Q1: [21 marks] You will be given two systems to choose from: one electrical and one mechanical. Select one system and proceed with the question part

Q1: [21 marks] You will be given two systems to choose from: one electrical and one mechanical. Select one system and proceed with the question parts. After choosing your system, you need to appropriately select its states, derive the dynamic model, and obtain the state-space equations. Additionally, you will need to check the controllability and observability properties of the system. By deriving the characteristic equation, you will investigate the open-loop damping and natural frequencies of the system and comment on the expected step response. Furthermore, you will design a full-state feedback controller to place the closed-loop poles in specific locations. Similarly, you will design an observer for the same system. Since you have derived the state-space equations, you will also be asked to obtain the transfer function of the system and finally draw the block diagram of the observer-based controller.

Q2: [15 marks] You will be given the transfer function in the s-domain of a second-order system. Your first task is to find the damping coefficient and natural frequency, as well as determine the desired characteristic polynomial that satisfies given rise time and settling time conditions. Then, you need to design a state feedback controller that ensures zero steady-state error for step-type input. As a result, your closed-loop system will be of order 3. Therefore, you are expected to find an additional pole location to obtain a new desired characteristic polynomial of 3rd order. Finally, based on the choice of characteristic polynomial in the previous parts, you will design an integral state-feedback controller. You will conclude the question by drawing the entire block diagram of the controlled system.

Q3: [12 marks] You will be provided with a set of nonlinear equations representing a system's dynamics, and you will be asked to find one equilibrium point given another. Please note that a nonlinear system may have more than one equilibrium point. Next, you need to linearize the system model around these equilibrium points to obtain a set of linear state-space equations with different A and B matrices. Finally, you will investigate the stability and controllability of each system around these equilibrium points by examining the eigenvalues of the system matrices and using other known techniques.

Q4: [12 marks] A MIMO system will be provided in transfer function form. You will obtain controllable and observable canonical forms. Additionally, another set of state-space dynamic equations will be provided, and you will be asked to discretize this system using an appropriate method such. as Euler/Tustin and investigate the effect of the sampling period on stability.

Q1: [21 marks] You will be given two systems to choose from: one electrical and one mechanical. Select one system and proceed with the question parts. After choosing your system, you need to appropriately select its states, derive the dynamic model, and obtain the state-space equations. Additionally, you will need to check the controllability and observability properties of the system. By deriving the characteristic equation, you will investigate the open-loop damping and natural frequencies of the system and comment on the expected step response. Furthermore, you will design a full-state feedback controller to place the closed-loop poles in specific locations. Similarly, you will design an observer for the same system. Since you have derived the state-space equations, you will also be asked to obtain the transfer function of the system and finally draw the block diagram of the observer-based controller.

Q2: [15 marks] You will be given the transfer function in the s-domain of a second-order system. Your first task is to find the damping coefficient and natural frequency, as well as determine the desired characteristic polynomial that satisfies given rise time and settling time conditions. Then, you need to design a state feedback controller that ensures zero steady-state error for step-type input. As a result, your closed-loop system will be of order 3. Therefore, you are expected to find an additional pole location to obtain a new desired characteristic polynomial of 3rd order. Finally, based on the choice of characteristic polynomial in the previous parts, you will design an integral state-feedback controller. You will conclude the question by drawing the entire block diagram of the controlled system.

Q3: [12 marks] You will be provided with a set of nonlinear equations representing a system's dynamics, and you will be asked to find one equilibrium point given another. Please note that a nonlinear system may have more than one equilibrium point. Next, you need to linearize the system model around these equilibrium points to obtain a set of linear state-space equations with different A and B matrices. Finally, you will investigate the stability and controllability of each system around these equilibrium points by examining the eigenvalues of the system matrices and using other known techniques.

Q4: [12 marks] A MIMO system will be provided in transfer function form. You will obtain controllable and observable canonical forms. Additionally, another set of state-space dynamic equations will be provided, and you will be asked to discretize this system using an appropriate method such. as Euler/Tustin and investigate the effect of the sampling period on stability.

Please ensure that you thoroughly prepare for the exam and feel free to reach out to me if you have any questions.

I am writing to inform you that the resit exam for Control Systems 2 will be conducted remotely in August. I will provide you with the exam date and time once the school announces the exam timetables. The exam will consist of 4 questions, each worth a total of 60 marks. Each question will have multiple parts. It is mandatory for all candidates to attempt all questions. We advise you to carefully read the questions before attempting them to ensure a smooth exam experience. The exam will have a duration of 2 hours, with an additional 45 minutes provided for scanning and uploading your scripts. Please note that you need to combine all your documents into a single PDF file before uploading. We kindly request that you do not upload documents in any other format. You can use the Adobe Scanner application, which is available free of charge on both the Google Play Store and Apple Store. We urge you to download the application beforehand, familiarise yourself with it, and ensure that it works correctly on your device. If you encounter any technical difficulties during the exam, please contact me via email. My contact details are provided in the left column under the Contacts tab.

You are permitted to use MATLAB or any other electronic device, as well as refer to your course notes and slides. Since the exam will be conducted remotely and you have the freedom to choose where to take the exam, please select a location with good internet reception and comfort.

Please note that any form of collaboration is strictly prohibited. We have the necessary tools and experience to investigate any instances of academic misconduct. Cheating or colluding will not be tolerated, and there will be serious consequences that may affect your future. Therefore, I strongly urge you to think twice before engaging in any dishonest behavior.

Now, let me provide you with some hints about the questions: