In the previous chapter, an adaptive control scheme was illustrated involving a number of controllers designed and tuned corresponding to a range of operating conditions. In this chapter, the focus is on designing a single controller which is able to guarantee the performance specification for a range of operating conditions. The concept of robust and low-order controller design by weighted and normalized eigenvalue-distance minimization (WNEDM) is applied for improving the damping of the inter-area modes. The technique was applied for a singleinput, single-output (SISO) power system model in [Pal et al., 2000, Pal, 19991 and was later extended for MIS0 systems in [Pal et al., 20041. The basic idea is to place the closed-loop eigen values of the system at certain desired locations in the left-half of the complex plane. he robustness issue is addressed by considering a family of operating conditions and optimizing over the worst case scenario. To start with, the design procedure is presented for a SISO system for easy understanding. Later on it is generalized in the multi-variable framework. A case study is presented based on the power system model described in Chapter 4. The objective is to provide additional damping to three inter-area modes by a single FACTS device employing remote signals. The problem is formulated to address multi-input-single-output (MISO) control design for a group of single-input-multi-output (SIMO) system models.
Eigen-Value-Distance MinimizationIn robust low-order controller design [Schmitendorf and Wilmers, 19911, the desired closed-loop pole locations are specified and a suitable controller is sought to move the open-loop poles towards the specified locations. An optimization problem is then solved with the controller parameters as the design