Brief history of automatic control (I) 1868 first article of control ‘on governor’s’ –by Maxwell 1877 Routh stability criterien 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 Linear system

Brief history of automatic control (II) 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 Linear system

three eras of control 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) Linear system

Control system analysis and design 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 Linear system

Time system Input signals Output signals Signals & systems Linear system

Signal Classification Continuous signal Discrete signal Linear system

System classification Finite-dimensional system (lumped-parameters system described by differential equations) –Linear systems –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 –Antenas –Heat conduction –Optical fiber etc…. Linear system

Some examples of linear system Electrical circuits with constant values of circuit passive elements see figure 1.10 Linear OPA circuits Mechanical system with constant values of k,m,b etc… see figure 1.11 Heartbeat dynamic see Page 22 Eye movement see Page 23 Commercial aircraft see Page 24 Linear system

Definition: A system is linear if superposition principle is satisfied Linearity : (a) homogeneous principle (b) addition principle (c) superposition principle => (a) +(b) Linear system

Continuous-time system ---characterized by differential equations Definition: input and output of the system are continuous functions of the continuous variable time. Discrete-time system ---characterized by different equations Definition: input and output of the system change at only discrete instants of time. Linear system

Linear time invariant (LTI)--continuous Described by a linear differential equation in time domain can be transferred to linear algebra form by using Laplace transform. Linear system