Compensation in PID control system for valve stiction based on equivalent-input-disturbance approach

This paper presents the design of a linear quadratic analog tracker (LQAT) based on the observer–Kalman-filter identification (OKID) method and the design of a modified functional observer-based equivalent input disturbance (EID) estimator for unknown square–non-square singular analog systems with unknown input and output disturbances. First, an equivalent mathematical model of the singular analog system is presented to simulate the time response of continuous-time linear singular analog systems to arbitrary inputs via the model conversion method. Then, for the unknown singular analog system, it constructs a linear quadratic analog tracker with state feedback and feed-forward gains based on the off-line OKID method. Furthermore, it extends the design methodology of the EID estimator for strictly proper regular systems with unknown matched–mismatched input and output disturbances to proper regular systems. It is important to mention that the newly developed modified functional observer for proper systems is used to estimate the unknown EID of singular analog systems and that the constraints on the dimensions of unknown disturbances can be eliminated by using the newly proposed EID estimation method. The contributions of this paper can be listed as follows: (1) based on both the OKID method and the discrete-to-continuous model conversion, the simulation of the time responses of the continuous-time linear singular models (which are not feasible using existing MATLAB toolboxes) become feasible; (2) for effective control of the unknown singular analog system, an off-line OKID method is proposed to design an LQAT with state feedback and feed-forward gains; and (3) based on the newly developed modified functional observer for the reduced-order proper regular system, the original EID estimator in the literature is newly extended to estimate the EID from the unknown strictly proper singular analog system, without the original dimensional constraints of the disturbances. It is important to mention that the disturbances of interest can be unknown matched–mismatched input and output disturbances.

In this paper, a robust H∞ control problem is considered for an uncertain singular system. An active disturbance rejection method called equivalent input disturbance (EID) is used to reduce the influence of exogenous disturbances and uncertainties on the system. At the first, there exists an EID, which can produces the same effect on the system as disturbances and uncertainties do in the control channel according to the EID concept. Then, an EID estimator is constructed to estimate the influence of EID on the system. Finally, based on Lyapunov stability theory, a static output feedback‐based robust H∞ controller combined with EID estimate is designed, guaranteeing that closed‐loop system is admissible (regular, impulse‐free, and stable) with a prescribed H∞ performance level. Compared with traditional H∞ control method, H∞ control based on EID method improve the control performance of the system. A numerical example demonstrates the validity of the method.

This article presents a proportional integral derivative (PID) control system for lower-limb rehabilitation robot that not only features satisfactory control performance for the pedal angle but also provides a function for pedal torque estimation. Nonlinear state feedback simplifies the stability analysis and control system design. The stability condition of the closed-loop system is derived based on a Lyapunov function. The PID controller ensures that the pedal angle tracks the reference trajectory. The equivalent input disturbance (EID) method in the control system was compared with the disturbance observer (DOB) and extended state observer (ESO) methods in terms of pedal torque estimation performance. The simulation results indicated that the EID method achieved a root mean square error of 0.37 N·m with 47.6% and 51.8% improvements over the DOB and ESO methods.

Cascade proportional integral derivative (PID) control systems are very important for successful applications. Most physical systems are complex in dynamics and cascade PID control systems offer effective solutions to their control problems, where a complex system is decomposed into several smaller and simpler systems for which PID control systems are designed for each of them. Understanding how the neglected dynamics affect the closed‐loop performance of the cascade control system is important for the design and applications. The chapter examines the variations of the closed‐loop poles of the cascade control system. One of the major advantages in using cascade control lies in its characteristics with regard to disturbance rejection. The chapter also examines the properties of input disturbance rejection in cascade control with both frequency response analysis and simulation studies. The input disturbance occurred at the inner‐loop system is much more effectively compensated in the cascade control structure.

Superheat steam temperature control is critical to the normal and optimal operation of a power plant. Usually, cascade proportional integral derivative (PID) control system is introduced to regulate the superheat temperature with the PID parameters fixed constant. However, Due to the gains and time constants of the controlled plant change significantly with disturbances, the control effects of the conventional PID are not ideal. In this paper, a new adaptive control strategy is proposed to improve conventional superheat steam temperature control. Based on cascade PID control system, recursive least squares (RLS) method is used to identify the plant parameters and then genetic algorithm (GA) is applied to adjust the parameters of the PID controllers. MATLAB simulation investigation indicates that, compared to the parameter fixed PID system, GA-self-tuned adaptive control system is able to reject endogenous and exogenous disturbances more effectively and rapidly, thus has better self-adaptation capability and robustness.

This paper describes a fault diagnosis method based on the equivalent-input-disturbance (EID) approach to power distribution feeders connected to a photovoltaic (PV) system. Node faults are treated as a system disturbance and are estimated using an EID estimator. First, a dynamic model that contains both the PV system and a power supply utility for the feeder is built. Second, an EID estimator is constructed to estimate the disturbance to the system on the control input channel. Third, a method for abstracting the amount caused by the PV system in the EID is presented to estimate the effect caused by faults. Simulation results demonstrate the validity and superiority of the method.

This paper develops a novel equivalent input disturbance (EID)-based adaptive sliding mode control (SMC) method for singularly perturbed systems (SPSs). Firstly, the block diagonalization approach is introduced to decompose the full-order SPSs exactly, and slow and fast subsystems are obtained by solving the upper and lower triangular matrices individually. Secondly, an EID is constructed to estimate the unknown disturbances with the observer gain and error system convergence analyzed. Then, depending on the decoupled reduced-order system models, a Lyapunov equation-based solution is adopted to construct a composite sliding surface. Finally, combined with the EID estimation, an adaptive SMC law is proposed to compensate the adverse effect of disturbances and the reachability condition is proven. The presented control strategy is free of any priori disturbances information while the satisfactory system performance can be guaranteed. Simulation results on two examples illustrate its superiority over the existing methods.

Design of Optimal PID Control with a Sensitivity Function for Resonance Phenomenon-involved Second-order Plus Dead-time System

Compensation in Repetitive Control System for Aperiodic Disturbances and Input Dead Zone

Sintering plays a key role in generating blast furnace burden in metallurgical processes. The continuous production and stable quality of sintering significantly depends on the stable and precise control of sintering ignition, which, however, is achieved through an input time delay system, and suffers from different and unknown disturbances. To reject disturbances and enhance the control precision of ignition temperature, this paper introduces a modified equivalent input disturbance (EID)‐based disturbance compensation that is suitable for controlling sintering ignition. First, the periodic properties of disturbances induced by gas pressure fluctuations are obtained based on spectral density decomposition. Second, to obtain the dynamics of sintering ignition, an iterative subspace modeling method is developed, which estimates not only the model parameters but also the length of time delay. By considering the periodic property, a control structure of sintering ignition based on the modified EID‐based compensation is proposed, in which an additional time‐delay element is designed to make the phase difference between EID estimation and real disturbance close to zero. Finally, the validity of the proposed method is verified by a simulation.

ABSTRACTIn this paper, the output tracking control problem for a class of switched nonlinear systems with multiple time-varying delays is studied based on equivalent-input-disturbance (EID) approach. More precisely, with the use of suitable Lyapunov-Krasovskii functional together with average dwell-time technique, an output feedback tracking controller is designed which makes that the states of resulting system can asymptotically track the desired trajectory. Further, the EID estimator is implemented to reject both matched and unmatched disturbances effectively without requiring any prior knowledge of the disturbances. Simulation results are presented to illustrate the effectiveness and potential of the developed EID-based output tracking control design technique. The results reveal the fact that the tracking controller based on EID provides a better tracking performance than the feedback controller based on sliding mode technique.

This article presents an improved equivalent-input-disturbance (EID) approach to handle unknown disturbances and plant uncertainties. The disturbances and uncertainties are treated as a lumped disturbance in an EID-based control system. The effect of the lumped disturbance is compensated by an EID estimator. A constraint between design parameters and uncertainties is imposed on the design of the estimator. In addition, there are insufficient analyses of the influence of uncertainties on the control performance and the stability of the system. A new filter is devised for an improved EID estimator in this article to remove the constraint. This ensures that the sensitivity of the system to disturbances at low frequencies can be freely decreased. An analysis of the system reveals that uncertainties not only influence disturbance-rejection and reference-tracking performance but also affect system stability. A sufficient stability criterion is derived with consideration of uncertainties. The validity of the presented method is demonstrated by simulation and experimental results.

Sliding mode control (SMC) has been considered as a powerful method for disturbances rejection. On the other hand, we have presented an equivalent-input disturbance (EID) approach to reject disturbances. This paper takes a dual-stage feed drive as an example to compare these two methods. The example shows that, while the EID approach obtains almost the same disturbance rejection performance for matched disturbances as that of the SMC does, it can reject unmatched disturbances. This shows the superiority of the EID approach over SMC method.

Laser Metal Deposition (LMD) has been developed for repair of damaged components and for the direct forming of three-dimensional structures. From the aspect of productivity, shape accuracy of the deposit must be improved to shorten the machining process after LMD. The objective of this work is to control build-up shape by adjusting weld pool size. Configurations of deposits made with various LMD process conditions were measured by cross sectional observation. In addition, signal intensity of heat radiation, plume emission and laser reflection from weld pool were monitored by photodiodes integrated in a laser processing head during the LMD process. The results showed strong correlation between weld pool size and signal intensity of heat radiation. An adaptive shape control system, which consists of an in-process monitoring system and Proportional-Integral-Derivative (PID) controller using that correlation, was developed for controlling build-up shape. Due to the linear relationship with weld pool size, laser power was selected as a PID output parameter adjusted by heat radiation signal. Since the target value of heat radiation signal can be changed flexibly during LMD process in our PID control system, deposit shape is successfully controlled as required with sufficient profile accuracy of build-up layers.Laser Metal Deposition (LMD) has been developed for repair of damaged components and for the direct forming of three-dimensional structures. From the aspect of productivity, shape accuracy of the deposit must be improved to shorten the machining process after LMD. The objective of this work is to control build-up shape by adjusting weld pool size. Configurations of deposits made with various LMD process conditions were measured by cross sectional observation. In addition, signal intensity of heat radiation, plume emission and laser reflection from weld pool were monitored by photodiodes integrated in a laser processing head during the LMD process. The results showed strong correlation between weld pool size and signal intensity of heat radiation. An adaptive shape control system, which consists of an in-process monitoring system and Proportional-Integral-Derivative (PID) controller using that correlation, was developed for controlling build-up shape. Due to the linear relationship with weld pool size, las...

This chapter presents the proportional integral derivative (PID) control of multi-rotor unmanned aerial vehicles as case studies. It discusses the dynamics of a quadrotor and a hexacopter for the PID control system design. Because of nonlinearities and physical parameter uncertainties, the attitude control systems for an unmanned aerial vehicle are proposed to be PID control systems in a cascade structure and the PID controller parameters are found using the auto-tuners. The auto-tuners are implemented on laboratory test rigs specifically designed for multi-rotor unmanned aerial vehicles and operated on the ground for the safety of the equipment. The purpose of using an auto-tuner for the attitude control system is to avoid the time consuming tasks of finding the physical parameters for the secondary and primary plants as well as the actuators. In addition, the dynamics of the closed-loop secondary system are taken into consideration in the primary control system through the application of the cascade auto-tuner.