ] and is shown in Figure 4 . The followers’ control is a mix of two controllers; the first is the local one and the second is the consensus controller, as shown in Figure 5 .…”

Nonlinear PID controller design for a 6-DOF UAV quadrotor system

“…Less control energy is obtained with the NLPID control while the error is changing continuously. In this paper the NLPID controller is desighned as in [26] with little modification in the integral Figure 4: Characteristics of the nonlinear gain function k(e) for i=1, k 11 = 20, k 12 = 5 [26] term of (6), where the term k 31 is added to increase the stability of the closed-loop system as will be shown later.…”

“…In this paper, a NLPID controller proposed in our previous work [26] which a nonlinear combinations of the error signal is used to stabilize a 6-DOF quadrotor system, its stability verified using Hurwitz stability and its performance compared with that of the most famous one, i.e., the LPID controller. The control system for the 6-DOF UAV consists of six NLPID controllers, three NLPID controllers for the translational system and the rest ones for the rotational system of the underlying UAV, with twelve tuning parameters for each NLPID controller, they are tuned using Genetic Algorithm (GA) and optimized toward the minimization of the proposed multi-objective OPI which is a weighted sum of the Integrated Time Absolute Error (ITAE) and the square of the control signal U (USQR).…”

Indirect Adaptive State-Feedback Control of Rotary Inverted Pendulum Using Self-Mutating Hyperbolic-Functions for Online Cost Variation

“…The augmentation of nonlinear scaling functions with linear compensators to self-adjust critical gains is extensively used in controlling non-minimum phase systems [26], [27]. The nonlinear-type state-feedback controllers significantly improve the system's response speed, damping against disturbances, tracking accuracy, and control input economy [28]- [30].…”