International Science and Technology Journal

The Linear Quadratic Regulator (LQR) is a well-known method that provides optimally controlled feedback gains to enable the closed-loop stable and high performance design of systems. The optimal control is concerned with operating a dynamic system at minimum cost. The case where the system dynamics are described by a set of linear differential equations and the cost is described by a quadratic function is called the LQ problem. One of the main results in the theory is that the linear–quadratic regulator (LQR), a feedback controller whose equations are given below, provides the solution. The basic principles of this paper is the Linear Quadratic (LQ) and a linear quadratic is a system containing one linear equation and one quadratic equation. Furthermore, the Optimal Control can be used to resolve some of these problems by not specifying exactly where the closed loop values should be directly, but instead by specifying some kind of performance objective function to be optimized. Other optimal control objectives and besides the (LQ) type, can be used to resolve issues of tradeoffs and extra design freedom. We first consider the finite time horizon case for general time varying linear systems, and then proceed to discuss the infinite time horizon case for Linear Time Invariant systems. Linear Quadratic Regulator (LQR) is an optimal multivariable feedback control approach that minimizes the excursion in state trajectories of a system while requiring minimum controller effort. The behavior of a (LQR) controller is determined by two parameters: state and control weighting matrices. These two matrices are main design parameters to be selected by designer and greatly influence the success of the (LQR) tuning console.