Conclusion
In this chapter, state variables were introduced which converts the transfer function to a set of first order differential equations. It is shown that the system equations have eigenvalues which are the same as the roots of the characteristic equation. Using computer program software such as MathCad, the eigenvalues and eigenvectors can be calculated easily. The eigenvectors were used to transform the system equa- tions to a set of decoupled first order differential equations. The concept of control- lability and observability were discussed with the transformed equations. There are other methods which are beyond the scope of this book and the interested readers are referred to more advanced books.
State variable feedback control theory is discussed and it is shown that by suit- able selections of the gain vector the eigenvalues can be moved to desirable lo- cation on the s-plane. Practical limitations of saturations and nonlinearities must be considered when designing state variable feedback control. For nonmeasurable state variables, state observer might be used. The observer must be faster than the system equations for successful control. The presence of noise always causes problems with observer and in most practical situation in servo control systems this control strategy must be avoided. As will be shown later by selection of intelligent state variables, it can be designed that all state variables be measurable for direct feedbac