7 Chapter 7Figure 7.1 Block diagram for a system suitable for cascade control.Figure 7.2 Block diagram of a cascade control system.Figure 7.3 Cascade closed-loop response signals (Example 7.2, primary contro...Figure 7.4 Closed-loop cascade control system.Figure 7.5 Sensitivity functions for the cascade control system (Example 7.3...Figure 7.6 Cascade closed-loop response to square wave disturbance signal wi...Figure 7.7 One controller for disturbance rejection.Figure 7.8 Deadzone nonlinearity.Figure 7.9 Closed-loop control response by neglecting the actuator dynamics ...Figure 7.10 Simulink simulation program for the cascade control system with ...Figure 7.11 Closed-loop control response using cascade control (Example 7.5,...Figure 7.12 Closed-loop control response using cascade control (Example 7.5,...Figure 7.13 Illustration of a quantization of signal
with quantization int...Figure 7.14 Closed-loop control response with quantization on the input sign...Figure 7.15 Simulink simulation program for cascade control with actuator qu...Figure 7.16 Cascade closed-loop control response with quantization on input ...Figure 7.17 Illustration of a backlash nonlinearity with
and
.Figure 7.18 The effect of backlash on closed-loop performance (Example 7.8, Figure 7.19 The effect of backlash on closed-loop performance (Example 7.8, Figure 7.20 Simulink simulation program for cascade control with a backlash ...Figure 7.21 The effect of backlash on cascaded closed-loop performance (Exam...Figure 7.22 Segment of data to illustrate the effect of backlash on cascaded...
8 Chapter 8Figure 8.1 Illustration of the design process and closed-loop responses (Exa...Figure 8.2 Closed-loop responses (Example 8.1) when using the phase margin. ...Figure 8.3 Illustration of the design process and closed-loop responses (Exa...Figure 8.4 Comparison of closed-loop responses of PI and PID control systems...Figure 8.5 Comparison of closed-loop responses of PID control systems with d...Figure 8.6 Comparison of closed-loop responses of PID control systems. (a) O...Figure 8.7 Frequency response. Key: line (1)
; line (2)
; line (3)
Figure 8.8 Nyquist plot. Key: line (1)
; line (2)
.Figure 8.9 Closed-loop control simulation for output stair case disturbance ...Figure 8.10 Calculated normalized proportional controller gain. (a)
,
. (b...Figure 8.11 Calculated gain and phase margins for PID controllers. (a) Gain ...Figure 8.12 Calculated gain and phase margins for PI controllers. (a) Gain m...Figure 8.13 Calculated gain and phase margins for PD controllers. (a) Gain m...Figure 8.14 Comparison of closed-loop performance for three types of control...Figure 8.15 Comparison of closed-loop PID control performance between the mo...
9 Chapter 9Figure 9.1 Block diagram of relay feedback control.Figure 9.2 Location of
on a Nyquist curve.Figure 9.3 Simulink diagram for the relay feedback control.Figure 9.4 Relay feedback control signals with hysteresis (Example 9.1). (a)...Figure 9.5 Block diagram of integrated relay feedback control.Figure 9.6 Location of
on a Nyquist curve when using an integrator with re...Figure 9.7 Relay feedback control signals with and without integrator (Examp...Figure 9.8 Frequency response estimation using FFT (Example 9.3). (a) Input ...Figure 9.9 Frequency response estimation using FFT (Example 9.4). (a) Input ...Figure 9.10 Block diagram of the frequency sampling filter model with reduce...Figure 9.11 Frequency response estimation using FSF (Example 9.5).Figure 9.12 Monte-Carlo simulation results with
random seeds in the presen...Figure 9.13 Monte-Carlo simulation results with
random seeds in the presen...Figure 9.14 Monte-Carlo simulation results for estimation of steady-state ga...Figure 9.15 Simulink diagram of auto-tuner for stable system.Figure 9.16 Nyquist plots using the PID controller parameters in Table 9.1. ...Figure 9.17 Closed-loop simulation results using the PID controller paramete...Figure 9.18 Closed-loop simulation results using the PID controller paramete...Figure 9.19 Block diagram of relay feedback control for an integrating syste...Figure 9.20 Input and output relay feedback control data (Example 9.6).Figure 9.21 Comparison between the estimated frequency point with the origin...Figure 9.22 Frequency response comparison (Example 9.6). (a) Nyquist diagram...Figure 9.23 Comparison of closed-loop performance for three types of control...Figure 9.24 Input and output relay feedback control data (Example 9.7).Figure 9.25 Comparison between the estimated frequency point with the origin...Figure 9.26 Comparison of closed-loop performance for three types of control...Figure 9.27 Frequency response comparison (Example 9.7). (a) Nyquist diagram...Figure 9.28 Relay feedback control signals from inner closed-loop system (Ex...Figure 9.29 Auto-tuning inner-loop control system (Example 9.8). (a) Nyquist...Figure 9.30 Relay feedback control signals from outer- closed-loop system (E...Figure 9.31 Auto-tuning outer-loop control system (Example 9.8). (a) Nyquist...
10 Chapter 10Figure 10.1 Inertial frame and body frame of the quadrotor.Figure 10.2 Representation of a hexacopter (Ligthart et al. (2017)).Figure 10.3 Attitude control system structure.Figure 10.4 Quadrotor test-bed.Figure 10.5 Experimental rig for a hexacopter.Figure 10.6 Relay feedback control signals from the inner-loop system: top f...Figure 10.7 Inner-loop step response in closed-loop control. Dashed line, re...Figure 10.8 Relay feedback control signals from outer-loop system: top figur...Figure 10.9 Comparative roll angle step response in closed-loop control.Figure 10.10 Roll angle step response of quadrotor using test rig.Figure 10.11 Inner loop relay test result.Figure 10.12 Attitude control system with approximated inner loop.Figure 10.13 Outdoor flight test.Figure 10.14 Flight data for roll axis.Figure 10.15 Flight data for pitch axis.Figure 10.16 Flight data for yaw axis.
(b) 
