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CE1.3a Figure 1.16 shows a single robot joint/link driven through a gear ratio n by an armature-controlled de servomotor. The input is the de armature voltage vA(1) and the output is the load-shaft angle OL(1). Derive the mathematical model for this system; i.e., develop the circuit differential equation, the electromechan- ical coupling equations, and the rotational mechanical differen- tial equation. Eliminate intermediate variables and simplify; it will be convenient to use a transfer-function approach. Assume the mass-moment of inertia of all outboard links plus any load JL(1) is a constant (a reasonable assumption when the gear ratio n = Wm/wr is much greater than 1, as it is in the case of industrial robots). The parameters in Figure 1.16 are summarized below. CE1.3b Derive a valid state-space description for the system of Figure 1.16. That is, specify the state variables and derive the ww by JM (1) FIGURE 1.16 Diagram for Continuing Exercise 3. VA(1) armature voltage ia(1) armature current JM kT armature inductance R armature resistance vg (1) back emf voltage bM wM(1) motor shaft velocity L(1) load inertia On (1) load shaft velocity back emf constant kB TM(1) motor torque motor inertia motor viscous damping OM(1) motor shaft angle load viscous damping torque constant gear ratio L(1) load shaft torque OL(1) load shaft angle coefficient matrices A, B, C, and D. Write out your results in matrix-vector form. Give the system order and matrix-vector dimensions of your result. Consider two distinct cases: i. Single-input, single-output: armature voltage VA (1) as the input and robot load shaft angle OL(1) as the output. ii. Single-input, single-output: armature voltage VA(1) as the input and robot load shaft angular velocity wr(t) as the output.

CE1.3a Figure 1.16 shows a single robot joint/link driven through a gear ratio n by an armature-controlled de servomotor. The input is the de armature voltage vA(1) and the output is the load-shaft angle OL(1). Derive the mathematical model for this system; i.e., develop the circuit differential equation, the electromechan- ical coupling equations, and the rotational mechanical differen- tial equation. Eliminate intermediate variables and simplify; it will be convenient to use a transfer-function approach. Assume the mass-moment of inertia of all outboard links plus any load JL(1) is a constant (a reasonable assumption when the gear ratio n = Wm/wr is much greater than 1, as it is in the case of industrial robots). The parameters in Figure 1.16 are summarized below. CE1.3b Derive a valid state-space description for the system of Figure 1.16. That is, specify the state variables and derive the ww by JM (1) FIGURE 1.16 Diagram for Continuing Exercise 3. VA(1) armature voltage ia(1) armature current JM kT armature inductance R armature resistance vg (1) back emf voltage bM wM(1) motor shaft velocity L(1) load inertia On (1) load shaft velocity back emf constant kB TM(1) motor torque motor inertia motor viscous damping OM(1) motor shaft angle load viscous damping torque constant gear ratio L(1) load shaft torque OL(1) load shaft angle coefficient matrices A, B, C, and D. Write out your results in matrix-vector form. Give the system order and matrix-vector dimensions of your result. Consider two distinct cases: i. Single-input, single-output: armature voltage VA (1) as the input and robot load shaft angle OL(1) as the output. ii. Single-input, single-output: armature voltage VA(1) as the input and robot load shaft angular velocity wr(t) as the output.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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CE1.3a Figure 1.16 shows a single robot joint/link driven through a gear ratio n by an armature-controlled de servomotor. The input is the de armature voltage va(t) and the output is the load-shaft angle OL(t). Derive the mathematical model for this system; i.e., develop the circuit differential equation, the electromechan- ical coupling equations, and the rotational mechanical differen- tial equation. Eliminate intermediate variables and simplify; it will be convenient to use a transfer-function approach. Assume the mass-moment of inertia of all outboard links plus any load JL(1) is a constant (a reasonable assumption when the gear ratio n = wm/wr_ is much greater than 1, as it is in the case of industrial robots). The parameters in Figure 1.16 are summarized below. CE1.3b Derive a valid state-space description for the system of Figure 1.16. That is, specify the state variables and eriv the R ww bM V(f) JM (1) (1) FIGURE 1.16 Diagram for Continuing Exercise 3. armature resistance back emf constant L. v'B (1) back emf voltage bM OM(1) motor shaft velocity JL(1) load inertia WL(1t) load shaft velocity VA(1) armature voltage armature inductance iA(1) armature current kB JM kT motor inertia motor viscous damping TM(1) motor torque torque constant gear ratio TL(1) load shaft torque OM(1) motor shaft angle load viscous damping OL (1) load shaft angle coefficient matrices A, B, C, and D. Write out your results in matrix-vector form. Give the system order and matrix-vector dimensions of your result. Consider two distinct cases: i. Single-input, single-output: armature voltage vA (1) as the input and robot load shaft angle O(t) as the output. ii. Single-input, single-output: armature voltage vA(t) as the input and robot load shaft angular velocity w(1) as the output.
Transcribed Image Text:CE1.3a Figure 1.16 shows a single robot joint/link driven through a gear ratio n by an armature-controlled de servomotor. The input is the de armature voltage va(t) and the output is the load-shaft angle OL(t). Derive the mathematical model for this system; i.e., develop the circuit differential equation, the electromechan- ical coupling equations, and the rotational mechanical differen- tial equation. Eliminate intermediate variables and simplify; it will be convenient to use a transfer-function approach. Assume the mass-moment of inertia of all outboard links plus any load JL(1) is a constant (a reasonable assumption when the gear ratio n = wm/wr_ is much greater than 1, as it is in the case of industrial robots). The parameters in Figure 1.16 are summarized below. CE1.3b Derive a valid state-space description for the system of Figure 1.16. That is, specify the state variables and eriv the R ww bM V(f) JM (1) (1) FIGURE 1.16 Diagram for Continuing Exercise 3. armature resistance back emf constant L. v'B (1) back emf voltage bM OM(1) motor shaft velocity JL(1) load inertia WL(1t) load shaft velocity VA(1) armature voltage armature inductance iA(1) armature current kB JM kT motor inertia motor viscous damping TM(1) motor torque torque constant gear ratio TL(1) load shaft torque OM(1) motor shaft angle load viscous damping OL (1) load shaft angle coefficient matrices A, B, C, and D. Write out your results in matrix-vector form. Give the system order and matrix-vector dimensions of your result. Consider two distinct cases: i. Single-input, single-output: armature voltage vA (1) as the input and robot load shaft angle O(t) as the output. ii. Single-input, single-output: armature voltage vA(t) as the input and robot load shaft angular velocity w(1) as the output.
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