Composite Control Approach Research Articles

On the connection between nonlinear differential-algebraic equations and singularly perturbed control systems in nonstandard form

Considers a class of control systems represented by nonlinear differential equations depending on a small parameter. The systems are not in the standard singularly perturbed form, and therefore, one of the challenges is to show that the control systems do represent singularly perturbed two-time-scale systems. Assumptions are introduced which guarantee that an equivalent representation for the systems can be obtained in the standard singularly perturbed form, thereby justifying the two-time-scale property. The equations for the slow dynamics are characterized by a set of differential-algebraic equations which have been studied previosly in the literature. The fast dynamics are characterized by differential equations. Both the slow and the fast dynamics are easily derived and are defined in terms of variables that define the original control system. Control design for the class of systems being considered is studied using the composite control approach.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On the adaptive control of flexible joint robots

This paper presents a composite control approach to the adaptive control of flexible joint robots. The scheme requires augmented measurements of torque by using strain gauges mounted on the joint transmission shafts. Simulation results for a three-degree-of-freedom direct drive flexible joint arm currently being developed at Oxford University are included to show the validity of the control scheme.

Non-standard singularly perturbed control systems and differential-algebraic equations

We consider a class of linear control systems represented by equations depending on a small parameter but which are not in the standard singularly perturbed form. One of the challenging system theoretic problem is to obtain an equivalent representation for the control system which, if possible, is in the standard singularly perturbed form. Assumptions are introduced which guarantee that an equivalent representation can be obtained which is in the standard singularly perturbed form, thereby justifying the two time scale property. The equations for the slow dynamics are characterized by a set of differential-algebraic equations which are easily derived from the original equations by setting the parameter to zero; the original assumptions guarantee the existence of solutions of the obtained differential-algebraic equations. The fast dynamics are characterized by different equations in terms of matrices that define the original control system. Control design for the system being considered is studied using the composite control approach. The problem of contract force and position regulation in a robot with its end effector in contact with a stiff surface is considered as an example

Steering control of singularly perturbed systems: a composite control approach

This paper presents a composite control approach to the problem of steering the state of a singularly perturbed system from a given initial state to a given final state, while minimizing a cost functional. The problem is treated for a class of nonlinear systems whose fast dynamics are weakly nonlinear in the fast variables and control inputs. The composite control comprises three components: a reduced control, a feedback boundary-layer stabilizing control and an open-loop right boundary-layer control. It is shown that application of the composite control results in a final state that is O(ϵ) close to the desired state, and a value of the cost that is O(ϵ) close to the optimal cost of the reduced problem.

Steering Control of Singularly Perturbed Systems: A Composite Control Approach

This paper presents a composite control approach to the problem of steering the state of a singularly perturbed system from a given initial state to a given final state, while minimizing a cost functional. The problem is treated for a class of nonlinear systems whose fast dynamics are weakly nonlinear in the fast variables and control inputs. The composite control comprises three components: A reduced control, a feedback boundary layer stabilizing control and a right boundary-layer control. It is shown that application of the composite control results in a final state that is O(ε) close to the desired state, and a value of the cost that is O(ε) close to the optimal cost of the reduced problem.