Robust Exact Model Matching for SISO systems via Finite Precision Dynamic Output Feedback

The problem of robust disturbance rejection for left invertible linear systems, with nonlinear uncertain structure and with measurable and nonmeasurable disturbances, is solved via an independent from the uncertainties static measurement output feedback law. The necessary and sufficient conditions for the problem to have a solution are established. The general explicit expression of the measurement output feedback matrix and the measurement disturbances feedback matrix are derived. The feedback invariant poles are determined. Sufficient conditions for robust disturbance rejection with simultaneous robust stability are also established. The rejection of the influence of the rotary gust disturbing the vertical velocity of the longitudinal motion of an aircraft is achieved.

The problem of robust disturbance rejection for left invertible linear systems, with nonlinear uncertain structure and with measurable and nonmeasurable disturbances, is studied and solved for the first time. The necessary and sufficient conditions for the problem to have a solution, via an independent of the uncertainties static feedback law, are established. The general explicit expression of the feedback matrix is derived. The feedback invariant poles are determined. Sufficient conditions for robust disturbance rejection with simultaneous robust stability, are established.

Uniform exact model matching for a class of linear time-varying analytic systems

The problem of asymptotic robust output command tracking is studied for the case of linear systems with nonlinear uncertain structure. The problem is solved using a compensator with static state feedback, unity output feedback and integral action. The controller is restricted to be independent from the uncertainties. The output of the closed loop system tracks polynomial type reference signals. Sufficient conditions for the problem to have a solution are established. The result of asymptotic robust output command tracking is applied to control the short period longitudinal motion of an aircraft. In the mathematical description of the aircraft an uncertain stability derivative is included. The steps to determine the controller are analytically presented. The effectiveness of the controller over a wide range of the system uncertainty, wind disturbances and actuator failure is illustrated through simulation to the nonlinear model.

The evaluation of a new robust control design method called Robust Model Matching (RMM) is treated by applying it to the design of electrical position servos. RMM is a practical method for the control of plants with wide parameter variations, however, the effect of RMM has not yet been sufficiently examined in experiments and simulations. RMM is applied to the design of electrical position servos, and is evaluated with simulations and experiments. The results of these simulations and/or experiments show that the electrical position servos designed by RMM can eliminate the undesirable influences of: (a) load variations; (b) torque disturbances; (c) non-linear friction; (d) dead zone in a power amplifier; and (e) uncertainty of a velocity sensor's output signal; upon controlled variables. It is also shown that electrical position servos can be robustly stabilized simultaneously by RMM controllers for plants with arbitrary bounded parameter variations.

This paper discusses an application of Robust Model Matching (RMM) to the spill position control of a fuel injection pump. Since the fuel injection servo mechanism is soaked in fuel oil, the parameters of the plant vary due to differences in the viscosity coefficient caused by wide changes in temperature. The invariable fuel injection characteristic is required to meet the demands of the drivability, exhaust emissions and fuel consumption, even though the parameters change. The RMM is an idea which makes up a robust control system against parameter uncertainties.In this paper, we design a robust discrete-time control system based on the RMM: (1) For the low sensitivity, to make small pulse transfer functions from equivalent disturbances to controlled variables. (2) For the robust stability, to increase the margin of pulse transfer functions from conceptual inputs to control variables. The experimental results show that this robust compensator makes up a robust control system against the parameter variations due to the change in temperature. And it is confirmed that the idea of the RMM is effective for the fuel injection pump which includes the variations, identification errors, friction, hysteresis and delay time of the calculation.

Structure at infinity and defect of transfer matrices with time-varying coefficients, with application to exact model-matching

In 1982, Papadimitriou and Yannakakis introduced the Exact Matching (EM) problem where given an edge colored graph, with colors red and blue, and an integer k, the goal is to decide whether or not the graph contains a perfect matching with exactly k red edges. Although they conjectured it to be NP-complete, soon after it was shown to be solvable in randomized polynomial time in the seminal work of Mulmuley et al., placing it in the complexity class RP. Since then, all attempts at finding a deterministic algorithm for EM have failed, thus leaving it as one of the few natural combinatorial problems in RP but not known to be contained in P, and making it an interesting instance for testing the hypothesis RP = P. Progress has been lacking even on very restrictive classes of graphs despite the problem being quite well known as evidenced by the number of works citing it. In this paper we aim to gain more insight into EM by studying a new optimization problem we call Top-k Perfect Matching (TkPM) which we show to be polynomially equivalent to EM. By virtue of being an optimization problem, it is more natural to approximate TkPM so we provide approximation algorithms for it. Some of the approximation algorithms rely on a relaxation of EM on bipartite graphs where the output is required to be a perfect matching with a number of red edges differing from k by at most k/2, which is of independent interest and generalizes to the Exact Weight Perfect Matching (EWPM) problem. We also consider parameterized algorithms and show that TkPM can be solved in FPT time parameterized by k and the independence number of the graph. This result again relies on new tools developed for EM which are also of independent interest.

The problem of asymptotic robust output command tracking with simultaneous disturbance attenuation is studied for the case of linear systems with nonlinear uncertain structure. The problem is solved using a compensator with static state feedback, unity output feedback and integral action. The controller is restricted to be independent from the uncertainties. The output of the closed loop system tracks polynomial type reference signals independently from polynomial type disturbance signals. Sufficient conditions for the problem to have a solution are established. The results are applied to the automating steering of a city bus with large speed and mass uncertainties. An analytic algorithm for the computation of the vehicle tracking controller is presented. The effectiveness of the controller is illustrated through simulation for various manoeuvres.

Given rational matrix functions G, H, and R, the author gives a necessary and sufficient condition for the existence of a causal solution to the equation G*H=R. The author also gives a formula for a solution of the equation when it exists, and uses this particular solution to parametrize the set of all causal solutions of the equation. The results are specialized to the case when the function G is identically equal to identity. Applications of the present results include exact model matching and disturbance decoupling problems. >

Given rational matrix functions, G, H, and R, a necessary and sufficient condition is given for the existence of a causal solution to the equation GXH=R. A formula is given for a solution of the equation when it exists, and this particular solution is used to parameterize the set of all causal solutions of the equation. The results are specialized to the case when the function G is identically equal to identity. Applications of the author's results include exact model matching and disturbance decoupling problems. >

A robust controller, facilitating yaw aircraft manoeuvres without affecting the respective roll modes, is designed for the case of uncertain air density, aircraft's mass and inertia. To handle the issue the robust input output decoupling technique is applied to the lateral motion dynamics of the aircraft. The condition under which the problem is solvable via state feedback appears to be generically true. The general form of the robust static decoupling controllers, as well as the general form of the resulting decoupled closed loop system, are derived. The conditions for robust decoupling with simultaneous robust stability are also established in terms of the lateral stability derivatives.

This paper focuses on the simultaneous robust stability and robust performance problem from the view point of a Quantitative Feedback Theory (QFT) design. We develop closed-form algorithms for computing QFT bounds for this problem class. These bounds are necessary for the QFT's nominal loop shaping.

Control of a Magnetic Levitation System by Robust Model Matching

Parameterized matching on non-linear structures