Integral Sliding Mode Control of Lur’e Singularly Perturbed Systems

This paper investigates the integral sliding mode control problem for Lur’e singularly perturbed systems with sector-constrained nonlinearities. First, we design a proper sliding manifold such that the motion of closed-loop systems with a state feedback controller along the manifold is absolutely stable. To achieve this, we give a matrix inequality-based absolute stability criterion; thus the above problem can be converted into a matrix inequality feasibility problem. In addition, the gain matrix can also be derived by solving the matrix inequality. Then, a discontinuous control law is synthesized to force the system state to reach the sliding manifold and stay there for all subsequent time. Finally, some numerical examples are given to illustrate the effectiveness of the proposed results

Identification and Control of Nonlinear Singularly Perturbed Systems Using Multi-time-scale Neural Networks

Many industrial systems are nonlinear with "slow" and "fast" dynamics because of the presence of some ``parasitic" parameters such as small time constants, resistances, inductances, capacitances, masses and moments of inertia. These systems are usually labeled as "singularly perturbed" or ``multi-time-scale" systems. Singular perturbation theory has been proved to be a useful tool to control and analyze singularly perturbed systems if the full knowledge of the system model parameters is available. However, the accurate and faithful mathematical models of those systems are usually difficult to obtain due to the uncertainties and nonlinearities. To obtain the accurate system models, in this research, a new identification scheme for the discrete time nonlinear singularly perturbed systems using multi-time-scale neural network and optimal bounded ellipsoid method is proposed firstly. Compared with other gradient descent based identification schemes, the new identification method proposed in this research can achieve faster convergence and higher accuracy due to the adaptively adjusted learning gain. Later, the optimal bounded ellipsoid based identification method for discrete time systems is extended to the identification of continuous singularly perturbed systems. Subsequently, by adding two additional terms in the weight's updating laws, a modified identification scheme is proposed to guarantee the effectiveness of the identification algorithm during the whole identification process. Lastly, through introducing some filtered variables, a robust neural network training algorithm is proposed for the system identification problem subjected to measurement noises. Based on the identification results, the singular perturbation theory is introduced to decompose a high order multi-time-scale system into two low order subsystems -- the reduced slow subsystem and the reduced fast subsystem. Then, two controllers are designed for the two subsystems separately. By using the singular perturbation theory, an adaptive controller for a regulation problem is designed in this research firstly. Because the system order is reduced, the adaptive controller proposed in this research has a simpler structure and requires much less computational resources, compared with other conventional controllers. Afterward, an indirect adaptive controller is proposed for solving the trajectory tracking problem. The stability of both identification and control schemes are analyzed through the Lyapunov approach, and the effectiveness of the identification and control algorithms are demonstrated using simulations and experiments

Final Scientific Report: Control Strategies for Complex Systems for Use in Aerospace Avionics

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryAir Force Office of Scientific Research (AFOSR), U.S. Air Force / AF-AFOSR 73-257

Control Strategies for Complex Systems for Use in Aerospace Avionics

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryAir Force Office of Scientific Research (AFSC) / AF-AFOSR 78-363

Design of an Integral Suboptimal Second-Order Sliding Mode Controller for the Robust Motion Control of Robot Manipulators

The formulation of an integral suboptimal second-order sliding mode ((ISSOSM) control algorithm, oriented to solve motion control problems for robot manipulators, is presented in this paper. The proposed algorithm is designed so that the so-called reaching phase, normally present in the evolution of a system controlled via the sliding mode approach, is reduced to a minimum. This fact makes the algorithm more suitable to be applied to a real industrial robot, since it enhances its robustness, by extending it also to time intervals during which the classical sliding mode is not enforced. Moreover, since the algorithm generates second-order sliding modes, while the model of the controlled electromechanical system has a relative degree equal to one, the control action actually fed into the plant is continuous, which provides a positive chattering alleviation effect. The assessment of the proposal has been carried out by experimentally testing it on a COMAU SMART3-S2 anthropomorphic industrial robot manipulator. The satisfactory experimental results, also compared with those obtained with a standard proportional-derivative controller and with the original suboptimal algorithm, confirm that the new algorithm can actually be used in an industrial context

Two dimensional agonistic control

The conventional method of precise multiple-axis motion control entails use of a multiple axis positioning system with each axis carrying not only the workpiece but also the positioning system of the remaining axes. The resultant structure is heavy, sluggish, and expensive. An alternative positioning technique is being investigated in which the motion of the workpiece is controlled by pulling it with tendons, each of which has its own actuator. Since the actuators can be mounted on the base of the structure instead of being carried by motion system of the other axes, they can be relatively large and powerful without the need for a massive structure such as is found in a conventional motion control system. This method of control is given the appellation agonistic, based on the usages of the word suggesting tension or a contest. Agonistic control system can be used for low cost accurate positioning of workpiece. The control task can be moving the workpiece from one point to another point and kept there or tracking a given trajectory. While the workpiece moves, the tendons should be always kept in tension. In this thesis, the model of two dimensional agonistic control (in the case of tendons of infinite elastic modulus) is established. It leads to a nonlinear multi-variable control problem. Based on this nonlinear model, a full-state feedback control law is synthesized. It is composed of two parts. The first part is a feedforward control to cancel the nonlinear dynamics. The second part is a PD control term which requires velocity information. In the practice, velocity measurement may be contaminated by noise. In order of only using position measurement in the control law, a nonlinear observer is designed to provide the velocity information. Numerical simulation is performed to verify the ability of the proposed control law. In reality, the tendon has some elasticity. This finite elasticity, if not accounted for, can render the closed-loop system unstable. The investigation shows that the effect of elastic tendons can be compensated for by appropriately modifying the control law designed for inelastic tendons. In particular, the control law is synthesized using the singular perturbation method. It consists of a fast control and a slow control. The fast control is used to stablize the oscillations incurred by the finite elasticity of the tendon. The slow control drives the system to track the desired trajectory. Robustness of the controller is enhanced by using sliding mode control. In the chapter 4, the design of observer in the elastic case is addressed. Linear uncertain system theory is used. The observer is globally stable. The use of decentralized control scheme makes very simple the controller design and reduces the computational complexity. It is very useful for real time agonistic control. A design approach is presented for the decentralized control scheme. A simple linear second order model is used instead of complex nonlinear model used in centralized version. In this approach, the tension in each tendon is treated as disturbance, estimated by an observer, to be compensated