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1.1 Brief History 1.2 Steps to study a control system 1.3 System classification 1.4 System response. Lecture 01 --Introduction. 1868 First article of control ‘on governor’s’ –by Maxwell 1877 Routh stability criterion 1892 Liapunov stability condition
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1.1Brief History 1.2 Steps to study a control system 1.3 System classification 1.4 System response Lecture 01 --Introduction Modern control systems
1868 First article of control ‘on governor’s’ –by Maxwell 1877 Routh stability criterion 1892 Liapunov stability condition 1895 Hurwitz stability condition 1932 Nyquist 1945 Bode 1947 Nichols 1948 Root locus 1949 Wiener optimal control research 1955 Kalman filter and controlbility observability analysis 1956 Artificial Intelligence Brief history of automatic control (I) Modern control systems
1957 Bellman optimal and adaptive control 1962 Pontryagin optimal control 1965 Fuzzy set 1972 Vidyasagar multi-variable optimal control and Robust control 1981 Doyle Robust control theory 1990 Neuro-Fuzzy Brief history of automatic control (II) Modern control systems
Classical control : 1950 before Transfer function based methods Time-domain design & analysis Frequency-domain design & analysis Modern control : 1950~1960 State-space-based methods Optimal control Adaptive control Post modern control : 1980 after H∞ control Robust control (uncertain system) Three eras of control Modern control systems
Step1: Modeling By physical laws By identification methods Step2: Analysis Stability, controllability and observability Step3: Control law design Classical, modern and post-modern control Step4: Analysis Step5: Simulation Matlab, Fortran, simulink etc…. Step6: Implement Control system analysis and design Modern control systems
Signals & systems Output signals Input signals Time system Modern control systems
Continuous signal Discrete signal Signal Classification Modern control systems
Finite-dimensional system (lumped-parameters system described by differential equations) Linear systems and nonlinear systems Continuous time and discrete time systems Time-invariant and time varying systems Infinite-dimensional system (distributed parameters system described by partial differential equations) Power transmission line Antennas Heat conduction Optical fiber etc…. System classification Modern control systems
Electrical circuits with constant values of circuit passive elements Linear OPA circuits Mechanical system with constant values of k,m,b etc Heartbeat dynamic Eye movement Commercial aircraft Some examples of linear system Modern control systems
Linear system A system is said to be linear in terms of the system input x(t) and the system output y(t) if it satisfies the following two properties of superposition and homogeneity. Superposition： Homogeneity： Modern control systems
Example Non linear system Modern control systems
example The system is governed by a linear ordinary differential equation (ODE) Linear time invariant system linearity Modern control systems
Examples : Circuit system Modern control systems
Examples Discrete system Time delay Modern control systems
Properties of linear system : (1) (2) Modern control systems
Time invariant system Time invariance A system is said to be time invariant if a time delay or time advance of the input signal leads to an identical time shift in the output signal. Modern control systems
Example 1.18 Time varying system Modern control systems
LTI System representations Continuous-time LTI system • Order-N Ordinary Differential equation • Transfer function (Laplace transform) • State equation (Finite order-1 differential equations) ) Discrete-time LTI system • Ordinary Difference equation • Transfer function (Z transform) • State equation (Finite order-1 difference equations) Modern control systems
Continuous-time LTI system Order-2 ordinary differential equation constants Linear system initial rest Transfer function Modern control systems
Homogenous solution Particular solution Natural response Forced response Zero-input response Zero-state response System response:Output signals due to inputs and ICs. 1. The point of view of Mathematic: ＋ 2. The point of view of Engineer: ＋ 3. The point of view of control engineer: ＋ Transient response Steady state response Modern control systems
(1) Particular solution: Example: solve the following O.D.E Modern control systems
(2) Homogenous solution: have to satisfy I.C. Modern control systems
(3) zero-input response: consider the original differential equation with no input. zero-input response Modern control systems
(4) zero-state response: consider the original differential equation but set all I.C.=0. zero-state response Modern control systems
(5) Laplace Method: Modern control systems
Complex response Zero state response Zero input response Forced response (Particular solution) Natural response (Homogeneous solution) Steady state response Transient response Modern control systems
