| Dynamic inversion, similar to feedback linearization in concept, is a nonlinear control design method which is based on cancelling the nonlinearities in the equations of motion by control inputs. Feedback properties of dynamic inversion control laws are directly related to the gains of the desired dynamics. However, the selection of these gains is still an unresolved issue and it has not been fully addressed. In the applications of the method these gains are chosen using past experience and adhoc rules.; In this research, a novel approach introduced in our earlier work is formalized and extended to multivariable cases. This approach is based on linearized models corresponding to different operating points on the equilibrium manifold. Utilizing the desired stability and robustness properties in terms of gain and phase margins of optimal or suboptimal linear quadratic full state feedback designs, via feedback loop mapping, under the structure of dynamic inversion control laws constitute the main theme of the approach. Feedback loop mapping is a procedure in which the feedback inputs of a sophisticated linear design and a linear dynamic inversion design are equated to each other, and the resulting algebraic equations are solved for the unknown dynamic inversion gains. Also, in the derivation of the control law, the steady state effects of the control inputs on the states of slower dynamics, e.g., the elevator effect on angle of attack from longitudinal aircraft dynamics, are taken into account for more appropriate inversions.; This approach is applied to control the longitudinal model of a fighter aircraft. The dynamic inversion control laws with linear quadratic feedback loops are analyzed in the frequency domain, and shown to have satisfactory gain and phase margins at actuator and sensor locations even with the high frequency actuator dynamics and the effective time delay in the loop. The control laws also have a good degree of tolerance to unstructured multiplicative uncertainties at the input. Nonlinear simulations show that the closed loop system has satisfactory transient response, and yields zero steady state errors to constant inputs and disturbances in the case where the desired dynamics structure includes integral control. |
