LPVTools Data Structures
LPVTools is implemented using object-oriented programming. The toolbox introduces several class-based data structures for modeling LPV systems. These data structures extend the functionality associated with standard MATLAB data structures from the Control Systems Toolbox and the Robust Control Toolbox into the LPV framework. This is pictorially represented in Table 1.
Table 1: Relation between LPVTools and MATLAB objects.
Table 1 shows the relation between the core LPVTools data objects and existing MATLAB objects. The first row of the table (``Nominal'') shows the basic MATLAB objects: Matrices are double objects, state-space systems are ss objects, and frequency responses are frd objects. The third row of the table (``Nominal Gridded LPV'') shows the corresponding core grid-based LPV objects. The core data structure for grid-based LPV models is the pss (denoting parameter-varying state space model), which stores the LPV system as a state space array (ss) defined on a finite, gridded domain. The notions of parameter-varying matrices and parameter-varying frequency responses arise naturally to complement the pss objects. LPV systems are time-varying and hence frequency responses can not be used to represent the system behavior as parameters vary. However frequency responses are useful to gain intuition about the system performance at fixed locations in the operating domain. LPVTools represents parameter varying matrices and frequency responses by pmat and pfrd data objects, respectively. These two data objects are both stored as a data array defined on a gridded domain. A pmat stores a double array, while a pfrd stores an array of frequency responses (frd object in the Control System Toolbox). The (pmat, pss, pfrd) objects should be viewed as parameter-varying extensions of the standard MATLAB and Control Systems Toolbox objects (double, ss, frd).
The second row of the table (``Uncertain'') shows the equivalent objects used to represent uncertainty: Uncertain matrices, state space systems, and frequency responses are represented by umat, uss, and ufrd objects, respectively (from the Robust Control Toolbox). The fourth row of Table 1 (``Uncertain Gridded LPV'') shows the corresponding parameter-varying objects with uncertainty: Uncertain parameter-varying matrices, state space systems, and frequency responses are represented by upmat, upss, and upfrd objects, respectively. These objects enable the integration of uncertainty into LPV models. The (upmat, upss, upfrd) objects should be viewed as parameter-varying extensions of the uncertain Robust Control Toolbox objects (umat, uss, ufrd).
LPVTools represents LFT-based parameter varying matrices and state-space systems by plftmat and plftss data objects, respectively. Uncertainty can be integrated into the plftmat, and plftss objects, allowing these data objects to model systems with, and without uncertainty. The plftmat and plftss objects should be viewed as LFT-based parameter-varying extensions of the standard MATLAB, Control System Toolbox, and Robust Control Toolbox objects double, ss, umat, and uss, as seen in rows five ("Nominal LFT LPV") and six ("Uncertain LFT LPV") in Table 1.