Development of nonlinear disturbance observer based control and nonlinear PID: A personal note

This paper gives an overview of early development of nonlinear disturbance observer design technique and the Disturbance Observer Based Control (DOBC) design. Some critical points raised in the development of the methods have been reviewed and discussed which are still relevant for many researchers or practitioners who are interested in this method. The review is followed by the development of a new type of nonlinear PID controller for a robotic manipulator and its experimental tests. It is shown that, under a number of assumptions, the DOBC consisting of a predictive control method and a nonlinear disturbance observer could reduce to a nonlinear PID with special features. Experimental results show that, compared with the predictive control method, the developed controller significantly improves performance robustness against uncertainty and friction. This paper may trigger further research and interests in the development of DOBC and related methods, and building up more understanding between this group of control methods with comparable ones (particularly control methods with integral action)

On a switching control scheme for nonlinear systems with ill-defined relative degree

This paper discusses the applicability of a switching control scheme for a nonlinear system with ill-defined relative degree. The control scheme switches between exact and approximate input-output linearisation control laws. Unlike a linear system under a switching control scheme, the equilibria of a nonlinear system may change with the switching. It is pointed out that this is not sufficient to cause instability. When the region of the approximate linearisation control law is attractive to the exact zero dynamics, it is possible that the closed-loop system under the switching control scheme is still stable. The results in this paper shows that the switching control scheme proposed in Tonlin and Sastry (Systems & Control Letters 35(3)(1998) 145-154) is applicable for a wider class of nonlinear systems

Disturbance observer based control for nonlinear systems

This paper presents a general framework for nonlinear systems subject to disturbances using disturbance observer based control (DOBC)techniques. A two-stage design procedure to improve disturbance attenuation ability of current linear/nonlinear controllers is proposed where the disturbance observer design is separated from the controller design. To facilitate this concept, a nonlinear disturbance observer is developed for disturbances generated by an exogenous system, and global exponential stability is established under certain condition. Furthermore, semiglobal stability condition of the composite controller consisting of a nonlinear controller and the nonlinear disturbance observer is established. The developed method is illustrated by the application to control of a two-link robotic manipulator

Predictive control for general nonlinear systems using approximation

This paper addresses a tracking problem for general nonlinear systems using model predictive control (MPC). After approximating the tracking error in the receding horizon by its Taylor series expansion to any specified order, an analytic solution to the MPC is developed and a closed-form nonlinear predictive controller is presented. Different from other nonlinear model predictive control (NMPC), there is a built-in integral action in the developed scheme and the implementation issues are discussed. Further more, it is pointed out that the proposed NMPC derived using approximation can stablise the original nonlinear systems if certain condition, which can be met by properly choosing predictive times and the order for Taylor expansion, is satisfied. Simulation demonstrates the effectiveness of the proposed NMPC

Maximisation of feasibility/stability regions of model predictive control for constrained linear systems

Stability of model predictive control could be achieved by adding a terminal weighting term in a performance index and the feasibility/stability region largely depends on the choice of the terminal weighting term and associated terminal control laws. For constrained linear systems, different from existing methods where the stability region is estimated by its terminal region, a new method to estimate feasibility/stability regions directly is proposed using a new representation of the behaviour of MPC. A design procedure is then developed to determine the terminal term such that the feasibbility/stability region of MPC algorithms is as large as possible. Examples show that the stability region is greatly enlarged

Disturbance-observer-based robust control for time delay uncertain systems

A robust control scheme is proposed for a class of systems with uncertainty and time delay based on disturbance observer technique. A disturbance observer is developed to estimate the disturbance generated by an exogenous system, and the design parameters of the disturbance observer are determined by solving linear matrix inequalities (LMIs). Based on the output of the disturbance observer, a robust control scheme is proposed for the time delay uncertain system. The disturbance-observer-based robust controller is combined of two parts: one is a linear feedback controller designed using LMIs and the other is a compensatory controller designed with the output of the disturbance observer. By choosing an appropriate Lyapunov function candidate, the stability of the closed-loop system is proved. Finally, simulation example is presented to illustrate the effectiveness of the proposed control scheme

Worst-case analysis of moving obstacle avoidance systems for unmanned vehicles

This paper investigates worst-case analysis of a moving obstacle avoidance algorithm for unmanned vehicles in a dynamic environment in the presence of uncertainties and variations. Automatic worst-case search algorithms are developed based on optimization techniques, and illustrated by a Pioneer robot with a moving obstacle avoidance algorithm developed using the potential field method. The uncertainties in physical parameters, sensor measurements, and even the model structure of the robot are taken into account in the worst-case analysis. The minimum distance to a moving obstacle is considered as an objective function in automatic search process. It is demonstrated that a local nonlinear optimization method may not be adequate, and global optimization techniques are necessary to provide reliable worst-case analysis. The Monte Carlo simulation is carried out to demonstrate that the proposed automatic search methods provide a significant advantage over random sampling approaches

Trajectory generation for autonomous soaring UAS

As unmanned aerial vehicles are expected to do more and more advanced tasks, improved range and persistence is required. This paper presents a method of using shallow layer cumulus convection to extend the range and duration of small unmanned aerial vehicles. A simulation model of an X-models XCalubur electric motor-glider is used in combination with a refined 4D parametric thermal model to simulate soaring flight. The parametric thermal model builds on previous successful models with refinements to more accurately describe the weather in northern Europe. The implementation of the variation of the MacCready setting is discussed. Methods for generating efficient trajectories are evaluated and recommendations are made regarding implementation

Control of sampled data systems with variable sampling rate

This paper addresses stability and performance of sampled-data systems with variable sampling rate, where the change between sam- pling rates is decided by a scheduler. A motivational example is pre- sented, where a stable continuous time system is controlled with two sampling rates. It is shown that the resulting system could be unsta- ble when the sampling changes between these two rates, although each individual closed-loop system is stable under the designed controller that minimizes the same continuous loss function. Two solutions are presented in this paper. The ¯rst solution is to impose restrictions on switching sequences such that only stable sequences are chosen. The second solution presented is more general, where a piecewise constant state feedback control law is designed which guarantees stability for all possible variations of sampling rate. Furthermore, the performance definedn by a continuous time quadratic cost function for the sampled-data system with variable sampling rate can be optimised using the proposed synthesis method

Optimisation-based verification process of obstacle avoidance systems for unicycle-like mobile robots

This paper presents an optimisation-based verification process for obstacle avoidance systems of a unicycle-like mobile robot. It is a novel approach for the collision avoidance verification process. Local and global optimisation based verification processes are developed to find the worst-case parameters and the worst-case distance between the robot and an obstacle. The kinematic and dynamic model of the unicycle-like mobile robot is first introduced with force and torque as the inputs. The design of the control system is split into two parts. One is velocity and rotation using the robot dynamics, and the other is the incremental motion planning for robot kinematics. The artificial potential field method is chosen as a path planning and obstacle avoidance candidate technique for verification study as it is simple and widely used. Different optimisation algorithms are applied and compared for the purpose of verification. It is shown that even for a simple case study where only mass and inertia variations are considered, a local optimization based verification method may fail to identify the worst case. Two global optimisation methods have been investigated: genetic algorithms (GAs) and GLOBAL algorithms. Both of these methods successfully find the worst case. The verification process confirms that the obstacle avoidance algorithm functions correctly in the presence of all the possible parameter variations