Handout 7: Lag and PI compensation Eric Feron Lag Compensation goals: Raise gain at low frequencies while leaving rossover &z higher frequencies untouched b≥0. When b=0: Add an integrator in the loop Typical lag Bode Plot

Handout 8: Lead compensation Eric Feron March 3, 2004 Lead Compensation goals: Raise phase (and gain) at high frequen- cies while not touching low-frequency system's characteristics: Can extend bandwidth of system Canonical lead element:

Handout 10: Notch compensation Eric Feron March 8, 2004 Notch Compensation goals: Kill nasty frequencies (eg resonant fre- quencies). Canonical Notch element:

Handout 13: More about plants with right half-plane zeros Eric Feron March 15, 2004 Right half-plane zeros and sensor/actuator design Influence of sensor position on system dynamics: Star Market

Handout 18: Dual-input describing functions Eric Feron April 5,2004 Dual-input describing functions are for mixed signals(sinusoid small constant signal) Approximating non-constant signals with constant ones

Handout 19: More about Dual-input describing functions- Limit cycle stability analysis Eric Feron April 16, 2004 Dual-input describing functions for Toggle switch Another servo-motor application

Handout 20: Phase Plane analysis: Introduction Eric Feron April 28, 2004 State space equations of second-order systems

能控性(controllability)和能观测性(observability)深刻地揭示了系统的内部结构关系,由 .e.Kalman于60年代初首先提出并研究的这两个重要概念,在现代控制理论的研究与实 践中,具有极其重要的意义,事实上,能控性与能观测性通常决定了最优控制问题解的存 在性。例如,在极点配置问题中,状态反馈的的存在性将由系统的能控性决定;在观测器 设计和最优估计中,将涉及到系统的能观测性条件

在4.2节中介绍控制系统设计的极点配置方法时,曾假设所有的状态变量均可有效地 用于反馈。然而在实际情况中,不是所有的状态度变量都可用于反馈。这时需要要估计不 可用的状态变量。需特别强调,应避免将一个状态变量微分产生另一个状态变量,因为噪 声通常比控制信号变化更迅速,所以信号的微分总是减小了信噪比

一、例题精解 【例题20.1】单相桥式可控整流电路如图20.1所示,已知R=20Q,要求U在0-60V的范围内连续可调。(1)估算变压器副边电压值U2(考虑电源电压的10%波动);