The problem of ensuring the accuracy for constant and harmonic input actions in systems with modal control is considered. An analytical method of combined formation of both the control accuracy and the type of transient process is proposed. The modal control possibilities for harmonic signals are shown, for which the synthesis method is usually applied to the desired frequency response. It also introduces a requirement of quality in terms of speed. This problem is being solved by drawing up an inequality system. These inequalities are illustrated graphically. Using a numerical example, the effectiveness of the proposed method for solving the problem is shown.

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.