Reference and command governors for systems with constraints

This paper provides a tutorial overview of reference governors and command governors, which are add-on control schemes for reference supervision and constraint enforcement in closed-loop feedback control systems. The main approaches to the development of such schemes for linear and nonlinear systems are described. The treatment of unmeasured disturbances and parametric uncertainties is addressed. Generalizations to extended command governors, feedforward reference governors, reduced order reference governors, parameter governors, networked reference governors, decentralized reference governors, and virtual state governors are summarized. Examples of applications of these techniques to automotive systems are given. A comprehensive list of references is included. Comments comparing reference and command governor approaches with Model Predictive Control and input shaping, and on future directions in reference and command governor research are included.

Reference and command governors: A tutorial on their theory and automotive applications

Researchers in the domain of unmanned aerial vehicles (UAVs) have recently shown a great deal of interest in the quadcopter domain due to its wide variety of applications. In addition to their military applications, quadcopters are now widely used in the civilian sector. This paper presents optimized controllers for attitude and altitude control of a quadcopter system. A novel conditioned adaptive barrier function integral terminal sliding mode controller (CABFIT-SMC) is designed to address the trajectory tracking problem of the quadcopter, and a sliding mode control (SMC) is implemented for comparative analysis. Four optimization algorithms (i.e., Ant Colony Optimization, Artificial Bee Colony, Particle Swarm Optimization, and Genetic Algorithm) have been used to optimize the proposed control laws. The quadcopter’s non-linear model is formulated through the Lagrange formalism in MATLAB ODE-45, incorporating gyroscopic moments and aerodynamic effects. A Lyapunov stability analysis is carried out to verify the system’s asymptotic stability. A graphical and tabular comparative analysis is provided for all optimized control laws. Five performance indexes, including mean absolute percentage error, root mean square error, integral square error, integral absolute error, and integral time absolute error, are used to determine the best control law. The proposed optimized controllers are evaluated for performance and consistency using a 3D-helical complex trajectory. Based on the rigorous performance evaluation, it has been demonstrated that the CABFIT-SMC controller optimized with the ABC algorithm achieved the most superior results, with the lowest MAPE value of 13.245, RMSE value of 0.0043, and transient response characteristics yielding the quickest rise and settling times. The commendable performance of the ABC-optimized CABFIT-SMC further reinforces its potential as a robust controller for precise attitude, altitude, heading, and position tracking in quadcopter systems. 

Multi-Optimization of Novel Conditioned Adaptive Barrier Function Integral Terminal SMC for Trajectory Tracking of a Quadcopter System

According to this plant control device, on the basis of a correction target- value candidate of control output, a reference governor uses a prediction model in which a closed loop system including a plant and a feedback controller are modeled to sequentially calculate across a limited prediction horizon a prediction value for a plant state quantity that includes a specific state quantity to which conditions are assigned. When doing so, if the prediction value of a specific state quantity conflicts with the conditions in relation to a correction target-value candidate, the reference governor excludes such correction target-value candidate from a final correction target value. As a result of the foregoing, the sufficiency of the conditions is guaranteed and the calculation load necessary for correction of the target values of control output is reduced.

Plant control device

A three-dimensional compressible large eddy simulation (LES) method was performed to explore the flow and heat transfer characteristics in the hole and mixing zone of a crossflow film cooling model. A traditional cylindrical hole and diffusion slot hole were selected as the cases for the film hole. The characteristics of the crossflow film flow-field and the influence of the internal crossflow on the film cooling of the diffusion slot hole were explained by the vortex flow in the hole and the instantaneous/time-averaged jet mixing. The results showed that helical motion is easily induced in the holes under the influence of crossflow. Asymmetric outlet flow behavior is the main reason for the asymmetric characteristics downstream of the hole. The difference in the blowing ratio results in the difference in the strength of the spiral vortex and the central vortex tube inside the hole. For the diffusion slot hole, the high-speed zone caused by the crossflow effect at the hole-inlet gradually evolves into strip shapes under the combined action of axial extrusion and spanwise diffusion. With the disappearance of the helical structure, the high-speed areas gradually converge on both sides of the hole exit in the span direction, and the streamline at the exit develops relatively smoothly. The inlet crossflow and the crossflow Reynolds number have little effect on the film cooling effectiveness of the diffusion slot hole. With an increase in the blowing ratio, the lateral diffusion capacity of the film is gradually enhanced. Furthermore, compared with the cylindrical hole, the instantaneous film fluctuation region of the diffusion slot hole case is smaller in range and more symmetrical in distribution. These findings advance the understanding of the film cooling of diffusion slot holes.

Large eddy simulation of film cooling flow from diffusion slot hole with crossflow coolant configuration

In this paper, we propose a gain scheduled reference governor for control of systems with constraints on the state and/or input variables. We use the reference governor with outer feedback constructed via model following control method. We apply this control scheme to design of long seek control of hard disk drives. To achieve short seek time for long seek distance problems, we consider gain scheduling with the reference governor; more precisely, we switch feedback gains according to the location of the state. Moreover, we examine the usefulness of the proposed method by applying it to benchmark problems of hard disk drive control.

Gain scheduled reference governor and its application to long seek control of hard disk drives

In this paper, we propose to use combination of the reference governor with outer feedback and model following control method for long seek control problem of hard disk drive. The real hard disk drive is a very high dimensional system and it is not adequate to use it as a control model. In the model following control scheme, a lower dimensional system is used as a control model to generate the control input and the reference input for the real hard disk drive. By using the reference governor with outer feedback for the control model, we can keep the constraint condition and get a good response. Moreover, we examine the effectiveness of the proposing method through the simulation for the benchmark problem.

Long seek control of hard disk drives using reference governor: An improved result

In this paper, we discuss the implementation of a control system using reference governor for the control of constraint systems. This control scheme uses the maximal output admissible set to determine the reference input r[k] at the time k. When the number of facets of the maximal output admissible set is very large, it might happen that the computing time to determine r[k] exceeds the sampling period. To reduce the computing time, we propose an efficient scheme to determine r[k] using the information of the facet Fik−1 which is used to determine r[k−1] and the set of facets which are adjacent to Fik−1 . Set of adjacent facets for every facet of the maximal output admissible set are computed in advance. Moreover, the effectiveness of proposing method is verified by simulation and experiment for a cart system with pendulum.

https://www.jstage.jst.go.jp/article/iscie/27/4/27_187/_pdf

拘束システムに対するリファレンスガバナの実装;拘束システムに対するリファレンスガバナの実装;On the Implementation of Reference Governor for Constraint Systems

Model following control (MFC) is one of practical methods to control high order systems. A model following controller contains an ideal model of the plant and a real control system tracks the behavior of the ideal model output. Several types of MFC schemes have been proposed [1–4]. In this paper, we adopt a MFC scheme which provides the output and the control input of the ideal model as reference input and feed-forward control input to the real system, respectively. This can improve the transient response of the real system but sometimes the output has a large overshoot when real systems have unstable zeros. We propose a modification of this scheme to reduce overshoot by inserting an additional compensator. Moreover, we apply the modified scheme to the hard disk drive seek control problem.

Model Following Control for Systems with High-Frequency Resonant Terms and Unstable Zeros

Aiming at the problem of parameter uncertainty and external interference in the trajectory tracking of quadrotor unmanned aerial vehicle (UAV), a discrete-time fast terminal sliding mode control (FTSMC) scheme is proposed in this paper. Firstly, the position model of the UAV is derived based on the dynamic equation, and the discrete-time model of the UAV is obtained and analyzed by Euler discretization technology. Then, by introducing a new discrete-time fast terminal sliding mode surface, and designing the fast sliding mode terminal control rate based on equivalent control, the UAV can track the desired trajectory with small steady-state error. Finally, in the experimental part, the feasibility and superiority of this scheme are verified by comparing with the traditional PID position control method.

Trajectory tracking method of UAV based on discrete-time terminal sliding mode

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