PID Passivity-Based Control of Nonlinear Systems with Applications. Romeo Ortega

Romeo Ortega

       José Guadalupe Romero

       Pablo Borja

       Alejandro Donaire

Acronyms

ACalternate currentAMMassumed modes methodCbIcontrol by interconnectionCLcontrolled LagrangiansDACdigital‐to‐analog converterDCdirect currentDOFdegree(s)‐of‐freedomELEuler–LagrangeFOCfield‐oriented controlGASglobally asymptotically stableGESglobal exponential stabilityHVDChigh‐voltage direct currentIAintegral actionIDAinterconnection and damping assignmentIISSintegral input‐to‐state stabilityISSinput‐to‐state stabilityLMIlinear matrix inequalityLTIlinear time‐invariantMDICSmatched disturbance integral controlled systemPBCpassivity‐based controlPDEpartial differential equationPEMproton exchange membranepHport‐HamiltonianPDproportional‐derivativePIproportional‐integralPIDproportional‐integral‐derivativePMSGpermanent magnet synchronous generatorPMSMpermanent magnet synchronous motorPWMpulse‐width modulationSPRstrictly positive realVSRvoltage source rectifiersVTOLvertical take‐off and landing

Notation

      Given a vector , the symbol denotes its Euclidean norm, i.e. . We denote the th element of as . The th element of the canonical basis of is represented by . To ease the readability, column vectors are also expressed as .

      Consider the matrix , then denotes the th column of , the th row of , and the th element of . Moreover, denotes the transpose of . Given a square matrix , . To simplify the notation, we express diagonal matrices as , where are the diagonal elements of the matrix.

      The symbol denotes the identity matrix. The symbol refers to the th eigenvalue of . In particular, , denote the largest and the smallest eigenvalue of , respectively. A matrix is said to be positive semidefinite if and for all , and is said to be positive definite if the inequality is strict, i.e. for all . is negative (semi)definite if is positive (semi)definite. For a positive definite matrix and a vector , we denote the weighted Euclidean norm as . The notation used for constant matrices is directly extended to the nonconstant case.

      Unless something different is stated, all the functions treated in this book are assumed to be smooth. Moreover, the symbol is reserved to express time, where we assume Скачать книгу