Robust H/sub ∞/ control of uncertain nonlinear system via state feedback

Robust transient stabilisation problem for a synchronous generator in a power network

“…A robust adaptive nonlinear feedback control (4)- (7), (9) has been designed for the generator g m which does not assume the knowledge of the overall system parameters excepting for the machine damping and inertia constants: an innovative design technique has been used since available techniques developed in [8], [13], [14], [15] do not apply to the model (3). The proposed controller guarantees the L 2 and L ∞ disturbance attenuation and asymptotic regulation properties (S1)-(S4) under assumptions i)-vi) on the network dynamics generalizing those required by the single machine-infinite bus approximation (which does not capture the typical multivariable nature with nonlinear complex coupling of power systems and does not take into account the effect of the generator g m dynamics on the remote nework dynamics) and allowing dynamic interactions between the local deviations of the generator states from the corresponding equilibrium values and the remote generators states (in order to comply with the typical instability phenomena in which the behaviour of generators in the network becomes oscillatory with increasing amplitudes).…”

“…3 Note that the control techniques developed in [8], [13], [14], [15] do not apply to the model (3) due to the presence of the uncertain term (θ 5r I 2 qr + θ 6r Per) multiplying the control input u f r . 4 Note that the dynamics of the relative angular speed ωr can be rewritten in the more compact forṁ …”

“…The single machine-infinite bus model, used in [3], [4], [5], [6], [7], [8], [9], [10], [11], [12] -which neglects the transient behaviour of the other generators as well as the interconnections between them, does not capture the typical multivariable nature with nonlinear complex coupling of power systems (see for instance the inter-area oscillations) and does not take into account the effect of the generator g m dynamics on the remote nework dynamics -is not used since interactions between the dynamics of the generator g m and the remote network machines are allowed: the transient behaviour of the remote generators states is allowed to depend on the local deviations of the generator states from the corresponding equilibrium values. Following the theoretical developments in [13], [14], [15] (even though they do not apply to the model considered in this paper in which an uncertain function multiplies the control input), a robust adaptive nonlinear feedback control is designed for the generator g m which does not assume the knowledge of the overall system parameters excepting for the machine damping and inertia constants. On the basis of upper and lower bounds on the uncertain model parameters, L 2 and L ∞ robustness and transient stabilization are guaranteed under a set of assumptions on the network dynamics which are weaker than those required by the single machine-infinite bus approximation.…”

Robust H∞ Control of Nonlinear Time-varying Delay Systems

“…Using polytopic describing uncertainty is more natural than traditional norm bound [12] , it has little conservation and the norm bound uncertainty can be converted into polytopic uncertainty. In recent years, more and more scholars pay great attention to the research on uncertain time-delay system H∞ control theory [13][14] . With the development of control theory, H∞ control is spread to the nonlinear system, there are many research achievements [15][16][17] .…”

Robust H∞ stabilisation with definite attenuance of an uncertain impulsive switche system

“…The main focus has been on H^ problems for linear systems [2,10], nonlinear systems [9], and systems without delay as well as with delays [2,5,9,10] and so on. In recent years, interest has been extended to the robust Hoc stability problem of impulsive dynamic systems.…”