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I)SYSTEM MODELS
1)Differential equations, 2)State space equations, 3)Model linearisation, 4)Transfer Function for SISO systems, 5)Transfer function for MIMO systems
II)FREQUENCY RESPONSE
1)Nyquist plot, 2)Bode plots, 3)Minimum phase systems
III)BASIC DYNAMIC ELEMENTS
1)Lumped parameter systems, ideal integrator, 1 st order lag, systems of 2nd order ideal differeintiator, 2)Systems with distributed parameters
IV)PROPERTIES OF DYNAMICS SYSTEMS
1)Solution of linear stationary equation, 2)Calculation of fundamental matrix, 3)Controllability of system, 4)Observability of system, 5)Stability of linear system, state space model, transfer function model, necessary conditions of stability, hurvitz stability criterium
V)FEEDBACK CONTROL SYSTEMS
1)Describtion of close-loop system, 2)Determination of frequency response of close-loop system
3)Properties of systems with feedback, disturbance influence compensation, dynamic shaping
linearisation
VI)STRUCTURE OF CONTROL SYSTEM
1)Systems with feedback (see chapter V), 2)Systems with feedforward, 3)Systems with feedback and feedforward, 4)Cascade systems
VII)STABILITY OF CLOSE-LOOP SYSTEMS
1)Hurwitz criterium, 2)Nyquist criterium of stability, 3)Computation application of Nyquist criterium, 4)Stability of systems with delay, 5)Smith pedictor
VIII)QUALITY OF CONTROL
1)Direct performance indices, 2)Methods based on root placement, stability degree, resonance degree, root locus, 3)Method basing on integral indices, linear performance index, quadratic performance index, 4)Method based on frequency response, condition of accurate tracking of sinusoid, condition of compensation of sinusoidal disturbance, criterium of maximum magnitude, magnitude and phase margin
IX)COMPENSATORS
1)Stabilisation by use of derivative, 2)Use of integral compensators, 3)Lag-lead compensators, 4)Regulators
X)DISCRETE TIME SYSTEMS
1)Operators on discrete time functions, 2)Z (Laurent) transform, 3)Properties of Z transform, 4)Initial and final value theorem (limit theorems), 5)Inverse transform, division of polynomials, partial fraction expansion, residual theorem, 6)Discrete time systems, pulse modulator, ideal sampler, 7)Close-loop system, discrete time transfer fiunction, close-loop system describtion, analysis of stability, application of hurwitz criterium
XI)MULTIVARIABLE CONTROL SYSTEMS
1)Series connection, 2)Parallel connection, 3)Feedback, 4)Close-loop systems describtion, 5)Stability analysis, 6)Representative block diagrams

1) Znajdź zakresy parametrów kontrolera PI, reprezentowanego przez \(\displaystyle{ K_i(s)}\), dla którego system jest stabilny. Ustal typ systemu w odniesieniu do sygnałów r(t) i d(t).
Doprawdy nie wiem, jak mam przy użyciu notacji LaTEX zamieścić obrazek. Na schemacie sa następujące wzory: \(\displaystyle{ K_c(s)}\) i \(\displaystyle{ \frac{5}{s(1+2s)}}\), gdzie sygnałem wejściowym jest r, zaś wyjściowym y.
2) Ustal wartość k taką, żeby margines wzmocnienia systemu był równy \(\displaystyle{ \delta k = \frac{4}{3}}\). Znajdź wartość phase margin dla uzyskanego wzmocnienia.
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