John F. Dorsey

Robust tracking control of robots by a linear feedback law

For the trajectory following problem of a robot manipulator, a simple linear robust fedback control law with constant gain matrix is proposed that makes the resulting error system uniformly ultimately bounded. This control law is very easy to implement by simply choosing a feedback gain according to the coefficients of a polynomial function of the tracking errors which is a bounding function for the terms in the Lagrange-Euler formulation. In the limit as the gain approaches infinity the error system becomes globally asymptotically stable. >

Robust control for the tracking of robot motion

In this paper we examine the stability of a proportional derivative (PD) controller for the trajectory-following problem of a robot manipulator. We use Lyapunovs second method to derive a uniform boundness result for the PD controller. We show that if the PD controller gains are chosen greater than a specific bound and if the initial tracking error is zero, the velocity and position tracking errors are uniformly bounded. We then develop two additional controllers that use auxiliary control inputs along with the PD controller. Both of these controllers are shown to yield a uniform ultimate boundness property for the tracking error.

Toward a globally robust decentralized control for large-scale power systems

A robust control scheme is presented that stabilizes a nonlinear model of a power system to a very large class of disturbances that includes any disturbances causing the system to exhibit sustained oscillation. The disturbance can be anywhere in the power system. The fact that the improvement in stability is significant and system wide leads to the name globally robust control. The control is local or decentralized in the sense that the control of each generator depends only on information available at that generator, and is derived using Lyapunovs direct method. The derivation is quite general, permitting a second-order representation of the turbine/governor and any generator model. Simulation results are presented which show the effectiveness of the proposed control against instabilities of current importance including sustained oscillations following a major system disturbance such as a fault or major line outage. The control is also effective for steady-state operation.

Application of robust control to sustained oscillations in power systems

Transient control of the sustained oscillations that can occur after a major disturbance to a power system is investigated. A control scheme for an n-generator system is first developed using a classical machine model, and then extended to a machine model that includes governor/turbine dynamics. The proposed control strategies are linear and require only local relative angle and velocity measurements for the classical model case, plus the measurement of mechanical power if governor/turbine dynamics are included. Using Lyapunovs direct method, the control is shown to be robust with respect to parameter and load variations, and topology changes in the power system. The overall power system is shown to be exponentially stable in the main so that any oscillation, anywhere in the system, can be damped efficiently. The results are obtained without any linearization of the power system model. Simulation results for the 30-bus New England system demonstrate the effectiveness of the proposed control. >

Robust control of robots by the computed torque law

Abstract For the trajectory following problem of a robot manipulator, the standard computed torque control law is shown to be robust with respect to unknown dynamics by judiciously choosing the feedback gains and the estimates of the nonlinear dynamics. The choices for the constant gains depend only on the coefficients of a polynomial bound of the unknown dynamics. The asymptotic stability of the position and velocity tracking errors is also investigated.

Exponentially stable trajectory following of robotic manipulators under a class of adaptive controls

For the trajectory following problem of a robot manipulator, a new class of adaptive controls is introduced. A control in this class consists of a robust control part and an adaptive part. It is shown that the adaptive control part can be chosen to be any of existing adaptation laws and that consequently existing results can be viewed as special cases of the proposed result. The robust control part is added to make the whole adaptive control system be robust with respect to possible unknown functional dynamics, estimation error, and disturbances. The choice of robust control part depends only on bounding functions of the uncertainties. The global and exponential stability of the position and velocity tracking errors is guaranteed under every control in the proposed class.

Robust estimation and control of robotic manipulators

For the trajectory following problem of a robot manipulator, a robust estimation and control scheme which requires only position measurements is proposed to guarantee uniform ultimate bounded stability under significant uncertainties and disturbances in the robot dynamics. The scheme combines a class of robust control laws with a robust estimator where the robust control law can be chosen to be either a modification of the standard computed torque control law or simply a linear and decentralized “PD” control law. The proposed robust estimator is also linear and decentralized for easy implementation. Constructive choices of the gains in the control law and estimator are proposed which depend only on the coefficients of a polynomial bounding function of the unknown dynamics. The asymptotic stability of the tracking errors and the estimation error is also investigated. Experimentation results verify the theoretical analysis.

Model reference robust control of a class of SISO systems

A new control design technique, model reference robust control (MRRC), is introduced for a class of SISO systems which contain unknown parameters, possible nonlinear uncertainties, and additive bounded disturbances. The design methodology is a natural, nontrivial extension of model reference adaptive control (MRAC) which is essential to achieving robust stability and performance for linear time-invariant systems. The methodology also represents an important step toward achieving robust stability for time-varying and nonlinear systems. MRRC requires only input and output measurements of the system, rather than the full state feedback and structural conditions on uncertainties required by existing robust control results. MRRC is developed from existing model reference control (MRC) in a manner similar to MRAC. An intermediate result gives conditions under which MRRC yields exponentially asymptotic stability. The general result yielding uniformly ultimately bounded stability is then developed. A scalar example provides intuition into why the control works against a wide class of uncertainties and reveals the implicit learning capability of MRRC. >

Coherency and Model Reduction: A State Space Point of View

Relationship Between Coherency, Controllability and Observability In state space analysis, controllability is a notion that measures the effect of an input to a particular state, while observability measures the effect of a state to the norm of the systems output vector. Uncontrollability and unobservability represent redundancy in the linear state space model. This paper presents the analytical connections between coherency of generators and redundant states in the linear state model. As discussed in Section 2, every pair of perfectly coherent generators results in uncontrollable states in the linear model. These states are exhibited in the form of zero singular values in the models controllability gramian (W2¿). If a reduced order model is formed by aggregating the coherent generators, then the zero singular values are removed from the controllability gramian of the reduced order model. Parallel results are then presented for the observability gramian (W2¿). The combined results on the connection between coherency and the two gramians provide the stimulus to investigate several topics relative to the coherent behavior of generators.

Reducing the order of very large power system models

Results are presented for reduced-order models of power systems as large as 254 generators and 2500 buses, using the modal-coherency method of model reduction. Extension of order estimation, based on balanced realizations, to larger systems is discussed. An alternative order-estimation approach based on the intergenerator coherency ranking table is introduced and compared to the balanced realization approach. The alternative approach is consistent with the balancing results and more than an order of magnitude faster. >