By Duncan C. McFarlane, Keith Glover
This monograph matters the layout of suggestions controllers for multivariable linear dynamic platforms. the actual method is to think about a coprime issue description of the plant's move functionality and to symbolize a family members of structures through perturbing the numerator and denominator. The layout of controllers to robustly stabilize any such family members is posed as an H? optimization challenge and a few specific suggestions are acquired. equally, methods for decreased order modelling and controller layout are derived. ultimately, the consequences are exploited to provide a scientific loop shaping keep an eye on method layout strategy that's assessed on a number of aerospace examples. The ebook could be applicable for complex undergraduate or graduate periods requiring just a first direction in state-space equipment. It additionally supplies a great creation to multivariable keep an eye on and using H? methods.
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Extra info for Robust Controller Design Using Normalized Coprime Factor Plant Descriptions
Sample text
3 will now be cxploitcd to generate controllcrs which guarantec a level of robust stability in a closed-loop systcm. Wc call such controllers robustly stabilizing controllera. ,,~a~, such that, for all A E T),, there exists a single controller which stabilizes ~ u ( P, A) is given by where K is chosen from all controllers which stabilize Fu(P,O). s an Hoo optimization problem where a controller K is chosen to minimize the Hoo norm of 40 a closed-loop transfer function, under the constraint that it nmst also stabilize the nominal plant.
E. ) (ii) cucirclc~ thc origin ~IA + ~113~imca an~iclockwi3c. 1 THI'CEE STABILIZATION UNCERTAIN SYSTEMS Introduction The most important objective in control system design is stability. This is a minimum requirement for any design. Also, an unavoidable fact in design is that the assumed model of the system being considered for compensation (called the nominal model) will differ in bchaviour from the actual system. This is because modeUing physical systems for control design invariably involves a trade-off between simplicity of the model and its accuracy in matching ~hc bchaviour of the actual system.
T'u(P, A,,)K)(jWo) = 0, which implies instability. e. A~ e (T)s, N T)u~). The reader is referred to this text for details of this construction. 3 gives a very general condition for robust stability and can bc applied to any perturbed systcm that can be written as an U L F T , ruld not just the three uncertainty models that wc have considercd in this chapter. 4 to construct a standard frmncwork for robust controller design. 3 to the spccific cases where the nominal plant is subject to additive, multiplicative and coprime factor uncertainty.
