Mathematical control of complex systems 2013

Mathematical control of complex systems have already become an ideal research area for control engineers, mathematicians, computer scientists, and biologists to understand, manage, analyze, and interpret functional information/dynamical behaviours from real-world complex dynamical systems, such as communication systems, process control, environmental systems, intelligent manufacturing systems, transportation systems, and structural systems. This special issue aims to bring together the latest/innovative knowledge and advances in mathematics for handling complex systems. Topics include, but are not limited to the following: control systems theory (behavioural systems, networked control systems, delay systems, distributed systems, infinite-dimensional systems, and positive systems); networked control (channel capacity constraints, control over communication networks, distributed filtering and control, information theory and control, and sensor networks); and stochastic systems (nonlinear filtering, nonparametric methods, particle filtering, partial identification, stochastic control, stochastic realization, system identification)

Robust position control of ultrasonic motor using VSS observer

Intrinsic properties of ultrasonic motor (high torque for low speed, high static torque, compact in size, etc.) offer great advantages for industrial applications. However, when load torque is applied, dead-zone occurs in control input. Therefore, sliding mode controller, which is a nonlinear controller, is adopted for ultrasonic motor. The state quantities, such as acceleration, speed, and position are needed to apply the sliding mode controller for position control. However, rotary encoder causes quantization errors in the speed information. This paper presents a robust position control method for ultrasonic motor by using Variable Structure System(VSS) observer. The state variables for sliding mode controller are estimated by the VSS observer. Besides, a small, low cost, and good response sliding mode controller is designed in this paper by using a micro computer that is essential in embedded system for the developments of industrial equipments. The effectiveness of the proposed method is verified by experimental results

Model based control strategies for a class of nonlinear mechanical sub-systems

This paper presents a comparison between various control strategies for a class of mechanical actuators common in heavy-duty industry. Typical actuator components are hydraulic or pneumatic elements with static non-linearities, which are commonly referred to as Hammerstein systems. Such static non-linearities may vary in time as a function of the load and hence classical inverse-model based control strategies may deliver sub-optimal performance. This paper investigates the ability of advanced model based control strategies to satisfy a tolerance interval for position error values, overshoot and settling time specifications. Due to the presence of static non-linearity requiring changing direction of movement, control effort is also evaluated in terms of zero crossing frequency (up-down or left-right movement). Simulation and experimental data from a lab setup suggest that sliding mode control is able to improve global performance parameters

Neural Network-based Finite-time Control of Nonlinear Systems with Unknown Dead-zones: Application to Quadrotors

Over the years, researchers have addressed several control problems of various classes of nonlinear systems. This article considers a class of uncertain strict feedback nonlinear system with unknown external disturbances and asymmetric input dead-zone. Designing a tracking controller for such system is very complex and challenging. This article aims to design a finite-time adaptive neural network backstepping tracking control for the nonlinear system under consideration. In addition,  all unknown disturbances and nonlinear functions are lumped together and approximated by radial basis function neural network (RBFNN). Moreover, no prior  information about the boundedness of the dead-zone parameters is required in the controller design. With the aid of a Lyapunov candidate function, it has been shown that the tracking errors converge near the origin in finite-time. Simulation results testify that the proposed control approach can force the output to follow the reference trajectory in a short time despite the presence of  asymmetric input dead-zone and external disturbances. At last, in order to highlight the effectiveness of the proposed control method, it is applied to a quadrotor unmanned aerial vehicle (UAV)

Decentralised delay-dependent static output feedback variable structure control

In this paper, an output feedback stabilisation problem is considered for a class of large scale interconnected time delay systems with uncertainties. The uncertainties appear in both isolated subsystems and interconnections. The bounds on the uncertainties are nonlinear and time delayed. It is not required that either the known interconnections or the uncertain interconnections are matched. Then, a decentralised delay-dependant static output feedback variable structure control is synthesised to stabilise the system globally uniformly asymptotically using the Lyapunov Razumikhin approach. A case study relating to a river pollution control problem is presented to illustrate the proposed approach

Delay-independent decentralised output feedback control for large-scale systems with nonlinear interconnections

In this paper, a stabilisation problem for a class of large-scale systems with nonlinear interconnections is considered. All the uncertainties are nonlinear and are subject to the effects of time delay. A decentralised static output feedback variable structure control is synthesised and the stability of the corresponding closed-loop system is analysed based on the Lyapunov Razumikhin approach. A set of conditions is developed to guarantee that the large-scale interconnected system is stabilised uniformly asymptotically. Further study shows that the conservatism can be reduced by employing additive controllers if the known interconnections are separated into matched and mismatched parts. It is not required that the subsystems are square. The designed controller is independent of time delay and thus it does not require memory. Simulation results show the effectiveness of the proposed approach

Observer-based adaptive sliding mode fault-tolerant control for the underactuated space robot with joint actuator gain faults

summary:An adaptive sliding mode fault-tolerant controller based on fault observer is proposed for the space robots with joint actuator gain faults. Firstly, the dynamic model of the underactuated space robot is deduced combining conservation law of linear momentum with Lagrange method. Then, the dynamic model of the manipulator joints is obtained by using the mathematical operation of the block matrices, hence the measurement of the angular acceleration of the base attitude can be omitted. Subsequently, a fault observer which can accurately estimate the gain faults is designed, and the estimated results are fed back to the adaptive sliding mode fault-tolerant controller. It is proved that the proposed control algorithm can guarantee the global asymptotic stability of the closed-loop system through the Lyapunov theorem. The simulation results authenticate the effectiveness and feasibility of the control strategy and observation scheme

An Adaptive Dynamic Surface Controller for Ultralow Altitude Airdrop Flight Path Angle with Actuator Input Nonlinearity

In the process of ultralow altitude airdrop, many factors such as actuator input dead-zone, backlash, uncertain external atmospheric disturbance, and model unknown nonlinearity affect the precision of trajectory tracking. In response, a robust adaptive neural network dynamic surface controller is developed. As a result, the aircraft longitudinal dynamics with actuator input nonlinearity is derived; the unknown nonlinear model functions are approximated by means of the RBF neural network. Also, an adaption strategy is used to achieve robustness against model uncertainties. Finally, it has been proved that all the signals in the closed-loop system are bounded and the tracking error converges to a small residual set asymptotically. Simulation results demonstrate the perfect tracking performance and strong robustness of the proposed method, which is not only applicable to the actuator with input dead-zone but also suitable for the backlash nonlinearity. At the same time, it can effectively overcome the effects of dead-zone and the atmospheric disturbance on the system and ensure the fast track of the desired flight path angle instruction, which overthrows the assumption that system functions must be known