A method of synthesis of modal control in servo systems with a differentiating observer of the reference action is proposed. It is shown that with the joint design of the modal controller and the observer, the uncertainty of the synthesis problem arises, which leads to the oscillation of the regulated value under step setting actions. To eliminate this uncertainty, the transition to the optimization problem of control synthesis was carried out. A numerical example of the formulation and solution of this problem is presented, which confirms the effectiveness of the proposed method.
The problem of synthesis of precision modal control systems is considered. It is noted that a common approach to solving this problem is to consistently meet the requirements for the nature of the transient process and for the indicators of its accuracy. This approach to synthesis is faced with the need to make design decisions under incomplete conditions. In practice, this circumstance leads to obtaining synthesis results with undesirable deviations from technical requirements. When designing precision control systems, such deviations are unacceptable. To eliminate the difficulties that arise, a transition to interval methods for formulating and solving modal synthesis problems is proposed. The theoretical possibility of the interval approach is based on the excessive variety of possible placement of eigenvalues in the spectrum of the characteristic matrix of the system. An example of an interval synthesis of a system with a modal controller and additional output feedback is considered. The restrictions on the spectrum of the specified matrix are formed, which determine the fulfillment of the requirements for the monotonicity of the transient process, the regulation time and the accuracy of the response to harmonic influences. It is noted that the variety of solutions obtained creates the preconditions for a multi-alternative approach to modal synthesis of systems.
The paper proposes a method for solving the Brockett problem based on the synthesis of robust modal control for systems with non-stationary parameters, which does not require complex adaptation algorithms that involve the introduction of a variable regulator matrix. A transition to the task of synthesizing the regulator is shown, using a certain optimality criterion with limitations, which provides similar values to those of the regulator coefficients. A practical numerical example of setting and solving this problem is presented, which confirms the effectiveness of the proposed method. To illustrate the results obtained, a root travel time curve was constructed for two systems: robust and non-robust.
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