Step 1: Basic Components of a Robot Control System:
1. **Sensors**: These are devices that gather data from the robot's surroundings or its internal states. Common sensors include cameras, ultrasonic sensors, and accelerometers.
2. **Actuators**: These are mechanical components that move or control parts of the robot, such as motors or hydraulic systems.
3. **Controller**: The brain of the robot, which interprets inputs from the sensors and sends commands to the actuators. It processes information and makes decisions.
4. **Software/Algorithms**: The software running on the controller uses various algorithms (e.g., path planning, obstacle avoidance) to control the robot's actions.
Step 2: Types of Control Systems:
There are two main types of control systems used in robotics:
- **Open-loop control system**: In this system, the controller sends commands to the robot's actuators without receiving feedback. It's typically used when feedback is unnecessary or difficult to obtain.
- **Closed-loop control system**: This system constantly receives feedback from sensors and adjusts the actuators' behavior in real-time to ensure accuracy and correct performance. It's more advanced and used in robots requiring high precision.
Step 3: Feedback and Sensor Integration:
Sensors play a critical role in closed-loop control systems. For example, a robot might use a camera to track its position relative to an object. The feedback from the sensor helps the controller adjust the robot's movements.
Step 4: Example of Robot Control System:
Consider a robot vacuum cleaner, which uses a closed-loop system. It has sensors to detect obstacles and the dirt level on the floor. Based on this feedback, the controller adjusts the speed and direction of the robot to efficiently clean the room.
Consider the unity-negative-feedback system shown in Figure (i) below, where gain \( K \geq 0 \). The root locus of this system is shown in Figure (ii) below.
For what value(s) of \( K \) will the system in Figure (i) have a pole at \( -1 + j1 \)?

Consider a message signal \( m(t) \) which is bandlimited to \( [-W, W] \), where \( W \) is in Hz. Consider the following two modulation schemes for the message signal:
• Double sideband-suppressed carrier (DSB-SC): \[ f_{DSB}(t) = A_c m(t) \cos(2\pi f_c t) \] • Amplitude modulation (AM): \[ f_{AM}(t) = A_c \left( 1 + \mu m(t) \right) \cos(2\pi f_c t) \] Here, \( A_c \) and \( f_c \) are the amplitude and frequency (in Hz) of the carrier, respectively. In the case of AM, \( \mu \) denotes the modulation index. Consider the following statements:
(i) An envelope detector can be used for demodulation in the DSB-SC scheme if \( m(t)>0 \) for all \( t \).
(ii) An envelope detector can be used for demodulation in the AM scheme only if \( m(t)>0 \) for all \( t \).
Which of the following options is/are correct?
A controller \( D(s) \) of the form \( (1 + K_D s) \) is to be designed for the plant \[ G(s) = \frac{1000\sqrt{2}}{s(s+10)^2} \] as shown in the figure. The value of \( K_D \) that yields a phase margin of \(45^\circ\) at the gain cross-over frequency of 10 rad/sec is _____________ (round off to one decimal place). 