Issues of the robust stabilization for axial-flow compressor dynamics with respect to the uncertainty in axisymmetric characteristics are presented. This is achieved by the design of sliding mode controllers. By assuming an actuation directly modulating the mass flow such as the close-coupled valve, the domain of attraction for the unstalled operating equilibrium will be enlarged to a great extent. Nonlocal robust stability of the operating equilibrium, with respect to the uncertainty in the unstable branch of axisymmetric compressor characteristic, is also provided by the proposed control laws. Moreover, it is demonstrated that the robust control scheme can be employed to fulfill the task of stall recovery. The proposed stabilization design does not require an explicit form for compressor characteristic.

The certainty equivalent control has achieved asymptotic tracking stability of linearizable systems in the presence of parametric uncertainty. However, two major drawbacks remain to be tackled, namely, the risk of running into singularity for the calculated control input and the poor transient behaviour arising frequently in a general adaptive system. For the first problem, a high gain control is activated in place of the certainty equivalent control until the risk is bypassed. Among others, it requires less control effort by taking advantages of the bounds for the input vector field. Moreover, the switching mechanism is smooth and hence avoids possible chattering behaviour. Next, to solve the second problem, a new type of update algorithm guaranteeing the exponential stability of the overall closed-loop system, on a weaker persistent excitation (PE) condition, is proposed. In particular, it requires no filtering of the regressor and hence is easier to implement. Simulation results demonstrating the validity of the proposed design are given in the final.

No abstract

No abstract

Abstmct-An adaptive compensation scheme for a servosystem with Coulomb and viscous friction is presented. The proposed compensator consists of a standard linearizing control and an on-line nonlinear adaptive observer for estimating the coefficients of the Coulomb and the viscous frictions. Without relying on persistent excitation, the proposed design ensures the asymptotic stability of both the tracking errors and the friction estimation errors for any bounded desired velocity trajectories. Moreover, the friction coefficients can be separately identified for any a nonconstant commanded velocity trajectory. Simulation results done on a one-dimensional servosystem demonstrate the effectiveness of the proposed scheme.